Exploring topological states with cold atoms and photons
|
|
- Melanie Andra Howard
- 6 years ago
- Views:
Transcription
1 Exploring topological states with cold atoms and photons Theory: Takuya Kitagawa, Dima Abanin, Erez Berg, Mark Rudner, Liang Fu, Takashi Oka, Immanuel Bloch, Eugene Demler Experiments: I. Bloch s group (MPQ/LMU) A. White s group (Queensland) Harvard-MIT $$ NSF, AFOSR MURI, DARPA OLE, MURI ATOMTRONICS
2 Universality in condensed matter physics Spontaneous symmetry breaking and order
3
4 Universality of physics fev pev nev µev mev ev kev MeV GeV TeV pk nk µk mk K Cold atoms experiments K room temperature LHC Higgs mode in ultracold atoms, 2012 Higgs mode of the standard model, 2012
5 Order beyond symmetry breaking In 1980 the first ordered phase beyond symmetry breaking was discovered Integer Quantum Hall Effect: 2D electron gas in strong magnetic field show plateaus in Hall conductance Current along x, measure voltage along y. On a plateau with an accuracy of 10-9 What is the quantum protectorate of such precise quantization?
6 Topological order In a topologically ordered state some physical quantity is given by a discreet topological invariant. Some physical response function is determined by this quantized invariant. Topological invariant: quantity that does not change under continuous deformations Example of topological invariant in geometry Gaussian curvature at every point on a surface Gauss-Bonnet theorem for closed surfaces g integer genus of a surface g=0 g=1
7 How to define topological invariant for electrons in solids? What kind of curvature can exist for electrons in solids?
8 Bloch s theorem and Brillouin zone One electron wavefunction in a crystal (periodic) potential can be written as k is crystal momentum restricted to Brillouin zone, a region of k-space with periodic boundaries. Function is periodic (same in every unit cell) As k changes, we map an energy band. Set of all bands is a band structure. But lattice momentum is periodic The Brillouin zone can play the role of the surface. Important property of quantum mechanics, the Berry phase, gives us the curvature.
9 Berry phase Consider a quantum-mechanical system in a nondegenerate ground state, e.g. spin ½ particle in a magnetic field. The adiabatic theorem says that if the Hamiltonian is changed slowly, the system remains in its instantaneous ground state. Berry phase: when the Hamiltonian goes around a closed loop in parameter space, the system acquires a geometrical phase relative to initial state (in addition to the usual dynamical phase). Gauge transformation of the Berry phase Gauge invariant quantities are Berry curvature and closed loop integrals
10 From Berry phase to Chern number The change in the electron wavefunction within the Brillouin zone leads to a Berry connection and Berry curvature Ky Brillouin zone Kx Integral of F is quantized to be integer: first Chern number. It is like Gauss-Bonnet theorem for the Brillouin zone. TKNN quantization of Hall conductivity for IQHE Thouless et al., PRL 1982
11 Topological order and edge states TKNN quantization exists only for insulators with completely filled bands. Conductance goes through gapless edge states. Existence of topological invariant requires edge states Topological invariant cannot change without closing of the insulating gap
12 Topology in one dimension: Berry phase and electric polarization Polarization as Berry phase Vanderbilt, King-Smith PRB 1993
