Topological protection, disorder, and interactions: Life and death at the surface of a topological superconductor
|
|
|
- Sydney Cobb
- 5 years ago
- Views:
Transcription
1 Topological protection, disorder, and interactions: Life and death at the surface of a topological superconductor Matthew S. Foster Rice University March 14 th, 2014 Collaborators: Emil Yuzbashyan (Rutgers), Hong-Yi Xie and Yang-Zhi Chou PRL 109, (2012); arxiv: ; In preparation
2 3D Topological Superconductor Volovik 88 Read and Green 00 Schnyder, Ryu, Furusaki, Ludwig 08 Kitaev 09 Quasiparticle bandstructure is fully-gapped, topologically twisted CI: spin SU(2) symmetry (spin singlet pairing) AIII: spin U(1) (e.g. spin triplet p-wave) DIII: no spin symmetry (e.g. 3 He B, Cu x Bi 2 Se 3? YPtBi?) Protected by time-reversal symmetry (in 3D)
3 3D Topological Superconductor Volovik 88 Read and Green 00 Schnyder, Ryu, Furusaki, Ludwig 08 Kitaev 09 Quasiparticle bandstructure is fully-gapped, topologically twisted CI: spin SU(2) symmetry (spin singlet pairing) AIII: spin U(1) (e.g. spin triplet p-wave) DIII: no spin symmetry (e.g. 3 He B, Cu x Bi 2 Se 3? YPtBi?) Protected by time-reversal symmetry (in 3D) Class CI: Schnyder, Ryu, Ludwig 09 Winding number Number of surface Dirac bands: 2 k = ν
4 Background: Overview Surface states of 3D bulk topological superconductors: Gapless Dirac ( Majorana ) quasiparticle surface bands With disorder: Quenched 2+1-D QCD (random non-abelian vector potentials) Idea: Test the limits of Topological protection : Disorder & interactions Disorder induces multifractal wavefunction fluctuations (critical delocalization) Multifractality, Chalker scaling: Disorder can enhance interactions Schnyder, Ryu, Furusaki, Ludwig 08; Kitaev 09 Feigelman, Ioffe, Kravtsov, Yuzbashyan 07 Feigelman, Ioffe, Kravtsov, Cuevas 10
5 Background: Surface states of 3D bulk topological superconductors: Gapless Dirac ( Majorana ) quasiparticle surface bands With disorder: Quenched 2+1-D QCD (random non-abelian vector potentials) Idea: Test the limits of Topological protection : Disorder & interactions Disorder induces multifractal wavefunction fluctuations (critical delocalization) Results and conclusions: Overview 1) Disorder-amplified interactions can sabotage topological protection (Class CI), inducing surface quantum Hall order (Class C). 2) Stable gapless surface states: AIII, DIII. Interacting fixed point for AIII. 3) Suppression of Altshuler-Aronov to surface spin, thermal conductance when TR is unbroken (AIII, DIII). Transport topological invariant? Foster and Yuzbashyan 12 Foster, Xie, Chou, Xie, Chou, Foster In preparation
6 Topological superconductor surface states Class CI Topologically-protected, gapless surface state (Bogoliubov) quasiparticles ν = 2k valleys, k = (1,2,3, ) Low energy surface Andreev state Hamiltonian: Schnyder, Ryu, Furusaki, Ludwig 08 Bernard and LeClair 02 Anomalous chiral symmetry (= physical time-reversal):
7 Topological superconductor surface states Fermion bilinears and time-reversal symmetry 1) Time-reversal even: Currents Spin SU(2) Valley Sp(2k) 2) Time-reversal odd: Densities Spin SU(2) Valley Sp(2k) 3) Time-reversal odd: Masses Invariant Valley (010..0) Physical interpretation of the mass? Class C Spin QHE
8 Dirty topological superconductor surface states Class CI Add TRI disorder: Valley Sp(2k) vector potentials only! Sources of : Impurities, vacancies External electric fields Edge, corner, dislocation potentials disorder Quenched 2+1-D QCD: Dirac fermions in a sea of frozen gauge fluctuations
9 Disorder & CFT ν = 2k valleys, k = (1,2,3, ), n replicas Clean CI surface state Hamiltonian: spin valley replica Invariant under combined spin x valley x replica SO(4nk) rotations: Conformal Field Theory: SO(4nk) 1 (free fermions) Class CI: Disorder couples only to valley Sp(2k) n Kac-Moody currents:
