Effect of Shot noise in the presence of ferromagnetic exchange potential on the surface of topological insulators

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International Research Journal of Applied and Basic Sciences 013 Available online at www.irjabs.

1 International Research Journal of Applied and Basic Sciences 013 Available online at ISSN X / Vol,6 (9): Science Eplorer Publications Effect of Shot noise in the presence of ferroagnetic echange potential on the surface of topological insulators Raieh Beiranvand 1, Raieh Beiranvand 1. Departent of Physics, aculty of Science and Engineering, Ayattollah Boroujerdi University, Broujerd, Iran.. aculty eber of Science and Engineering, Ayattollah Boroujerdi University, Broujerd, Iran. Corresponding author eail: raieh.beiranvand@yahoo.co ABSTRACT: In this paper we investigate the ano factor of an N junction in clean liit in the present of ferroagnetic echange potential. ano factor shows an oscillatory behavior due to coherent interference of Dirac ferions which transported and reflected by double interfaces. This behavior is signature of Dirac ferions in topological insulator. INTRODUCTION Topological insulators (TI) were predicted theoretically[1-4] and recently were confired eperientally[5-7]. A topological insulator (TI) have bulk band gap like an ordinary insulator but have a gapless conducting states on their surface[8]. These surface conducting states are robust even in the presence of deforation or strong disorder[1]. These states are due to spin-orbit coupling and protected by tie reversal syetry[3]. Spin-orbit interaction plays an ajor role in coupling of charge carrier and spin degrees of freedo[9]. Because of these properties, TI is an interesting aterial for spintronics[10-14]. or three diensional TI, strong (weak) TI is defined by odd (even) nuber of Dirac cone in oentu space[3]. So there are interesting phenoena such anoalous agneto-resistance[9], fractional quantu Hall effect [15, 16] and π Berry s phase[17]. TI can accept ferroagnet or superconductor properties due to proiity effect[18-0]. So a situation which spin and charge coupled Dirac ferions coincide with ferroagnetic or superconducting properties have attracted huge attentions[1-31]. On the other hand, studying transport properties is useful for applicatory properties of TI in electronics and spintronics. Since electrons have particle-wave duality, one ight epect fluctuations in electrical current to play a diagnostic role such as photons [3]. The discreteness of charge ay cause electrical fluctuations which are known as Shot noise. A convenient easure of sub-poissonian shot noise is the ano factor () which is the ratio of the actual shot noise and the Poisson noise that would be easured[33]. In this paper we investigate tunneling conductance and transport properties of Dirac ferions on the surface of topological insulators for N N junctions within the clean liit and low teperature regie. The topological insulator we used here is ade of HgTe or Bi Se 3. This entioned alloys have single Dirac cone in their Brillouin one in which two diensional Dirac equation govern the carrier of charge. In sec. we use two diensional Dirac Hailtonian and derive conducting state in noral and ferroagnetic region. Using boundary conditions we can calculate analytical fors for transission and reflection probabilities. We calculate electronic conductance of the entioned syste. In sec. 3 using the calculated conductance, the anoalous properties of ano factor have investigated. The ain concern is to clear the difference of our syste with traditional etallic or graphene like systes. In sec. 4 we end with conclusions and a brief discussion about difference between etallic and topological insulator case. Theory of tunneling conductance On the surface of topological insulators Dirac ferions are governed by two diensional Dirac Hailtonian which in k-space is given by[34]: H v. k I (1) Where is Pauli atrices in spin space and I is identity atri. Also v is eri velocity and μ is cheical potential. Unlike in the graphene case which pseudospin coupled to oentu, in TI real spin coupled to oentu. This feature with ai of tie-reversal syetry lead to create protected states which robust in the presence of disorders. When a ferroagnetic electrode with agnetiation is deposited on