13 Su-Schrieffer-Heeger Model B A B A B When d z (k)=0, states with t>0 and t<0 are topologically distinct.
14 Domain wall states in SSH Model An interface between topologically different states has protected midgap states Absorption spectra on neutral and doped trans (CH) x
15 Topological states of matter Integer and Fractional 3D topological insulators Quantum Hall effects Quantum Spin Hall effect Exotic properties: quantized conductance (Quantum Hall systems, Quantum Spin Hall Sysytems) fractional charges (Fractional Quantum Hall systems, Polyethethylene) This talk: How to explore topology of band structures with synthetic matter: cold atoms and photons Extend to dynamics. Unique topological properties of dynamics
16 Order parameters can be measured Magnetization order parameter in ferromagnets Nematic order parameter in liquid crystals
17 Outline Zak/Berry phase measurements as a probe of band topology in OL Bloch+Ramsey interference experiments with cold atoms Theory + Experiments by MPQ group Phys. Rev. Lett. 110: (2013) Nature Physics 9, 795 (2013) Exploring edge states in topological phases with photons T. Kitagawa et al., PRA 82:33429 (2010) Phys. Rev. B 82, (2010) Nature Comm. 3:882 (2012)
18 Probing band topology with Ramsey/Bloch interference
19 Tools of atomic physics: Bloch oscillations C. Salomon et al., PRL (1996)
20 Tools of atomic physics: Ramsey interference /2 pulse Evolution /2 pulse + measurement ot S z gives relative phase accumulated by the two spin components Evolution Used for atomic clocks, gravitometers, accelerometers, magnetic field measurements
21 Zak phase probe of band topology in 1d One dimensional superlattices Su Schrieffer Heeger model Theory: Takuya Kitagawa (Harvard), Dima Abanin (Harvard/Perimeter), Eugene Demler (Harvard) Experiments Marcos Atala, Monika Aidelsburger, Julio Barreiro, Immanuel Bloch (LMU/MPQ) Phys. Rev. Lett. 110: (2013) Nature Physics 9, 795 (2013)
22 SSH model of polyacetylene Su, Schrieffer, Heeger, 1979 B A B A B Analogous to bichromatic optical lattice potential I. Bloch et al., LMU/MPQ
23 A B A B A Dimerized model
24 Characterizing SSH model using Zak phase Two hyperfine spin states experience the same optical potential a /2a 0 /2a Zak phase is equal to Problem: experimentally difficult to control Zeeman phase shift
25 Spin echo protocol for measuring Zak phase Dynamic phases due to dispersion and magnetic field fluctuations cancel. Interference measures the difference of Zak phases of the two bands in two dimerizations. Expect phase
26 Bloch oscillations measurements in LMU/MPQ With -pulse but no swapping of dimerization
27 Bloch oscillations measurements in LMU/MPQ With p-pulse and with swapping of dimerization
28 Zak phase measurements in LMU/MPQ
29 Zak phase measurements can be used to probe topological properties of Bloch bands in 2D and 3D D. Abanin, T. Kitagawa, I. Bloch, E. Demler Phys. Rev. Lett. 110: (2013) F. Grusdt, D. Abanin, E. Demler Phys. Rev. A 89, (2014)
30 Measuring Berry curvature in 2d and Chern num Integral of the Berry phase around the Dirac point Manifestation of Berry phase of Dirac points in grapheme: IQHE plateaus are shifted by 1/2 Interferometric probe of Berry curvature and Chern number in 2d systems Extension to more exotic states: Quantum Spin Hall Effect states and Topological Insulators in 3D. Grusdt et al., Phys. Rev. A 89, (2014)
31 Discreet time quantum walk with photons Observing edge states on topological domain boundaries Topological properties of dynamics Theory: T. Kitagawa et al., Phys. Rev. A 82:33429 (2010) Phys. Rev. B 82, (2010) Experiments: T. Kitagawa et al., Nature Comm. 3:882 (2012)
32 Definition of 1D discrete Quantum Walk 1D lattice, particle starts at the origin Spin rotation Spindependent Translation Analogue of classical random walk. Introduced in quantum information: Q Search, Q computations
33
34 Quantum walk with photons Rotation is implemented by half-wave plates Translation by bi-refringent calcite crystals that displace only horizontally polarized light A. White s group in Queensland T. Kitagawa et al., Nature Comm. 3:882 (2012) Earlier realization of QW with photons: A. Schrieber et al., PRL (2010)
35 From discreet time quantum walks to Topological Hamiltonians T. Kitagawa et al., Phys. Rev. A 82, (2010)
36 Discrete quantum walk Spin rotation around y axis Translation One step Evolution operator
37 Effective Hamiltonian of Quantum Walk Interpret evolution operator of one step as resulting from Hamiltonian. Stroboscopic implementation of H eff Spin-orbit coupling in effective Hamiltonian
38 From Quantum Walk to Spin-orbit Hamiltonian in 1d k-dependent Zeeman field Winding Number Z on the plane defines the topology! Winding number takes integer values. Can we have topologically distinct quantum walks?