10 Disorder & CFT: Multifractal spectra CFT solution via conformal embeddings Reviewed in (e.g.) J. Fuchs, Affine Lie Algebras and Quantum Groups Winding number ν = # valleys Fractionalization : Level n valley KM sector localizes Nersesyan, Tsvelik, Wenger 94 Multifractal LDoS moments: Level k primary fields Exact Results Foster, Yuzbashyan 12 Mudry, Chamon, Wen 96 Caux, Kogan, Tsvelik 96 Foster (unpublished)
11 Disorder & CFT: Multifractal spectra Class AIII: TRI TSC with spin U(1) symmetry (e.g., p-wave spin triplet) Foster, Ludwig 08 Schnyder, Ryu, Furusaki, Ludwig 08 Disorder: Valley currents (non-abelian) Spin U(1) current (abelian) Hamiltonian: Spin current disorder strength: Exact Results Foster, Yuzbashyan 12 Mudry, Chamon, Wen 96 Caux, Kogan, Tsvelik 96 Foster (unpublished)
12 Topological protection? Disorder and interactions Extended, multifractal surface states: No Anderson localization = topological protection! BUT Add generic, weak interparticle interactions, consistent with bulk symmetries [time-reversal, spin SU(2) for CI]
13 Physical picture: Chalker scaling, multifractality, and interactions Chalker scaling: Overlapping peaks and valleys in multifractal eigenstates with nearby energies Chalker, Daniell 88 Chalker 90 Cuevas, Kravtsov 07 Anderson insulator: No overlap for nearby energies Feigelman, Ioffe, Kravtsov, Yuzbashyan 07 Feigelman, Ioffe, Kravtsov, Cuevas 10
14 Method 1: Scaling interactions with disorder Clean limit: DoS determines relevance of short-ranged interactions Clean Dirac: interactions irrelevant!
15 Method 1: Scaling interactions with disorder Clean limit: DoS determines relevance of short-ranged interactions Clean Dirac: interactions irrelevant! Dirty case: scaling dimension of disorder-averaged LDoS scaling dimension of disorder-averaged interaction Constraint: multifractal scaling dimension of second LDoS moment Compute exactly via CFT IQHP: Lee and Wang 96
16 Method 1: Scaling interactions with disorder Clean limit: DoS determines relevance of short-ranged interactions Clean Dirac: interactions irrelevant! Dirty case: scaling dimension of disorder-averaged LDoS scaling dimension of disorder-averaged interaction Maximally relevant interaction: Convexity property for a multifractal extended surface state: (independent dimensions!) Duplantier and Ludwig 1991 Wavefunction multifractality can amplify short-ranged interactions!
17 Method 2: Many valleys, WZW-FNLsM 1) Embed, fractionalize: SO(4nk) 1 Sp(2n) k C.f. Altland, Simons, Ziirnbauer 02 2) Bosonize: Sp(2n) k = principal chiral NLsM plus WZW term 3) 2+1-D version: Field becomes matrix in replicas and frequencies Finkelstein 83 4) Incorporate interactions (local in time and replicas) Under perturbative control for large winding numbers
18 Class CI (Spin SU(2) symmetry): Disorder and interactions Hamiltonian Interaction channels: Cooper pairing of surface quasiparticles (time-reversal invariance) Spin exchange (spin is conserved = hydrodynamic mode) Spin current-current Order parameters break time-reversal: Spin polarization Imaginary s-wave pairing mass Class C Spin QHE
19 Class CI: Disorder and interactions Hamiltonian CFT: Relevant! (Multifractal enhancement) Irrelevant Irrelevant Order parameters break time-reversal: Spin polarization Imaginary s-wave pairing mass Class C Spin QHE
20 Class CI: Disorder and interactions Foster, Yuzbashyan 12 Due to disorder, interactions are always relevant; flow to strong coupling Expect time-reversal breaks spontaneously. Interactions plus disorder can sabotage surface topological protection.
