Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling
|
|
- Edwina Murphy
- 6 years ago
- Views:
Transcription
1 Commun. Theor. Phys. 60 (2013) Vol. 60, No. 1, July 15, 2013 Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling HOU Jing-Min ( ) and WANG Guo-Xiang ( ) Department of Physics, Southeast University, Nanjing , China (Received October 22, 2012; revised manuscript received March 11, 2013) Abstract We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z 2 topological indices. According to the Z 2 topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states. PACS numbers: f, Fd, r, b Key words: topological insulators, ruby lattice, rashba spin-coupling 1 Introduction Recently, the study of topological phases has become an exciting area of research in condensed matter physics. [1 2] Topological matters are classified according to topological invariants rather than symmetries. The integer quantum Hall states are classified by the TKNN number, [3] which is nonzero when time-reversal symmetry is broken. Time-reversal invariant band insulators can be classified by a Z 2 topological index. [4 5] In two dimensions, topological insulators and normal band insulator are characterized by the Z 2 topological index ν = 1 and ν = 0, respectively. Time-reversal invariant band insulators can be generalized to three dimensions and classified according to four Z 2 topological indices (ν 0 ; ν 1 ν 2 ν 3 ) with ν i = 0, 1. [6 8] Topological insulators have a bulk gap and topologically protected gapless helical edge states or helical surface states when placed next to a vacuum or an ordinary band insulator because topological invariants cannot change as long as a material remains insulating. The remarkable metallic boundaries of topological insulators may result in new spintronic or magnetoelectric devices and a new architecture for topological quantum bits. Theoretical studies have demonstrated that several tight-binding models with the spin-orbit coupling, such as honeycomb, [4] diamond, [6] kagome, [9] checkerboard, [10] decorated honeycomb, [11] Lieb and perovskite, [12] squareoctagon, [13] ruby, [14] pyrochlore, [15] and octahedrondecorated cubic [16] lattices support two-dimensional or three-dimensional topological insulators. For real materials, HgTe quantum wells were first found to support two-dimensional topological insulators. [17 18] Fu and Kane firstly predicted that Bi 1 x Sb x supports a three-dimensional topological insulator, [19] which was conformed experimentally by Hsieh et al. in [20] Later, Bi 2 Se 3 was discovered to support a threedimensional insulator experimentally as a second generation material, [21] which also was supported by theoretical calculations. [21 22] Additionally, Ref. [22] also predicted that Bi 2 Te 3 and Sb 2 Te 3 are second generation materials supporting three-dimensional topological insulators. The later experimental studies on Bi 2 Te [23 25] [25] 3 and Sb 2 Te 3 identified their topological band structures. Recently, several ternary compounds are identified as topological insulators. [26 30] Very Recently, based on the firstprinciples calculations, Miao et al. find that, due to the effect of the intrinsic polarization fields, GaN/InN/GaN quantum well undergo inverted band transition and become a topological insulator. [31] This is an important progress because semiconductor systems have advantages of integration in practical devices. The above theoretical models and real materials considered the intrinsic spin-orbit coupling, which is a mirrorsymmetric interaction. In this communication, we shall demonstrate that a model with the Rashba spin-orbit coupling, a mirror-symmetry-broken interaction, can also support topological insulators. Specifically, we shall consider the ruby lattice as shown in Fig. 1 with the Rashba spin-orbit coupling and study its topological insulators. The ruby lattice with the mirror-symmetric intrinsic spinorbit coupling were firstly investigated by Hu et al. [14] 2 Model We consider the ruby lattice as shown in Fig. 1. The ruby lattice consists of six triangular sublattices denoted as A, B, C, D, E, and F, respectively. Every six lattice sites from sublattices A, B, C, D, E, and F, respectively, make up a hexagon. The hexagons are separated by triangles and squares. Here, we assume that the distance between two nearest-neighbor lattice sites is d and the lattice constant of all sublattices is a = (1 + 3)d. With the tight-binding approximation, we can write the second Supported by the National Natural Science Foundation of China under Grant Nos and jmhou@seu.edu.cn c 2013 Chinese Physical Society and IOP Publishing Ltd
2 130 Communications in Theoretical Physics Vol. 60 quantized Hamiltonian of the lattice as follows, H 0 = t c iσ c jσ t 1 c iσ c jσ, (1) i,j,σ [i,j],σ where c iσ is the annihilation operator destructing an electron with spin σ on the site r i of the ruby lattice, i, j represents nearest-neighbor hopping within the same hexagon with amplitude t and [i, j] denotes nearest-neighbor hopping between two different hexagons with amplitude t 1. In momentum space, Hamiltonian (1) can be represented by H 0 = Ψ k H0 kψ k k with Ψ k = (c Ak, c Bk, c Ck, c Dk, c Ek, c F k, c Ak, c Bk, c Ck, c Dk, c Ek, c F k ) T, which are ordered according to the sequence denoted in Fig. 1 for every spin state. Here, Hk 0 takes the following form, 0 t t 1 e ik 0 t 1 e iky t t 0 t t 1 e iky 0 t 1 e ik+ ( ) 1 0 Hk 0 t 1 e ik t 0 t t 1 e ik+ 0 =, (2) t 1 e iky t 0 t t 1 e ik t 1 e iky 0 t 1 e ik+ t 0 t t t 1 e ik+ 0 t 1 e ik t 0 where k ± = ( 3k x ± k y )/2, and the 2 2 matrix is the unit matrix in spin space. Since H 0 is spin-decoupling, Hk 0 is block-diagonal, i.e. two blocks representing spin-up and spin-down electrons are the same. of bands and the fourth and fifth pairs of bands touch at K point, near which Dirac cones occurs. Fig. 1 Schematic diagram of the ruby lattice, which consists of six sublattices denoted by A, B, C, D, E, and F, respectively. We evaluate the eigenenergies of Hamiltonian (2). The Brillouin zone for t 1 = t is shown in Fig. 2(a), which is similar to that of honeycomb lattice. Figure 2(b) shows the corresponding spectrum, which contains twelve bands which come from the six sites in every unit cell for spinup and spin-down electrons. Due to spin decoupling, these bands are double degenerate and divided into six pairs. For this special case, all the bands are connected or touched with other bands. Thus, the system is metal for all filling fractions but 1 and 0 filling fractions in this case. The second third and fourth pairs of bands touch together at Γ point and the fifth and sixth pairs of bands touch at the same point. Along the Γ M line in momentum space, the third and fourth pairs of bands are degenerate and they separate near M point. the first and second pairs Fig. 2 (Color online) (a) The Brillouin zone of the ruby lattice. (b) Band structures of the ruby lattice with t 1 = t, λ R = 0, λ CDW = 0. Here, the horizontal axis represents the wave vectors along the path in the first Brillouin zone indicated by the red lines in (a). Now, in order to find topological insulators on the ruby lattice, we proceed to introduce Rashba spin-orbit coupling between nearest-neighbor sites as follows, H R = iλ R c iα (σ αβ d ij ) z c jβ, (3) {ij},αβ