39 Split-step DTQW
40 Split-step DTQW Phase Diagram
41 Detection of Topological phases: localized states at domain boundaries
42 Phase boundary of distinct topological phases has bound states Bulks are insulators Topologically distinct, so the gap has to close near the boundary a localized state is expected
43 Split-step DTQW with site dependent rotations Apply site-dependent spin rotation for
44 Experimental demonstration of topological quantum walk with photons Kitagawa et al., Nature Comm Rotation is implemented by half-wave plates Translation by birefringent calcite crystals that displace only horizontally polarized light
45 Topological Hamiltonians in 2D with quantum walk Schnyder et al., PRB (2008) Kitaev (2009)
46 What we discussed so far Split time quantum walks provide stroboscopic implementation of different types of single particle Hamiltonians By changing parameters of the quantum walk protocol we can obtain effective Hamiltonians which correspond to different topological classes
47 Topological properties unique to dynamics
48 Topological properties of evolution operator Time dependent periodic Hamiltonian Floquet operator Floquet operator U k (T) gives a map from a circle to the space of unitary matrices. It is characterized by the topological invariant This can be understood as energy winding. This is unique to periodic dynamics. Energy defined up to 2 /T
49 Example of topologically non-trivial evolution operator and relation to Thouless topological pumping Spin ½ particle in 1d lattice. Spin down particles do not move. Spin up particles move by one lattice site per period group velocity n 1 describes average displacement per period. Quantization of 1 describes topological pumping of particles. This is another way to understand Thouless quantized pumping
50 Experimental demonstration of topological quantum walk with photons Kitagawa et al., Nature Comm. 3:882 (2012) Boundary with topologically similar evolution operators Boundary with topologically different evolution operators
51 Floquet states beyond in 2d beyond quantum walk
52 Topological Floquet states in 2d Kitagawa et al., PRB (2010)
53 Topological Floquet states in 2d Oka and Aoki, PRB (2009) Kitagawa et al., PRB (2010) Lindner, Refael, Galiski, Nat. Phys. (2011) Observation of Floquet-Bloch states on the surface of a topological insulator Gedik et al., Science (2013)
54 Summary First direct measurement of Zak phase of a 1d band Prospect of measuring topological properties of 2d bands Observation of edge states in topological phases realized with photons
55 How to measure Berry phase of Bloch states C Naïve approach: Move atom on a closed trajectory around Dirac point Measure accumulated phase Problems with this approach: Need to move atom on a complicated curved trajectory Need to separate dynamical phase
56 From Berry phase to Zak phase Integral of the Berry phase is only well defined on a closed trajectory is not gauge invariant C gauge invariant integral of Berry curvature Brillouin zone is a torus. There are two types of closed trajectories Zak Zak phase: integral of Berry phase over reciprocal lattice vector
57 Zak phase measurements in LMU/MPQ
58 Universality of collective modes M. Enders et al., Observation of Higgs mode in 2D superfluid in ultracold atoms Nature 2012 fev pev nev µev mev ev kev MeV GeV TeV pk nk µk mk K current experiments K first BEC of alkali atoms He N room temperature LHC
59
60
61
62
Takuya Kitagawa, Dima Abanin, Immanuel Bloch, Erez Berg, Mark Rudner, Liang Fu, Takashi Oka, Eugene Demler
Exploring topological states with synthetic matter Takuya Kitagawa, Dima Abanin, Immanuel Bloch, Erez Berg, Mark Rudner, Liang Fu, Takashi Oka, Eugene Demler Harvard-MIT $$ NSF, AFOSR MURI, DARPA OLE,
More informationExploring Topological Phases With Quantum Walks
Exploring Topological Phases With Quantum Walks Tk Takuya Kitagawa, Erez Berg, Mark Rudner Eugene Demler Harvard University References: PRA 82:33429 and PRB 82:235114 (2010) Collaboration with A. White
More informationInterferometric probes of quantum many-body systems of ultracold atoms
Interferometric probes of quantum many-body systems of ultracold atoms Eugene Demler Harvard University Collaborators: Dima Abanin, Thierry Giamarchi, Sarang Gopalakrishnan, Adilet Imambekov, Takuya Kitagawa,
More informationsynthetic condensed matter systems
Ramsey interference as a probe of synthetic condensed matter systems Takuya Kitagawa (Harvard) DimaAbanin i (Harvard) Mikhael Knap (TU Graz/Harvard) Eugene Demler (Harvard) Supported by NSF, DARPA OLE,
More informationThe Center for Ultracold Atoms at MIT and Harvard Theoretical work at CUA. NSF Visiting Committee, April 28-29, 2014
The Center for Ultracold Atoms at MIT and Harvard Theoretical work at CUA NSF Visiting Committee, April 28-29, 2014 Paola Cappellaro Mikhail Lukin Susanne Yelin Eugene Demler CUA Theory quantum control
More informationMeasuring many-body topological invariants using polarons
1 Anyon workshop, Kaiserslautern, 12/15/2014 Measuring many-body topological invariants using polarons Fabian Grusdt Physics Department and Research Center OPTIMAS, University of Kaiserslautern, Germany
More informationFloquet theory of photo-induced topological phase transitions: Application to graphene
Floquet theory of photo-induced topological phase transitions: Application to graphene Takashi Oka (University of Tokyo) T. Kitagawa (Harvard) L. Fu (Harvard) E. Demler (Harvard) A. Brataas (Norweigian
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 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 informationQuantum Quenches in Chern Insulators
Quantum Quenches in Chern Insulators Nigel Cooper Cavendish Laboratory, University of Cambridge CUA Seminar M.I.T., November 10th, 2015 Marcello Caio & Joe Bhaseen (KCL), Stefan Baur (Cambridge) M.D. Caio,
More information3.15. Some symmetry properties of the Berry curvature and the Chern number.