21 Class AIII (Spin U(1) symmetry): Disorder and interactions Hamiltonian Interaction channels: Cooper pairing of surface quasiparticles (time-reversal invariance) z-spin exchange (z-spin is conserved = hydrodynamic mode) z-spin current-current Order parameters break time-reversal: Spin polarization Imaginary s-wave pairing mass Class C Spin QHE
22 Class AIII: Disorder and interactions Hamiltonian CFT: Window of stability:
23 Class AIII: WZW-FNLsM (many valleys) Parameters Dimensionless inverse spin conductance Spin current disorder strength Cooper pairing of surface quasiparticles (time-reversal invariance) Spin exchange (spin is conserved = hydrodynamic mode) Foster, Ludwig 06, 08 Dell Anna 06 Xie, Chou, Foster (unpublished)
24 Class AIII: WZW-FNLsM (many valleys) Parameters Dimensionless inverse spin conductance Spin current disorder strength Cooper pairing of surface quasiparticles (time-reversal invariance) Spin exchange (spin is conserved = hydrodynamic mode) For (universal fixed point value) Landauer spin conductance is universal without interactions. True even with interactions? Yes, to one-loop. Higher loops? Tsvelik 95 Ostrovsky, Gornyi, Mirlin 06 Topological transport invariant? Xie, Chou, Foster In preparation
25 Class AIII: WZW-FNLsM (many valleys) CFT: Window of Stability Simplified interaction plane flow (λ = 1/k): Retain only BCS non-linearity (Anderson s theorem) Qualitatively the same as full WZW-FNLsM results for λ > 1/k 2 In both cases: New interaction-stabilized fixed point Foster, Xie, Chou In preparation
26 Class AIII: Disorder and interactions Foster, Xie, Chou In preparation CFT: For weak disorder, interactions irrelevant. Stable surface. CFT: Stronger disorder, interactions relevant. WZW-FNLsM: critical interacting fixed point. Stable surface is possible. Weakly-coupled (perturbatively accessible) for finite window of disorder
27 Class DIII (No spin symmetry): Disorder and interactions Hamiltonian Foster, Xie, Chou In preparation Interaction channel: Cooper pairing of surface quasiparticles (time-reversal invariance) CFT: Always Irrelevant! No multifractal enhancement Knowing behavior of average density of states is not enough! Class CI: Class DIII:
28 Background: Surface states of 3D bulk topological superconductors: Gapless Dirac ( Majorana ) quasiparticle surface bands With disorder: Quenched 2+1-D QCD (random non-abelian vector potentials) Idea: Test the limits of Topological protection : Disorder & interactions Disorder induces multifractal wavefunction fluctuations (critical delocalization) Results and conclusions: Review 1) Disorder-amplified interactions can sabotage topological protection (Class CI), inducing surface quantum Hall order (Class C). 2) Stable gapless surface states: AIII, DIII. Interacting fixed point for AIII. 3) Suppression of Altshuler-Aronov to surface spin, thermal conductance when TR unbroken (AIII, DIII). Transport topological invariant? Foster and Yuzbashyan 12 Foster, Xie, Chou, Xie, Chou, Foster In preparation
29
30
31 Numerical tests: Critical DOS, multifractal scaling Minimal case: 2 valley Dirac (Classes CI and AIII) CFT predictions: Global density of states Multifractal spectrum Numerical scheme: Momentum-space disordered Dirac fermion (avoids fermion doubling) Bardarson, Tworzydlo, Brouwer, Beenakker 07 Nomura, Koshino, Ryu 07 Y. Z. Chou, Foster arxiv:
32 Numerical tests: Critical DOS, multifractal scaling Minimal case: 2 valley Dirac (Classes CI and AIII) CFT predictions: Global density of states Multifractal spectrum Numerical scheme: Momentum-space disordered Dirac fermion (avoids fermion doubling) Bardarson, Tworzydlo, Brouwer, Beenakker 07 Nomura, Koshino, Ryu 07 Y. Z. Chou, Foster arxiv:
33 Numerical tests: Critical DOS, multifractal scaling Numerics suggests delocalization and conformal invariance are both topologically protected Non-trivial statement for classes AIII, DIII: Runaway to Gade regime? Guruswamy, LeClair, Ludwig 00 Runaway to diffusive metal? Senthil and Fisher 00 Assume no interactions. Why should we pin λ = 1/k? Universal Dirac Landauer conductance unchanged by disorder. Interpret λ as inverse (spin) conductance (as in localization theory) Tsvelik 95; Ostrovsky, Gornyi, Mirlin 06
Electron transport and quantum criticality in disordered graphene. Alexander D. Mirlin
Electron transport and quantum criticality in disordered graphene Alexander D. Mirlin Research Center Karslruhe & University Karlsruhe & PNPI St. Petersburg P. Ostrovsky, Research Center Karlsruhe & Landau
Symmetric Surfaces of Topological Superconductor