3 No. 1 Communications in Theoretical Physics 131 where {i, j} represents two nearest-neighbor sites i, j that belong to the same hexagon or the two different hexagons, and λ R is the amplitude of Rashba spin-orbit coupling of the two nearest-neighbor sites. σ = (σ x, σ y, σ z ) is the vector of Pauli spin matrices. d ij are the nearest neighbor bond unit vector traversed between sites i and j. In momentum space, the Hamiltonian for Rashba spin-orbit coupling (3) can be expressed as with H R = k Ψ k HR k Ψ k Since H R k with Ψ k = (c Ak, c Bk, c Ck, c Dk, c Ek, c F k, c Ak, c Bk, c Ck, c Dk, c Ek, c F k ) T. does not decouple for the two spin projections, it is a matrix as follows, R = H R k = iλ R ( 0 R R 0 ), (4) 0 1 e i(k +5π/6) 0 e i(ky π/2) e i2π/3 1 0 e iπ/3 e i(ky π/2) 0 e i(k+ π/6) e i(k +π/6) e i2π/3 0 e i2π/3 e i(k+ π/6) 0 0 e i(ky π/2) e iπ/3 0 1 e i(k +π/6) e i(ky π/2) 0 e i(k+ 5π/6) 1 0 e i2π/3 e iπ/3 e i(k+ 5π/6) 0 e i(k +5π/6) e iπ/3 0, (5) where k ± = ( 3k x ± k y )/2. In our model we also consider the effect of a charge-density-wave (CDW) on-site potential, which can be written as H CDW = λ CDW ξ i c iσ c iσ, (6) where ξ i is +1 for sublattices A, C, E, and 1 for sublattices B, D, F. We can rewrite this term as H CDW = k Ψ k HCDW k Ψ k. Here the single-particle expression Hk CDW has the form as follows, ( ) 1 0 Hk CDW = λ CDW , (7) where the 2 2 matrix is the unit matrix in spin space. In momentum space, the total single particle Hamiltonian is H k = Hk 0 + HR k + HCDW k. The bands and eigenstates can be obtained by exactly diagonalizing H k. The classification of two-dimensional topological insulators is presented in Ref. [6]. For a time-reversalsymmetry system, the energy eigenstates must come in pairs due to Kramer s theorem. The Bloch functions satisfy ψ n ( k) = Θ ψ n (k), (8) where Θ = iσ 2 K is the time-reversal operator with σ 2 being the spin operator and K being the complex conjugate operator. Thus, one only need to consider Bloch functions in a half of the Brillouin zone, say B. The Bloch functions in another half of the Brillouin zone can be fixed by time-reversal transformation. The Z 2 invariant characterizing two-dimensional topological insulators can be i,σ expressed as [32] ν = 1 [ ] dk A(k) d 2 kf(k) mod 2, (9) 2π B B where A(k) = i n ψ n(k) k ψ n (k) is the Berry connection and F(k) = k A(k) z is the Berry curvature. Fu and Kane have found a simple method to identify the Z 2 invariants for the system with the presence of inversion symmetry. [19] Our model is not inversion-symmetric due to the existence of the Rashba spin-orbit coupling and the CDW on-site potentials. Fortunately, Fukui and Hatsugai provide an n-field method to evaluate the Z 2 invariant in the systems without inversion symmetry. [33] This method enables one to implement numerical calculations of the Z 2 invariant in a lattice Brillouin zone. We will evaluate the Z 2 invariant in our system with this method. For convenience, we discretize a cell in the reciprocal lattice. For the case with M filled bands, we write the eigenstates for the same k l as a form of multiplet as Ψ(k l ) = ( ψ 1 (k l ),..., ψ M (k l ) ). A link variable is defined as, U µ (k l ) = N 1 µ det[ψ (k l )Ψ(k l + ˆb µ )], (10) where N µ (k l ) det[ψ (k l )Ψ(k l + ˆb µ )] with ˆb µ is the unit vector on the mesh of the discrete Brillouin zone. The discrete Berry connection is introduced as, A µ (k l ) = i ln U µ (k l ), (11) and the corresponding discrete Berry curvature is defined as, F(k l ) = i ln[u 1 (k l )U 2 (k l + ˆd 1 )U1 1 (k l + ˆd 2 )U2 1 (k l)].(12) An integer field n(k l ) for the Brillouin zone is defined as, n(k l ) = 1 2π [ 1A 2 (k l ) 2 A 1 (k l ) F(k l )]. (13) The Z 2 topological invariant is given by the sum of the n-field in half of the Brillouin zone as ν = k l B n(k l) mod 2.
4 132 Communications in Theoretical Physics 3 Topological Insulators In this section, we will show that the ruby lattice with Rashba spin-orbit coupling supports topological insulators. In order to illustrate our results clearly, we first consider a specific case with t1 = t, λr = 2t and λcdw = 0.5t. For this specific case, we calculate the bands and the edge bands with a zigzag boundary as shown in Figs. 3(a) and 3(b), respectively. From Fig. 3(a), we can find that the degeneracy of spin-down and spin-up states is lifted but at some special points such as Γ, M. There are gaps between two neighbor pairs of bands except between the first and second pairs of bands. Thus, for this special case, the system is an insulator for 1/3, 1/2, 2/3, 5/6 filling fractions and a Vol. 60 metal for 1/6 filling fraction. In this special case, the system is a topological insulator for 1/3, 1/2, 5/6 filling fractions and a normal insulator for 2/3 filling fraction, which can be verified from the edge states as shown in Fig. 3(b). There is a single time-reversed pair of gapless edge states on each edge that traverse the bulk gap between the second and third pairs of bands. This imply that the system is a topological insulator for 1/3 filling fraction. For 1/2 and 5/6 filling fractions, the similar gapless edge states traverse the gap near the Fermi level can be found. However, the edge states do not fully traverse the gap between the fourth and fifth pairs of bands, which imply that the system is a normal insulator for 2/3 filling fraction. Fig. 3 (Color online) (a) Band structures and (b) edge states of the ruby lattice with t1 = t, λr = 2t and λcdw = 0.5t. In (b), the red and green lines represent the edge states located at two different side of the ruby lattice. Fig. 4 (Color online) The n-field configuration of the ruby lattice with t1 = t, λr = 2t and λcdw = 0.5t for (a) 1/3 filling, (b) 1/2 filling, (c) 2/3 filing, and (d) 5/6 filling, respectively. Here, the shaded area indicate the half of the Brillouin zone B. Here, the red and green circles denote n = 1 and n = 1, respectively, and the blank lattice cell denotes n = 0.