50 Phys620.nb z M 3 at the K point z M 3 3 t ' sin 3 t ' sin (3.36) (3.362) Therefore, as long as M 3 3 t ' sin, the system is an topological insulator ( z flips sign). If M 3 3 t ' sin, z is always positive
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 informationTopological Phenomena in Periodically Driven Systems: Disorder, Interactions, and Quasi-Steady States Erez Berg
Topological Phenomena in Periodically Driven Systems: Disorder, Interactions, and Quasi-Steady States Erez Berg In collaboration with: Mark Rudner (Copenhagen) Netanel Lindner (Technion) Paraj Titum (Caltech
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 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 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 informationTopological phenomena in quantum walks: elementary introduction to the physics of topological phases
Quantum Inf Process (01) 11:1107 1148 DOI 10.1007/s1118-01-045-4 Topological phenomena in quantum walks: elementary introduction to the physics of topological phases Takuya Kitagawa Received: 9 December
More informationImpurities and disorder in systems of ultracold atoms
Impurities and disorder in systems of ultracold atoms Eugene Demler Harvard University Collaborators: D. Abanin (Perimeter), K. Agarwal (Harvard), E. Altman (Weizmann), I. Bloch (MPQ/LMU), S. Gopalakrishnan
More informationExplana'on of the Higgs par'cle
Explana'on of the Higgs par'cle Condensed ma7er physics: The Anderson- Higgs excita'on Press release of Nature magazine Unity of Physics laws fev pev nev µev mev ev kev MeV GeV TeV pk nk µk mk K Cold atoms
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 informationExploring new aspects of
Exploring new aspects of orthogonality catastrophe Eugene Demler Harvard University Harvard-MIT $$ NSF, AFOSR MURI, DARPA OLE, MURI ATOMTRONICS, MURI POLAR MOLECULES Outline Introduction: Orthogonality
More informationFloquet Topological Insulators and Majorana Modes
Floquet Topological Insulators and Majorana Modes Manisha Thakurathi Journal Club Centre for High Energy Physics IISc Bangalore January 17, 2013 References Floquet Topological Insulators by J. Cayssol
More informationSpin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
More informationTOPOLOGICAL BANDS IN GRAPHENE SUPERLATTICES
TOPOLOGICAL BANDS IN GRAPHENE SUPERLATTICES 1) Berry curvature in superlattice bands 2) Energy scales for Moire superlattices 3) Spin-Hall effect in graphene Leonid Levitov (MIT) @ ISSP U Tokyo MIT Manchester
More informationMapping the Berry Curvature of Optical Lattices
Mapping the Berry Curvature of Optical Lattices Nigel Cooper Cavendish Laboratory, University of Cambridge Quantum Simulations with Ultracold Atoms ICTP, Trieste, 16 July 2012 Hannah Price & NRC, PRA 85,
More informationTopological Phases of Matter Out of Equilibrium
Topological Phases of Matter Out of Equilibrium Nigel Cooper T.C.M. Group, Cavendish Laboratory, University of Cambridge Solvay Workshop on Quantum Simulation ULB, Brussels, 18 February 2019 Max McGinley
More informationLes états de bord d un. isolant de Hall atomique
Les états de bord d un isolant de Hall atomique séminaire Atomes Froids 2/9/22 Nathan Goldman (ULB), Jérôme Beugnon and Fabrice Gerbier Outline Quantum Hall effect : bulk Landau levels and edge states
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 informationBerry Phase Effects on Electronic Properties
Berry Phase Effects on Electronic Properties Qian Niu University of Texas at Austin Collaborators: D. Xiao, W. Yao, C.P. Chuu, D. Culcer, J.R.Shi, Y.G. Yao, G. Sundaram, M.C. Chang, T. Jungwirth, A.H.MacDonald,
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 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 informationIntroduction to topological insulators