2 Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), , 013 surface of the TI, because of the proiity of TI and ferroagnet, an additional ter appear into equation (1) as follow[9]: H v. () 0 We consider and N N junction which the thickness of noral region is d. We assue the TI is located in y-plane and ferroagnetic electrode is deposited on TI such ˆi ˆj k ˆ () (d is well-known step function. So in ( 0, θ, φ) coordinate we have (See ig. 1): SinCos 0 SinSin y 0 Cos 0. () y (3) d θ φ y erroagnet Topological Insulator igure 1. (Color Line) Scheatic odel of N N junctions on top of topological insulator. We assue that junctions are located at =0 and =d. The 3D agnetiation direction is defined by polar angle θ and aiuth angle φ. By solving Eq. (1) for <0 region, Dirac spinors read as: 1 1 e I i e ikikyy Where k and k y are coponents of wave vector in and y directions, respectively. Also, sign refer to the -aes direction and β is incidental angle of Dirac ferions on the interface of N junction. k and β defined as: vk 1 y Sin ( ) k ( ) k v y In which ε is the ecitation energy of Dirac ferions easured fro eri surface. or ferroagnetic region between 0<<d Dirac spinors are given by: 1 e II(, y) ( ) e i aes. Which ik ikyy k is coponent of wave vector in ferroagnetic region and α is angle between k and - k and α are defined as: v k 1 y y Sin ( ) ( ) k ( ) ( ) Cos v v (4) (6) (5) (7) 166

Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), 165-169, 013 The Spinors in >d is the sae as region <0 and equal to Eqs. (4) and (5).

3 Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), , 013 The Spinors in >d is the sae as region <0 and equal to Eqs. (4) and (5). or an incidental particle fro <0 into the N interface at =0, the transverse wave vector k y and the ecitation energy ε are conserved in scattering process. The Dirac wave function in each region ust satisfy the below boundary condition at =0: r a a (8) I I 1 II II And at =d t a a (9) I 1 II II By solving Eqs. (8) and (9), we drive transission probability T t for N N junction as follow: 4Cos Cos 1 ( ) (10) T 4Sink d (1 )(1 Cos[k d]cos[ ] Cos[k d] Cos[ ] 4Sin [k d]sin Sin ( ) The Eq. (10) is the ain result of this section. Using the transport coefficient and conductance forula[35], one can calculate the conductance of entioned structure with arbitrary agnetiation. G0 G( ) T cos d (11) Here G0 N( )We / vis noral conductance and N( ) ev / ( v ) is the density of state of Dirac ferions and W is the width of junction. igure. (Color line) The electronic conductance of structure for agnetiation direction and. Here we have fied ecitation energy ε=0.01μ and 0={0.μ, 0.4μ, 0.6μ,0.8μ} for blue, red, green and violet curves, respectively. The electronic conductance of our structure is plotted vs. Kd in ig., here K / v is the eri vector of the syste. The oscillations of conductance are a sign of coherent interference of Dirac ferions at two interfaces. By using the conductance, one can calculate the Shot noise of the syste. This quantity ay have any applications in spintronics. Shot Noise of N N structure The ano factor of entioned structure is calculated by the following forula[36]: T(1 T)Cosd G( ) 167

Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), 165-169, 013 igure3. (Color line) The ano factor of N N junction for agnetiation direction θ π and φ π. Here we have fied ecitation energy ε=0.