5 No. 1 Communications in Theoretical Physics In order to exactly identify the topological insulators, we apply the n-field method to calculate the Z2 topological invariant. Figures 4(a) 4(d) show the n-field configuration of the ruby lattice with t1 = t, λr = 2t and λcdw = 0.5t for 1/3, 1/2, 2/3 and 5/6 filling fractions, respectively. From Fig. 4(a), we find that the sum of n in the half of Brillouin zone B is odd, i.e. the system with with t1 = t, λr = 2t and λcdw = 0.5t for 1/3 filling fraction is a topological insulator. Figures 4(b) and 4(d) show 133 that the sum of n in the half of Brillouin zone B are also odd, so the system with t1 = t, λr = 2t and λcdw = 0.5t for 1/2 and 5/6 filling fractions are topological insulators. However, from Fig. 4(c), we find that the sum of n in the half of Brillouin zone B is even, so we conclude that the system with t1 = t, λr = 2t, and λcdw = 0.5t for 2/3 filling fraction is a normal insulator. From the analyses of the n-field configuration and the edge states, we obtain the same results. Fig. 5 (Color online) Phase diagrams of the ruby lattice with λcdw = 0 for (a) 1/6 filling, (b) 1/3 filling, (c) 1/2 filling, (d) 2/3 filling, and (e) 5/6 filling. Here, the blue color denotes a trivial band insulator; the white color denotes topological insulators; the green color denotes a metal phase. For completeness, we calculate the bands and the Z2 topological invariants for the cases with various parameters. According to the results, we draw a series of phase diagrams as shown in Figs. 5 and 6. Here, Figs. 5 and 6 show the λr t1 phase diagrams of the ruby lattice with λcdw = 0 and λcdw = 0.5t for various filling fractions, respectively. From these phase diagrams, we arrive at some results. First, the ruby lattice with Rashba spinorbit coupling supports topological insulators for 1/6, 1/3, 1/2, 2/3, and 5/6 filling fractions. Besides topological insulators, there exist normal insulator and metal phases for various filling fractions. Secondly, the system is a normal insulator or a metal for all filling fractions while λr vanishes, that is to say, the Rashba spin-orbit coupling is the key factor for the presence of topological insulators. Thirdly, by comparing Figs. 5 and 6, we can see that the CDW on-site potential makes the normal and topological insulator regimes enlarged. In addition, we need to ex- plain that the system is a normal insulator at the point with t1 = 0 and λr = 0 for all filling fractions, which is easily understood for when t1 and λr approach to zero the ruby lattice becomes separated hexagons. It is obvious that the system is a normal insulator at the point t1 = 0 and λr = 0 for 1/6, 1/2 and 5/6 filling fractions. However, for 1/3 and 2/3 filling fractions, the system is a metal near the point t1 = 0 and λr = 0. For t1 = 0 and λr = 0, the second and third pairs of bands are degenerate and become flat bands, which means that electrons are localized. Similarly, the third and fourth pairs of bands are degenerate flat bands. In other words, the system with t1 = 0 and λr = 0 for 1/3 and 2/3 filling fractions is a normal insulator. However, a tiny change from t1 = 0 and λr = 0 for parameters t1 and λr makes the degenerate flat bands become two pairs of dispersive bands that are crossover each other, then the lattice with two or four pairs of bands occupied becomes a metal.
6 Communications in Theoretical Physics 134 Vol. 60 Fig. 6 (Color online) Phase diagrams of the ruby lattice with λcdw = 0.5t for (a) 1/6 filling, (b) 1/3 filling, (c) 1/2 filling, (d) 2/3 filling, and (e) 5/6 filling. Here, the blue color denotes a trivial band insulator; the white color denotes topological insulators; the green color denotes a metal phase. 4 Conclusion In summary, we have shown that the ruby lattice with Rashba spin-orbit coupling supports topological insulators for 1/6, 1/3, 1/2, 2/3, and 5/6 filling fractions. We have calculated the band structure and edge band structure for the tight-binding model of the ruby lattice with Rashba spin-orbit coupling for a special case. We have evaluated the Z2 topological invariants with the n-field method for various filling fractions and drawn the phase diagrams. We have analyzed and discussed the characters of the band structures and the edge states of different References [1] M.Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82 (2010) [2] X.L. Qi and S.C. Zhang, Rev. Mod. Phys. 83 (2011) [3] D.J. Thouless, M. Kohmoto, M.P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49 (1982) 405. [4] C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95 (2005) [5] C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95 (2005) [6] L. Fu, C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 98 (2007) [7] J.E. Moore and L. Balents, Phys. Rev. 75 (2007) [8] R. Roy, Phys. Rev. B 79 (2009) [9] H.M. Guo and M. Franz, Phys. Rev. B 80 (2009) phases. The model might as well be built from optical lattices due to their diversity and controllability.[34] The hopping parameters t and t1 can be tuned by adjusting the depth of optical lattices and the CDW potential can be realized by adjusting the configuration and frequency of lasers that make up optical lattices. Here, we mainly investigated the non-interacting systems. If the interactions between atoms is considered, the phase diagram will become complicated and more phases, such as topological Mott insulators, will appear.[35] [10] K. Sun, H. Yao, E. Fradkin, and S.A. Kivelson, Phys. Rev. Lett. 103 (2009) [11] A. Ru egg, J. Wen, and G.A. Fiete, Phys. Rev. B 81 (2010) [12] C. Weeks and M. Franz, Phys. Rev. B 82 (2010) [13] M. Kargarian and G.A. Fiete, Phys. Rev. B 82 (2010) [14] X. Hu, M. Kargarian, and G.A. Fiete, Phys. Rev. B 84 (2011) [15] H.M. Guo and M. Franz, Phys. Rev. Lett. 103 (2009) [16] J.M. Hou, W.X. Zhang, and G.X. Wang, Phys. Rev. B 84 (2011) [17] B.A. Bernevig, T.L. Hughes, and S.C. Zhang, Science 314 (2006) 1757.