Introduction to topological insulators Janos Asboth1, Laszlo Oroszlany2, Andras Palyi3 1: Wigner Research Centre for Physics, Hungarian Academy of Sciences 2: Eotvos University, Budapest 3: Technical University,
More informationLoop current order in optical lattices
JQI Summer School June 13, 2014 Loop current order in optical lattices Xiaopeng Li JQI/CMTC Outline Ultracold atoms confined in optical lattices 1. Why we care about lattice? 2. Band structures and Berry
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 informationSSH Model. Alessandro David. November 3, 2016
SSH Model Alessandro David November 3, 2016 Adapted from Lecture Notes at: https://arxiv.org/abs/1509.02295 and from article: Nature Physics 9, 795 (2013) Motivations SSH = Su-Schrieffer-Heeger Polyacetylene
More informationTopological phases of matter give rise to quantized physical quantities
Quantized electric multipole insulators Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017). Quantized electric multipole insulators. Science, 357(6346), 61 66. Presented by Mark Hirsbrunner, Weizhan
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 informationClassification theory of topological insulators with Clifford algebras and its application to interacting fermions. Takahiro Morimoto.
QMath13, 10 th October 2016 Classification theory of topological insulators with Clifford algebras and its application to interacting fermions Takahiro Morimoto UC Berkeley Collaborators Akira Furusaki
More informationDynamical phase transition and prethermalization. Mobile magnetic impurity in Fermi superfluids
Dynamical phase transition and prethermalization Pietro Smacchia, Alessandro Silva (SISSA, Trieste) Dima Abanin (Perimeter Institute, Waterloo) Michael Knap, Eugene Demler (Harvard) Mobile magnetic impurity
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 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 informationSpin-injection Spectroscopy of a Spin-orbit coupled Fermi Gas
Spin-injection Spectroscopy of a Spin-orbit coupled Fermi Gas Tarik Yefsah Lawrence Cheuk, Ariel Sommer, Zoran Hadzibabic, Waseem Bakr and Martin Zwierlein July 20, 2012 ENS Why spin-orbit coupling? A
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 informationExperimental reconstruction of the Berry curvature in a topological Bloch band
Experimental reconstruction of the Berry curvature in a topological Bloch band Christof Weitenberg Workshop Geometry and Quantum Dynamics Natal 29.10.2015 arxiv:1509.05763 (2015) Topological Insulators
More informationBerry Phase Effects on Charge and Spin Transport
Berry Phase Effects on Charge and Spin Transport Qian Niu 牛谦 University of Texas at Austin 北京大学 Collaborators: Shengyuan Yang, C.P. Chuu, D. Xiao, W. Yao, D. Culcer, J.R.Shi, Y.G. Yao, G. Sundaram, M.C.
More informationAditi Mitra New York University
Entanglement dynamics following quantum quenches: pplications to d Floquet chern Insulator and 3d critical system diti Mitra New York University Supported by DOE-BES and NSF- DMR Daniel Yates, PhD student
More informationQuantum anomalous Hall states on decorated magnetic surfaces
Quantum anomalous Hall states on decorated magnetic surfaces David Vanderbilt Rutgers University Kevin Garrity & D.V. Phys. Rev. Lett.110, 116802 (2013) Recently: Topological insulators (TR-invariant)
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 informationLECTURE 3 - Artificial Gauge Fields
LECTURE 3 - Artificial Gauge Fields SSH model - the simplest Topological Insulator Probing the Zak Phase in the SSH model - Bulk-Edge correspondence in 1d - Aharonov Bohm Interferometry for Measuring Band
More informationInteger quantum Hall effect for bosons: A physical realization
Integer quantum Hall effect for bosons: A physical realization T. Senthil (MIT) and Michael Levin (UMCP). (arxiv:1206.1604) Thanks: Xie Chen, Zhengchen Liu, Zhengcheng Gu, Xiao-gang Wen, and Ashvin Vishwanath.