4 Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), , 013 igure3. (Color line) The ano factor of N N junction for agnetiation direction θ π and φ π. Here we have fied ecitation energy ε=0.01μ and 0={0.μ, 0.4μ, 0.6μ,0.8μ} for blue, red, green and violet curves, respectively. As shown in ig. 3, the ano factor shows an oscillatory behavior which is not siilar to etallic case[33]. This anner is due to oscillatory behavior of conductance (see ig. ). As the agnitude of 0 rises, the aplitude of oscillatory behavior of becoes large. When the width of junction becoes larger, this unfavorite behavior becoes soother. By tuning the agnitude of ferroagnetic echange potential and width of junction, one can design the Shot noise in arbitrary value that is good for easureents or purpose of anipulated device. CONCLUSIONS We theoretically investigated coherent transport of Dirac ferions on the surface of TI under the presence of echange ferroagnetic potential. We show that oscillatory behavior of conductance and ano factor is result of coherent interference of carriers that ove between two sooth junctions. This behavior of ano factor is not siilar to one that occurs in etallic junction. So we predict that this behavior is a signature of eistence of Dirac ferions on the surface of TI. ACKNOWLEDGMENTS The author appreciates very useful discussion with M. Salehi. I would like to thank the office of Research Manageent of Ayattollah Boroujerdi University. REERENCES Kane CL, Mele EJ Quantu Spin Hall Effect in Graphene. Physical Review Letters, 95(): p Kane CL, Mele EJ. 005.Z_{} Topological Order and the Quantu Spin Hall Effect. Physical Review Letters, 95(14): p u L, Kane CL. 007.Topological insulators with inversion syetry. Physical Review B, 76(4): p u L, Kane CL, Mele EJ. 007.Topological Insulators in Three Diensions. Physical Review Letters, 98(10): p Hsieh D, et al. 008.A topological Dirac insulator in a quantu spin Hall phase. Nature, 45(7190): p Xia Y, et al. 009.Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat Phys, 5(6): p Hsieh TH, et al. 01.Topological crystalline insulators in the SnTe aterial class. Nat Coun, 3: p. 98. Hasan MZ, Kane CL. 010.Colloquiu: Topological insulators. Reviews of Modern Physics, 8(4): p Yokoyaa T, Tanaka Y, Nagaosa N.010. Anoalous agnetoresistance of a two-diensional ferroagnet/ferroagnet junction on the surface of a topological insulator. Physical Review B, 81(1): p Hsieh D, et al. 009.Observation of Unconventional Quantu Spin Tetures in Topological Insulators. Science, 33(5916): p Misawa T, Yokoyaa T, Murakai S Electroagnetic spin polariation on the surface of topological insulator. Physical Review B, 84(16): p Burkov AA, Hawthorn DG. 010.Spin and Charge Transport on the Surface of a Topological Insulator. Physical Review Letters, 105(6): p Akinori N, et al. 010.Spin-polaried surface bands of a three-diensional topological insulator studied by high-resolution spin- and angleresolved photoeission spectroscopy. New Journal of Physics, 1(6): p Hsieh D, et al A tunable topological insulator in the spin helical Dirac transport regie. Nature, 460(759): p Wang Y, et al. 01.ractional quantu Hall effect in topological flat bands with Chern nuber two. Physical Review B, 86(0): p Zaletel MP, Mong RSK, Pollann. 013.Topological Characteriation of ractional Quantu Hall Ground States fro Microscopic Hailtonians. Physical Review Letters, 110(3): p Qi XL, Hughes TL, Zhang SC. 008.Topological field theory of tie-reversal invariant insulators. Physical Review B, 78(19): p Linder J, et al Interplay between superconductivity and ferroagnetis on a topological insulator. Physical Review B, 81(18): p ischer MH, et al Large Spin Torque in Topological Insulator/erroagnetic Metal Bilayers. Ariv, Akherov AR, Nilsson J, Beenakker CWJ. 009.Electrically Detected Interferoetry of Majorana erions in a Topological Insulator. Physical Review Letters, 10(1): p

5 Intl. Res. J. Appl. Basic. Sci. Vol., 6 (9), , 013 Sticlet D, Bena C, Sion P. 01. Spin and Majorana Polariation in Topological Superconducting Wires. Physical Review Letters, 108(9): p Sasaki S, et al. 01.Odd-Parity Pairing and Topological Superconductivity in a Strongly Spin-Orbit Coupled Seiconductor. Physical Review Letters, 109(1): p u L, Kane CL. 008.Superconducting Proiity Effect and Majorana erions at the Surface of a Topological Insulator. Physical Review Letters, 100(9): p Wang J, et al. 01.Interplay between topological insulators and superconductors. Physical Review B, 85(4): p Tanaka Y, et al. 009.Theory of topological spin current in noncentrosyetric superconductors. Physical Review B, 79(6): p Lababidi M, Zhao E. 01.Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures. Physical Review B, 86(16): p Cheng M. 01.Superconducting proiity effect on the edge of fractional topological insulators. Physical Review B, :) 01(68. p Sara SD, Li Q. 013.Many-body effects and possible superconductivity in the D etallic surface states of 3D topological insulators. Ariv, Rodrigo JG, et al. 01. Topological superconductivity in lead nanowires. Ariv, v1. Qi XL, Zhang SC. 010.Topological insulators and superconductors. Ariv, v1. Black-Schaffer AM, Balatsky AV. 013.Proiity-induced unconventional superconductivity in topological insulators.ariv, Beenakker CWJ, Sch onenberger C., Quantu Shot Noise. arxiv v1. Blanter YM, Büttiker M Shot noise in esoscopic conductors. Physics Reports, 336(1 ): p Mondal S, et al. 010.Tuning the Conductance of Dirac erions on the Surface of a Topological Insulator. Physical Review Letters, 104(4): p Beenakker CWJ. 006.Specular Andreev Reflection in Graphene. Physical Review Letters, 97(6): p Jian-Hui Y, et al. 01.Charge transport and shot noise on the surface of a topological insulator with a agnetic odulation. Chinese Physics B, 1(4): p

Topological 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