7 No. 1 Communications in Theoretical Physics 135 [18] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.L. Qi, and S.C. Zhang, Science 318 (2007) 766. [19] L. Fu and C.L. Kane, Phys. Rev. B 76 (2007) [20] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, and M.Z. Hasan, Nature (London) 542 (2008) 970. [21] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, and M.Z. Hasan, Nature Phys. 5 (2009) 398. [22] H. Zhang, C.X. Liu, X.L. Qi, X. Dai, Z. Fang, and S.C. Zhang, Nature Phys. 5 (2009) 438. [23] Y.L. Chen, J.G. Analytis, J.H. Chu, Z.K. Liu, S.K. Mo, X.L. Qi, H.J. Zhang, D.H. Lu, X. Dai, Z. Fang, S.C. Zhang, I.R. Fisher, Z. Hussain, and Z.X. Shen, Science 325 (2009) 178. [24] D. Hsieh, Y. Xia, D. Qian, L. Wray, J.H. Dil, F. Meier, J. Osterwalder, L. Patthey, J.G. Checkelsky, N.P. Ong, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, and M.Z. Hasan, Nature (London) 460 (2009) [25] D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J.H. Dil, J. Osterwalder, L. Patthey, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, and M.Z. Hasan, Phys. Rev. Lett. 103 (2009) [26] T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, Phys. Rev. Lett. 105 (2010) [27] Y.L. Chen, Z.K. Liu, J.G. Analytis, J.H. Chu, H.J. Zhang, B.H. Yan, S.K. Mo, R.G. Moore, D.H. Lu, I.R. Fisher, S.C. Zhang, Z. Hussain, and Z.X. Shen, Phys. Rev. Lett. 105 (2010) [28] D. Xiao, Y. Yao, W. Feng, J. Wen, W. Zhu, X.Q. Chen, G.M. Stocks, and Z. Zhang, Phys. Rev. Lett. 105 (2010) [29] S. Chadov, X. Qi, J. Kübler, G.H. Fecher, C. Felser, and S.C. Zhang, Nat. Mater. 9 (2010) 541. [30] H. Lin, L.A. Wray, Y. Xia, S. Xu, S. Jia, R.J. Cava, A. Bansil, and M.Z. Hasan, Nat. Mater. 9 (2010) 546. [31] M.S. Miao, Q. Yan, C.G. Van de Walle, W.L. Lou, L.L. Li, and K. Chang, Phys. Rev. Lett. 109 (2012) [32] L. Fu and C.L. Kane, Phys. Rev. B 74 (2006) [33] T. Fukui and Y. Hatsugai, J. Phys. Soc. Jpn. 76 (2007) [34] M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, Adv. Phys. 56 (2007) 243. [35] S. Raghu, X.L. Qi, C. Honerkamp, and S.C. Zhang, Phys. Rev. Lett. 100 (2008)
Introductory lecture on topological insulators. Reza Asgari
Introductory lecture on topological insulators Reza Asgari Workshop on graphene and topological insulators, IPM. 19-20 Oct. 2011 Outlines -Introduction New phases of materials, Insulators -Theory quantum
More informationInfluence of tetragonal distortion on the topological electronic structure. of the half-heusler compound LaPtBi from first principles
Influence of tetragonal distortion on the topological electronic structure of the half-heusler compound LaPtBi from first principles X. M. Zhang, 1,3 W. H. Wang, 1, a) E. K. Liu, 1 G. D. Liu, 3 Z. Y. Liu,
More informationarxiv: v1 [cond-mat.other] 20 Apr 2010
Characterization of 3d topological insulators by 2d invariants Rahul Roy Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK arxiv:1004.3507v1 [cond-mat.other] 20 Apr 2010
More informationarxiv: v1 [cond-mat.str-el] 5 Jan 2011
Mott Physics and Topological Phase Transition in Correlated Dirac Fermions Shun-Li Yu 1, X. C. Xie 2,3,4, and Jian-Xin Li 1 1 National Laboratory of Solid State Microstructures and Department of Physics,
More informationIntroduction to topological insulators. Jennifer Cano
Introduction to topological insulators Jennifer Cano Adapted from Charlie Kane s Windsor Lectures: http://www.physics.upenn.edu/~kane/ Review article: Hasan & Kane Rev. Mod. Phys. 2010 What is an insulator?
More informationGROWTH OF QUANTUM WELL FILMS OF TOPOLOGICAL INSULATOR BI 2 SE 3 ON INSULATING SUBSTRATE
GROWTH OF QUANTUM WELL FILMS OF TOPOLOGICAL INSULATOR BI 2 SE 3 ON INSULATING SUBSTRATE CUI-ZU CHANG, KE HE *, LI-LI WANG AND XU-CUN MA Institute of Physics, Chinese Academy of Sciences, Beijing 100190,
More informationarxiv: v2 [cond-mat.mes-hall] 31 Mar 2016
Journal of the Physical Society of Japan LETTERS Entanglement Chern Number of the ane Mele Model with Ferromagnetism Hiromu Araki, Toshikaze ariyado,, Takahiro Fukui 3, and Yasuhiro Hatsugai, Graduate
More informationTopological Defects inside a Topological Band Insulator
Topological Defects inside a Topological Band Insulator Ashvin Vishwanath UC Berkeley Refs: Ran, Zhang A.V., Nature Physics 5, 289 (2009). Hosur, Ryu, AV arxiv: 0908.2691 Part 1: Outline A toy model of
More informationTopological Insulators
Topological Insulators A new state of matter with three dimensional topological electronic order L. Andrew Wray Lawrence Berkeley National Lab Princeton University Surface States (Topological Order in
More informationarxiv: v1 [cond-mat.mes-hall] 29 Jul 2010
Discovery of several large families of Topological Insulator classes with backscattering-suppressed spin-polarized single-dirac-cone on the surface arxiv:1007.5111v1 [cond-mat.mes-hall] 29 Jul 2010 Su-Yang
More informationMassive Dirac fermions and spin physics in an ultrathin film of topological insulator
Title Massive Dirac fermions and spin physics in an ultrathin film of topological insulator Author(s) Lu, HZ; Shan, WY; Yao, W; Niu, Q; Shen, SQ Citation Physical Review B - Condensed Matter And Materials
More informationPOEM: Physics of Emergent Materials
POEM: Physics of Emergent Materials Nandini Trivedi L1: Spin Orbit Coupling L2: Topology and Topological Insulators Reference: Bernevig Topological Insulators and Topological Superconductors Tutorials:
More informationTopological insulators. Pavel Buividovich (Regensburg)
Topological insulators Pavel Buividovich (Regensburg) Hall effect Classical treatment Dissipative motion for point-like particles (Drude theory) Steady motion Classical Hall effect Cyclotron frequency
More informationTopological Physics in Band Insulators II
Topological Physics in Band Insulators II Gene Mele University of Pennsylvania Topological Insulators in Two and Three Dimensions The canonical list of electric forms of matter is actually incomplete Conductor