More informationSpinor Bose gases lecture outline
Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor Bose-Einstein condensates 3. Imaging spin textures 4. Spin-mixing dynamics 5. Magnetic excitations We re here Coupling
More informationLearning about order from noise
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Alain Aspect, Adilet Imambekov, Vladimir Gritsev, Takuya Kitagawa,
More informationFloquet Topological Insulator:
Floquet Topological Insulator: Understanding Floquet topological insulator in semiconductor quantum wells by Lindner et al. Condensed Matter Journal Club Caltech February 12 2014 Motivation Motivation
More informationLearning about order from noise
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Mikhail Lukin, Anatoli
More informationQuantum noise studies of ultracold atoms
Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Mikhail Lukin, Anatoli Polkovnikov Funded by NSF,
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 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 informationTopological pumps and topological quasicrystals
Topological pumps and topological quasicrstals PRL 109, 10640 (01); PRL 109, 116404 (01); PRL 110, 076403 (013); PRL 111, 6401 (013); PRB 91, 06401 (015); PRL 115, 195303 (015), PRA 93, 04387 (016), PRB
More informationProximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface
Proximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum Work done in collaboration with: F. Nogueira
More informationNonequilibrium dynamics of interacting systems of cold atoms
Nonequilibrium dynamics of interacting systems of cold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Anton Burkov, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Mikhail Lukin,
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 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 informationTopology and many-body physics in synthetic lattices
Topology and many-body physics in synthetic lattices Alessio Celi Synthetic dimensions workshop, Zurich 20-23/11/17 Synthetic Hofstadter strips as minimal quantum Hall experimental systems Alessio Celi
More informationVortex States in a Non-Abelian Magnetic Field
Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM
More informationVortices and other topological defects in ultracold atomic gases
Vortices and other topological defects in ultracold atomic gases Michikazu Kobayashi (Kyoto Univ.) 1. Introduction of topological defects in ultracold atoms 2. Kosterlitz-Thouless transition in spinor
More informationNanostructured Carbon Allotropes as Weyl-Like Semimetals
Nanostructured Carbon Allotropes as Weyl-Like Semimetals Shengbai Zhang Department of Physics, Applied Physics & Astronomy Rensselaer Polytechnic Institute symmetry In quantum mechanics, symmetry can be
More informationTopological Properties of Quantum States of Condensed Matter: some recent surprises.
Topological Properties of Quantum States of Condensed Matter: some recent surprises. F. D. M. Haldane Princeton University and Instituut Lorentz 1. Berry phases, zero-field Hall effect, and one-way light
More informationv. Tε n k =ε n k T r T = r, T v T = r, I v I = I r I = v. Iε n k =ε n k Berry curvature: Symmetry Consideration n k = n k
Berry curvature: Symmetry Consideration Time reversal (i.e. motion reversal) 1 1 T r T = r, T v T = v. Tε n k =ε n k n k = n k Inversion Symmetry: 1 1 I r I = r, I v I = v. Iε n k =ε n k n k = n k θ
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 informationTopological Insulators and Ferromagnets: appearance of flat surface bands
Topological Insulators and Ferromagnets: appearance of flat surface bands Thomas Dahm University of Bielefeld T. Paananen and T. Dahm, PRB 87, 195447 (2013) T. Paananen et al, New J. Phys. 16, 033019 (2014)
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 informationFully symmetric and non-fractionalized Mott insulators at fractional site-filling
Fully symmetric and non-fractionalized Mott insulators at fractional site-filling Itamar Kimchi University of California, Berkeley EQPCM @ ISSP June 19, 2013 PRL 2013 (kagome), 1207.0498...[PNAS] (honeycomb)
More informationBerry-phase Approach to Electric Polarization and Charge Fractionalization. Dennis P. Clougherty Department of Physics University of Vermont
Berry-phase Approach to Electric Polarization and Charge Fractionalization Dennis P. Clougherty Department of Physics University of Vermont Outline Quick Review Berry phase in quantum systems adiabatic
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 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: 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 informationQuantum Spin Liquids and Majorana Metals