More informationEffective Field Theories of Topological Insulators
Effective Field Theories of Topological Insulators Eduardo Fradkin University of Illinois at Urbana-Champaign Workshop on Field Theoretic Computer Simulations for Particle Physics and Condensed Matter
More informationSTM studies of impurity and defect states on the surface of the Topological-
STM studies of impurity and defect states on the surface of the Topological- Insulators Bi 2 Te 3 and Bi 2 Se 3 Aharon Kapitulnik STANFORD UNIVERSITY Zhanybek Alpichshev Yulin Chen Jim Analytis J.-H. Chu
More informationHIGHER INVARIANTS: TOPOLOGICAL INSULATORS
HIGHER INVARIANTS: TOPOLOGICAL INSULATORS Sponsoring This material is based upon work supported by the National Science Foundation Grant No. DMS-1160962 Jean BELLISSARD Georgia Institute of Technology,
More informationTopological Insulators and Superconductors. Tokyo 2010 Shoucheng Zhang, Stanford University
Topological Insulators and Superconductors Tokyo 2010 Shoucheng Zhang, Stanford University Colloborators Stanford group: Xiaoliang Qi, Andrei Bernevig, Congjun Wu, Chaoxing Liu, Taylor Hughes, Sri Raghu,
More informationTopological Insulators and Superconductors
Topological Insulators and Superconductors Lecture #1: Topology and Band Theory Lecture #: Topological Insulators in and 3 dimensions Lecture #3: Topological Superconductors, Majorana Fermions an Topological
More informationNotes on Topological Insulators and Quantum Spin Hall Effect. Jouko Nieminen Tampere University of Technology.
Notes on Topological Insulators and Quantum Spin Hall Effect Jouko Nieminen Tampere University of Technology. Not so much discussed concept in this session: topology. In math, topology discards small details
More informationSUPPLEMENTARY INFORMATION
A Dirac point insulator with topologically non-trivial surface states D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, and M.Z. Hasan Topics: 1. Confirming the bulk nature of electronic bands by
More informationHartmut Buhmann. Physikalisches Institut, EP3 Universität Würzburg Germany
Hartmut Buhmann Physikalisches Institut, EP3 Universität Würzburg Germany Part I and II Insulators and Topological Insulators HgTe crystal structure Part III quantum wells Two-Dimensional TI Quantum Spin
More informationarxiv: v2 [cond-mat.str-el] 22 Oct 2018
Pseudo topological insulators C. Yuce Department of Physics, Anadolu University, Turkey Department of Physics, Eskisehir Technical University, Turkey (Dated: October 23, 2018) arxiv:1808.07862v2 [cond-mat.str-el]
More informationTopological Insulators
Topological Insulators Aira Furusai (Condensed Matter Theory Lab.) = topological insulators (3d and 2d) Outline Introduction: band theory Example of topological insulators: integer quantum Hall effect
More informationA new class of topological insulators from I-III-IV half-heusler. compounds with strong band inversion strength
A new class of topological insulators from I-III-IV half-heusler compounds with strong band inversion strength X. M. Zhang, 1 G. Z. Xu, 1 Y. Du, 1 E. K. Liu, 1 Z. Y. Liu, 2 W. H. Wang 1(a) and G. H. Wu
More informationMassive Dirac Fermion on the Surface of a magnetically doped Topological Insulator
SLAC-PUB-14357 Massive Dirac Fermion on the Surface of a magnetically doped Topological Insulator Y. L. Chen 1,2,3, J.-H. Chu 1,2, J. G. Analytis 1,2, Z. K. Liu 1,2, K. Igarashi 4, H.-H. Kuo 1,2, X. L.
More informationFrom graphene to Z2 topological insulator
From graphene to Z2 topological insulator single Dirac topological AL mass U U valley WL ordinary mass or ripples WL U WL AL AL U AL WL Rashba Ken-Ichiro Imura Condensed-Matter Theory / Tohoku Univ. Dirac
More informationDisordered topological insulators with time-reversal symmetry: Z 2 invariants
Keio Topo. Science (2016/11/18) Disordered topological insulators with time-reversal symmetry: Z 2 invariants Hosho Katsura Department of Physics, UTokyo Collaborators: Yutaka Akagi (UTokyo) Tohru Koma
More informationLecture notes on topological insulators
Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan (Dated: November 1, 18) Contents I. D Topological insulator 1 A. General
More informationThe Quantum Spin Hall Effect
The Quantum Spin Hall Effect Shou-Cheng Zhang Stanford University with Andrei Bernevig, Taylor Hughes Science, 314,1757 2006 Molenamp et al, Science, 318, 766 2007 XL Qi, T. Hughes, SCZ preprint The quantum
More informationTopological insulator (TI)
Topological insulator (TI) Haldane model: QHE without Landau level Quantized spin Hall effect: 2D topological insulators: Kane-Mele model for graphene HgTe quantum well InAs/GaSb quantum well 3D topological
More informationarxiv: v2 [cond-mat.str-el] 5 Jan 2016
Quantized spin models Broken symmetry phases Colossal magnetoresistance in topological Kondo insulator Igor O. Slieptsov and Igor N. Karnaukhov G.V. Kurdyumov Institute for Metal Physics, 36 Vernadsky
More informationSurface Majorana Fermions in Topological Superconductors. ISSP, Univ. of Tokyo. Nagoya University Masatoshi Sato
Surface Majorana Fermions in Topological Superconductors ISSP, Univ. of Tokyo Nagoya University Masatoshi Sato Kyoto Tokyo Nagoya In collaboration with Satoshi Fujimoto (Kyoto University) Yoshiro Takahashi
More informationTopological Kondo Insulator SmB 6. Tetsuya Takimoto
Topological Kondo Insulator SmB 6 J. Phys. Soc. Jpn. 80 123720, (2011). Tetsuya Takimoto Department of Physics, Hanyang University Collaborator: Ki-Hoon Lee (POSTECH) Content 1. Introduction of SmB 6 in-gap
More informationSymmetry Protected Topological Phases
CalSWARM 2016 Xie Chen 06/21/16 Symmetry Protected Topological Phases 1 Introduction In this lecture note, I will give a brief introduction to symmetry protected topological (SPT) phases in 1D, 2D, and
More informationSpin Hall and quantum spin Hall effects. Shuichi Murakami Department of Physics, Tokyo Institute of Technology PRESTO, JST