Quantum Spin Liquids and Majorana Metals Maria Hermanns University of Cologne M.H., S. Trebst, PRB 89, 235102 (2014) M.H., K. O Brien, S. Trebst, PRL 114, 157202 (2015) M.H., S. Trebst, A. Rosch, arxiv:1506.01379
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 informationInterference experiments with ultracold atoms
Interference experiments with ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Anton Burkov, Robert Cherng, Adilet Imambekov, Serena Fagnocchi, Vladimir Gritsev, Mikhail Lukin,
More informationSpinon magnetic resonance. Oleg Starykh, University of Utah
Spinon magnetic resonance Oleg Starykh, University of Utah May 17-19, 2018 Examples of current literature 200 cm -1 = 6 THz Spinons? 4 mev = 1 THz The big question(s) What is quantum spin liquid? No broken
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 informationYtterbium quantum gases in Florence
Ytterbium quantum gases in Florence Leonardo Fallani University of Florence & LENS Credits Marco Mancini Giacomo Cappellini Guido Pagano Florian Schäfer Jacopo Catani Leonardo Fallani Massimo Inguscio
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 informationStrongly Correlated Systems of Cold Atoms Detection of many-body quantum phases by measuring correlation functions
Strongly Correlated Systems of Cold Atoms Detection of many-body quantum phases by measuring correlation functions Anatoli Polkovnikov Boston University Ehud Altman Weizmann Vladimir Gritsev Harvard Mikhail
More informationCrystalline Symmetry and Topology. YITP, Kyoto University Masatoshi Sato
Crystalline Symmetry and Topology YITP, Kyoto University Masatoshi Sato In collaboration with Ken Shiozaki (YITP) Kiyonori Gomi (Shinshu University) Nobuyuki Okuma (YITP) Ai Yamakage (Nagoya University)
More informationDirac fermions in condensed matters
Dirac fermions in condensed matters Bohm Jung Yang Department of Physics and Astronomy, Seoul National University Outline 1. Dirac fermions in relativistic wave equations 2. How do Dirac fermions appear
More informationAdiabatic particle pumping and anomalous velocity
Adiabatic particle pumping and anomalous velocity November 17, 2015 November 17, 2015 1 / 31 Literature: 1 J. K. Asbóth, L. Oroszlány, and A. Pályi, arxiv:1509.02295 2 D. Xiao, M-Ch Chang, and Q. Niu,
More information(1) Topological terms and metallic transport (2) Dynamics as a probe of Majorana fermions
(1) Topological terms and metallic transport (2) Dynamics as a probe of Majorana fermions Harvard, September 16, 2014 Joel Moore University of California, Berkeley, and Lawrence Berkeley National Laboratory
More informationTopological Physics in Band Insulators IV
Topological Physics in Band Insulators IV Gene Mele University of Pennsylvania Wannier representation and band projectors Modern view: Gapped electronic states are equivalent Kohn (1964): insulator is
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 informationUniversal phase transitions in Topological lattice models
Universal phase transitions in Topological lattice models F. J. Burnell Collaborators: J. Slingerland S. H. Simon September 2, 2010 Overview Matter: classified by orders Symmetry Breaking (Ferromagnet)
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
More informationTopology of electronic bands and Topological Order
Topology of electronic bands and Topological Order R. Shankar The Institute of Mathematical Sciences, Chennai TIFR, 26 th April, 2011 Outline IQHE and the Chern Invariant Topological insulators and the
More informationInterband effects and orbital suceptibility of multiband tight-binding models
Interband effects and orbital suceptibility of multiband tight-binding models Frédéric Piéchon LPS (Orsay) with A. Raoux, J-N. Fuchs and G. Montambaux Orbital suceptibility Berry curvature ky? kx GDR Modmat,
More informationRoom temperature topological insulators
Room temperature topological insulators Ronny Thomale Julius-Maximilians Universität Würzburg ERC Topolectrics SFB Tocotronics Synquant Workshop, KITP, UC Santa Barbara, Nov. 22 2016 Correlated electron
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 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 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 informationHarvard University Physics 284 Spring 2018 Strongly correlated systems in atomic and condensed matter physics
1 Harvard University Physics 284 Spring 2018 Strongly correlated systems in atomic and condensed matter physics Instructor Eugene Demler Office: Lyman 322 Email: demler@physics.harvard.edu Teaching Fellow
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 information