YKIS2007 (Kyoto) Nov.16, 2007 Spin Hall and quantum spin Hall effects Shuichi Murakami Department of Physics, Tokyo Institute of Technology PRESTO, JST Introduction Spin Hall effect spin Hall effect in
More informationSymmetry, Topology and Phases of Matter
Symmetry, Topology and Phases of Matter E E k=λ a k=λ b k=λ a k=λ b Topological Phases of Matter Many examples of topological band phenomena States adiabatically connected to independent electrons: - Quantum
More informationTopological insulators
http://www.physik.uni-regensburg.de/forschung/fabian Topological insulators Jaroslav Fabian Institute for Theoretical Physics University of Regensburg Stara Lesna, 21.8.212 DFG SFB 689 what are topological
More informationarxiv: v1 [cond-mat.mes-hall] 17 Jan 2013
Electrically Tunable Topological State in [111] Perovskite Materials with Antiferromagnetic Exchange Field Qi-Feng Liang, 1,2 Long-Hua Wu, 1 and Xiao Hu 1 1 International Center for Materials Nanoarchitectornics
More informationThis article is available at IRis:
Author(s) D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dill, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan This article is available
More informationTopological insulators
Oddelek za fiziko Seminar 1 b 1. letnik, II. stopnja Topological insulators Author: Žiga Kos Supervisor: prof. dr. Dragan Mihailović Ljubljana, June 24, 2013 Abstract In the seminar, the basic ideas behind
More informationEffects of biaxial strain on the electronic structures and band. topologies of group-v elemental monolayers
Effects of biaxial strain on the electronic structures and band topologies of group-v elemental monolayers Jinghua Liang, Long Cheng, Jie Zhang, Huijun Liu * Key Laboratory of Artificial Micro- and Nano-Structures
More informationWhat is a topological insulator? Ming-Che Chang Dept of Physics, NTNU
What is a topological insulator? Ming-Che Chang Dept of Physics, NTNU A mini course on topology extrinsic curvature K vs intrinsic (Gaussian) curvature G K 0 G 0 G>0 G=0 K 0 G=0 G
More informationSymmetry Protected Topological Insulators and Semimetals
Symmetry Protected Topological Insulators and Semimetals I. Introduction : Many examples of topological band phenomena II. Recent developments : - Line node semimetal Kim, Wieder, Kane, Rappe, PRL 115,
More informationarxiv: v2 [cond-mat.mes-hall] 11 Feb 2010
Massive Dirac fermions and spin physics in an ultrathin film of topological insulator arxiv:98.31v [cond-mat.mes-hall] 11 Feb 1 Hai-Zhou Lu 1 Wen-Yu Shan 1 Wang Yao 1 Qian Niu and Shun-Qing Shen 1 1 Department
More informationRecent developments in topological materials
Recent developments in topological materials NHMFL Winter School January 6, 2014 Joel Moore University of California, Berkeley, and Lawrence Berkeley National Laboratory Berkeley students: Andrew Essin,
More informationExperimental Reconstruction of the Berry Curvature in a Floquet Bloch Band
Experimental Reconstruction of the Berry Curvature in a Floquet Bloch Band Christof Weitenberg with: Nick Fläschner, Benno Rem, Matthias Tarnowski, Dominik Vogel, Dirk-Sören Lühmann, Klaus Sengstock Rice
More informationarxiv: v2 [cond-mat.mes-hall] 11 Oct 2016
Nonsymmorphic symmetry-required band crossings in topological semimetals arxiv:1606.03698v [cond-mat.mes-hall] 11 Oct 016 Y. X. Zhao 1, and Andreas P. Schnyder 1, 1 Max-Planck-Institute for Solid State
More informationOrganizing Principles for Understanding Matter
Organizing Principles for Understanding Matter Symmetry Conceptual simplification Conservation laws Distinguish phases of matter by pattern of broken symmetries Topology Properties insensitive to smooth
More informationBerry s phase in Hall Effects and Topological Insulators
Lecture 6 Berry s phase in Hall Effects and Topological Insulators Given the analogs between Berry s phase and vector potentials, it is not surprising that Berry s phase can be important in the Hall effect.
More informationChern number and Z 2 invariant
Chern number and Z 2 invariant Hikaru Sawahata Collabolators: Yo Pierre Mizuta, Naoya Yamaguchi, Fumiyuki Ishii Graduate School of Natural Science and Technology, Kanazawa University 2016/11/25 Hikaru
More informationAntiferromagnetic topological insulators
Antiferromagnetic topological insulators Roger S. K. Mong, Andrew M. Essin, and Joel E. Moore, Department of Physics, University of California, Berkeley, California 9470, USA Materials Sciences Division,
More informationFirst-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov
First-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov ES'12, WFU, June 8, 212 The present work was done in collaboration with David Vanderbilt Outline:
More informationTopological Superconductivity and Superfluidity
Topological Superconductivity and Superfluidity SLAC-PUB-13926 Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang Department of Physics, McCullough Building, Stanford University, Stanford,
More informationarxiv: v1 [cond-mat.mes-hall] 28 Feb 2010
A new platform for topological quantum phenomena: Topological Insulator states in thermoelectric Heusler-related ternary compounds arxiv:1003.0155v1 [cond-mat.mes-hall] 28 Feb 2010 H. Lin, 1,2 L.A. Wray,
More informationARPES experiments on 3D topological insulators. Inna Vishik Physics 250 (Special topics: spectroscopies of quantum materials) UC Davis, Fall 2016
ARPES experiments on 3D topological insulators Inna Vishik Physics 250 (Special topics: spectroscopies of quantum materials) UC Davis, Fall 2016 Outline Using ARPES to demonstrate that certain materials
More informationTopological insulator with time-reversal symmetry
Phys620.nb 101 7 Topological insulator with time-reversal symmetry Q: Can we get a topological insulator that preserves the time-reversal symmetry? A: Yes, with the help of the spin degree of freedom.
More informationTime Reversal Invariant Ζ 2 Topological Insulator
Time Reversal Invariant Ζ Topological Insulator D Bloch Hamiltonians subject to the T constraint 1 ( ) ΘH Θ = H( ) with Θ = 1 are classified by a Ζ topological invariant (ν =,1) Understand via Bul-Boundary
More informationDistribution of Chern number by Landau level broadening in Hofstadter butterfly
Journal of Physics: Conference Series PAPER OPEN ACCESS Distribution of Chern number by Landau level broadening in Hofstadter butterfly To cite this article: Nobuyuki Yoshioka et al 205 J. Phys.: Conf.
More informationWeyl fermions and the Anomalous Hall Effect
Weyl fermions and the Anomalous Hall Effect Anton Burkov CAP congress, Montreal, May 29, 2013 Outline Introduction: Weyl fermions in condensed matter, Weyl semimetals. Anomalous Hall Effect in ferromagnets
More informationarxiv: v2 [cond-mat.mes-hall] 27 Dec 2012
Topological protection of bound states against the hybridization Bohm-Jung Yang, 1 Mohammad Saeed Bahramy, 1 and Naoto Nagaosa 1,2,3 1 Correlated Electron Research Group (CERG), RIKEN-ASI, Wako, Saitama
More informationPOEM: Physics of Emergent Materials
POEM: Physics of Emergent Materials Nandini Trivedi L1: Spin Orbit Coupling L2: Topology and Topological Insulators Tutorials: May 24, 25 (2017) Scope of Lectures and Anchor Points: 1.Spin-Orbit Interaction
More informationSuperconductivity and non-metallicity induced by doping the. topological insulators Bi 2 Se 3 and Bi 2 Te 3
Superconductivity and non-metallicity induced by doping the topological insulators Bi 2 Se 3 and Bi 2 Te 3 Y. S. Hor 1, J. G. Checkelsky 2, D. Qu 2, N. P. Ong 2, and R. J. Cava 1 1 Department of Chemistry,
More informationSpecific Heat and Electrical Transport Properties of Sn 0.8 Ag 0.2 Te Superconductor
Specific Heat and Electrical Transport Properties of Sn 0.8 Ag 0.2 Te Superconductor Yoshikazu Mizuguchi 1 *, Akira Yamada 2, Ryuji Higashinaka 2, Tatsuma D. Matsuda 2, Yuji Aoki 2, Osuke Miura 1, and
More informationQuantitative Mappings from Symmetry to Topology
Z. Song, Z. Fang and CF, PRL 119, 246402 (2017) CF and L. Fu, arxiv:1709.01929 Z. Song, T. Zhang, Z. Fang and CF arxiv:1711.11049 Z. Song, T. Zhang and CF arxiv:1711.11050 Quantitative Mappings from Symmetry
More informationLecture III: Topological phases
Lecture III: Topological phases Ann Arbor, 11 August 2010 Joel Moore University of California, Berkeley, and Lawrence Berkeley National Laboratory Thanks Berkeley students: Andrew Essin Roger Mong Vasudha
More informationTopological Insulator Surface States and Electrical Transport. Alexander Pearce Intro to Topological Insulators: Week 11 February 2, / 21
Topological Insulator Surface States and Electrical Transport Alexander Pearce Intro to Topological Insulators: Week 11 February 2, 2017 1 / 21 This notes are predominately based on: J.K. Asbóth, L. Oroszlány
More informationTopological states of matter in correlated electron systems
Seminar @ Tsinghua, Dec.5/2012 Topological states of matter in correlated electron systems Qiang-Hua Wang National Lab of Solid State Microstructures, Nanjing University, Nanjing 210093, China Collaborators:Dunghai
More informationHartmut Buhmann. Physikalisches Institut, EP3 Universität Würzburg Germany
Hartmut Buhmann Physikalisches Institut, EP3 Universität Würzburg Germany Outline Insulators and Topological Insulators HgTe quantum well structures Two-Dimensional TI Quantum Spin Hall Effect experimental
More informationBuilding Frac-onal Topological Insulators. Collaborators: Michael Levin Maciej Kosh- Janusz Ady Stern
Building Frac-onal Topological Insulators Collaborators: Michael Levin Maciej Kosh- Janusz Ady Stern The program Background: Topological insulators Frac-onaliza-on Exactly solvable Hamiltonians for frac-onal
More informationDirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators. Nagoya University Masatoshi Sato
Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators Nagoya University Masatoshi Sato In collaboration with Yukio Tanaka (Nagoya University) Keiji Yada (Nagoya University) Ai Yamakage
More informationwhere a is the lattice constant of the triangular Bravais lattice. reciprocal space is spanned by
Contents 5 Topological States of Matter 1 5.1 Intro.......................................... 1 5.2 Integer Quantum Hall Effect..................... 1 5.3 Graphene......................................
More informationBasics of topological insulator
011/11/18 @ NTU Basics of topological insulator Ming-Che Chang Dept of Physics, NTNU A brief history of insulators Band insulator (Wilson, Bloch) Mott insulator Anderson insulator Quantum Hall insulator
More informationIntrinsic Topological Insulator Bi 2 Te 3 Thin Films on Si and Their Thickness Limit
Intrinsic Topological Insulator Bi 2 Te 3 Thin Films on Si and Their Thickness Limit www.materialsviews.com By Yao-Yi Li, Guang Wang, Xie-Gang Zhu, Min-Hao Liu, Cun Ye, Xi Chen, Ya-Yu Wang, Ke He, Li-Li
More informationDirac semimetal in three dimensions
Dirac semimetal in three dimensions Steve M. Young, Saad Zaheer, Jeffrey C. Y. Teo, Charles L. Kane, Eugene J. Mele, and Andrew M. Rappe University of Pennsylvania 6/7/12 1 Dirac points in Graphene Without
More informationarxiv: v2 [cond-mat.mtrl-sci] 20 Feb 2018
Experimental observation of node-line-like surface states in LaBi arxiv:1711.11174v2 [cond-mat.mtrl-sci] 20 Feb 2018 Baojie Feng, 1, Jin Cao, 2 Meng Yang, 3 Ya Feng, 4,1 Shilong Wu, 5 Botao Fu, 2 Masashi
More informationSpin orbit interaction in graphene monolayers & carbon nanotubes
Spin orbit interaction in graphene monolayers & carbon nanotubes Reinhold Egger Institut für Theoretische Physik, Düsseldorf Alessandro De Martino Andreas Schulz, Artur Hütten MPI Dresden, 25.10.2011 Overview
More informationarxiv: v2 [cond-mat.mes-hall] 10 Jul 2017
Tunable edge states and their robustness towards disorder M. Malki and G. S. Uhrig Lehrstuhl für Theoretische Physik 1, TU Dortmund, Germany (Dated: July 11, 2017) arxiv:1611.10098v2 [cond-mat.mes-hall]
More informationQuantum Spin Hall Effect in Inverted Type II Semiconductors
Quantum Spin Hall Effect in Inverted Type II Semiconductors Chaoxing Liu 1,2, Taylor L. Hughes 2, Xiao-Liang Qi 2, Kang Wang 3 and Shou-Cheng Zhang 2 1 Center for Advanced Study, Tsinghua University,Beijing,
More informationGraphene and Planar Dirac Equation
Graphene and Planar Dirac Equation Marina de la Torre Mayado 2016 Marina de la Torre Mayado Graphene and Planar Dirac Equation June 2016 1 / 48 Outline 1 Introduction 2 The Dirac Model Tight-binding model
More informationarxiv: v4 [math-ph] 24 Dec 2016
NOTES ON TOPOLOGICAL INSULATORS RALPH M. KAUFMANN, DAN LI, AND BIRGIT WEHEFRITZ-KAUFMANN arxiv:1501.02874v4 [math-ph] 24 Dec 2016 Abstract. This paper is a survey of the Z 2 -valued invariant of topological
More informationSingle particle Green s functions and interacting topological insulators
1 Single particle Green s functions and interacting topological insulators Victor Gurarie Nordita, Jan 2011 Topological insulators are free fermion systems characterized by topological invariants. 2 In
More informationElectrons in a periodic potential
Chapter 3 Electrons in a periodic potential 3.1 Bloch s theorem. We consider in this chapter electrons under the influence of a static, periodic potential V (x), i.e. such that it fulfills V (x) = V (x
More informationStructure and Topology of Band Structures in the 1651 Magnetic Space Groups
Structure and Topology of Band Structures in the 1651 Magnetic Space Groups Haruki Watanabe University of Tokyo [Noninteracting] Sci Adv (2016) PRL (2016) Nat Commun (2017) (New) arxiv:1707.01903 [Interacting]
More informationRole of spatial symmetry in crystalline topological insulator
Role of spatial symmetry in crystalline topological insulator Benoit Roberge Universite de Sherbrooke (Dated: 13 décembre 2013) The study of novel topological phases of matter in 3D topological insulator
More informationarxiv: v1 [cond-mat.mes-hall] 5 Feb 2018
Semimetal behavior of bilayer stanene I. Evazzade a,, M. R. Roknabadi a, T. Morshedloo b, M. Modarresi a, Y. Mogulkoc c,d, H. Nematifar a a Department of Physics, Faculty of Science, Ferdowsi University
More informationEmergent topological phenomena in antiferromagnets with noncoplanar spins
Emergent topological phenomena in antiferromagnets with noncoplanar spins - Surface quantum Hall effect - Dimensional crossover Bohm-Jung Yang (RIKEN, Center for Emergent Matter Science (CEMS), Japan)
More informationEffective theory of quadratic degeneracies
Effective theory of quadratic degeneracies Y. D. Chong,* Xiao-Gang Wen, and Marin Soljačić Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Received 28
More informationEmergent Frontiers in Quantum Materials:
Emergent Frontiers in Quantum Materials: High Temperature superconductivity and Topological Phases Jiun-Haw Chu University of Washington The nature of the problem in Condensed Matter Physics Consider a
More information3D topological insulators and half- Heusler compounds
3D topological insulators and half- Heusler compounds Ram Seshadri Materials Department, and Department of Chemistry and Biochemistry Materials Research Laboratory University of California, Santa Barbara
More informationQuantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
arxiv:cond-mat/0611399v1 [cond-mat.mes-hall] 15 Nov 006 Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells B. Andrei Bernevig, 1, Taylor L. Hughes, 1 and Shou-Cheng Zhang 1
More informationTopological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators
Topological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators Satoshi Fujimoto Dept. Phys., Kyoto University Collaborator: Ken Shiozaki
More informationarxiv: v1 [cond-mat.str-el] 6 May 2010
MIT-CTP/4147 Correlated Topological Insulators and the Fractional Magnetoelectric Effect B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil Department of Physics, Massachusetts Institute of Technology,
More informationChern Insulator Phase in a Lattice of an Organic Dirac Semimetal. with Intracellular Potential and Magnetic Modulations
Chern Insulator Phase in a Lattice of an Organic Dirac Semimetal with Intracellular Potential and Magnetic Modulations Toshihito Osada* Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha,
More information5 Topological insulator with time-reversal symmetry
Phys62.nb 63 5 Topological insulator with time-reversal symmetry It is impossible to have quantum Hall effect without breaking the time-reversal symmetry. xy xy. If we want xy to be invariant under, xy
More informationTopological Photonics with Heavy-Photon Bands
Topological Photonics with Heavy-Photon Bands Vassilios Yannopapas Dept. of Physics, National Technical University of Athens (NTUA) Quantum simulations and many-body physics with light, 4-11/6/2016, Hania,
More informationteam Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber
title 1 team 2 Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber motivation: topological states of matter 3 fermions non-interacting, filled band (single particle physics) topological
More informationE E F (ev) (a) (a) (b) (c) (d) (A ) (A ) M
Pis'ma v ZhET, vol. 96, iss. 12, pp. 870 { 874 c 2012 December 25 New topological surface state in layered topological insulators: unoccupied Dirac cone S. V. Eremeev +1), I. V. Silkin, T. V. Menshchikova,
More informationTopological insulators and the quantum anomalous Hall state. David Vanderbilt Rutgers University
Topological insulators and the quantum anomalous Hall state David Vanderbilt Rutgers University Outline Berry curvature and topology 2D quantum anomalous Hall (QAH) insulator TR-invariant insulators (Z
More informationUltrafast study of Dirac fermions in out of equilibrium Topological Insulators
Ultrafast study of Dirac fermions in out of equilibrium Topological Insulators Marino Marsi Laboratoire de Physique des Solides CNRS Univ. Paris-Sud - Université Paris-Saclay IMPACT, Cargèse, August 26
More information