Symmetric Surfaces of Topological Superconductor Sharmistha Sahoo Zhao Zhang Jeffrey Teo Outline Introduction Brief description of time reversal symmetric topological superconductor. Coupled wire model
Quantum transport of 2D Dirac fermions: the case for a topological metal
Quantum transport of 2D Dirac fermions: the case for a topological metal Christopher Mudry 1 Shinsei Ryu 2 Akira Furusaki 3 Hideaki Obuse 3,4 1 Paul Scherrer Institut, Switzerland 2 University of California
disordered topological matter time line
disordered topological matter time line disordered topological matter time line 80s quantum Hall SSH quantum Hall effect (class A) quantum Hall effect (class A) 1998 Nobel prize press release quantum Hall
Cenke Xu. Quantum Phase Transitions between Bosonic Symmetry Protected Topological States without sign problem 许岑珂
Quantum Phase Transitions between Bosonic Symmetry Protected Topological States without sign problem Cenke Xu 许岑珂 University of California, Santa Barbara Quantum Phase Transitions between bosonic Symmetry
Universal transport at the edge: Disorder, interactions, and topological protection
Universal transport at the edge: Disorder, interactions, and topological protection Matthew S. Foster, Rice University March 31 st, 2016 Universal transport coefficients at the edges of 2D topological
Field Theory Description of Topological States of Matter. Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti)
Field Theory Description of Topological States of Matter Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti) Topological States of Matter System with bulk gap but non-trivial at energies below
Quenched BCS superfluids: Topology and spectral probes
Quenched BCS superfluids: Topology and spectral probes Matthew S. Foster, Rice University May 6 th, 2016 Quenched BCS superfluids: Topology and spectral probes M. S. Foster 1, Maxim Dzero 2, Victor Gurarie
Reducing and increasing dimensionality of topological insulators
Reducing and increasing dimensionality of topological insulators Anton Akhmerov with Bernard van Heck, Cosma Fulga, Fabian Hassler, and Jonathan Edge PRB 85, 165409 (2012), PRB 89, 155424 (2014). ESI,
Classification 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
Quantum interference meets topology: Quantum Hall effect, topological insulators, and graphene. Alexander D. Mirlin
Quantum interference meets topology: Quantum Hall effect, topological insulators, and graphene Alexander D. Mirlin Karlsruhe Institute of Technology & PNPI St. Petersburg P. Ostrovsky, Karlsruhe Institute
Anderson localization, topology, and interaction
Anderson localization, topology, and interaction Pavel Ostrovsky in collaboration with I. V. Gornyi, E. J. König, A. D. Mirlin, and I. V. Protopopov PRL 105, 036803 (2010), PRB 85, 195130 (2012) Cambridge,
Topological 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
Topological Insulators in 3D and Bosonization
Topological Insulators in 3D and Bosonization Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter: bulk and edge Fermions and bosons on the (1+1)-dimensional
Field Theory Description of Topological States of Matter
Field Theory Description of Topological States of Matter Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter Quantum Hall effect: bulk and edge Effective field
Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition
Termination of typical wavefunction multifractal spectra at the Anderson metal-insulator transition Matthew S. Foster, 1,2 Shinsei Ryu, 3 Andreas W. W. Ludwig 4 1 Rutgers, the State University of New Jersey
Crystalline 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)
SPIN-LIQUIDS ON THE KAGOME LATTICE: CHIRAL TOPOLOGICAL, AND GAPLESS NON-FERMI-LIQUID PHASE
SPIN-LIQUIDS ON THE KAGOME LATTICE: CHIRAL TOPOLOGICAL, AND GAPLESS NON-FERMI-LIQUID PHASE ANDREAS W.W. LUDWIG (UC-Santa Barbara) work done in collaboration with: Bela Bauer (Microsoft Station-Q, Santa
Classification of Symmetry Protected Topological Phases in Interacting Systems
Classification of Symmetry Protected Topological Phases in Interacting Systems Zhengcheng Gu (PI) Collaborators: Prof. Xiao-Gang ang Wen (PI/ PI/MIT) Prof. M. Levin (U. of Chicago) Dr. Xie Chen(UC Berkeley)
A Short Introduction to Topological Superconductors
A Short Introduction to Topological Superconductors --- A Glimpse of Topological Phases of Matter Jyong-Hao Chen Condensed Matter Theory, PSI & Institute for Theoretical Physics, ETHZ Dec. 09, 2015 @ Superconductivity
Topological 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
can be moved in energy/momentum but not individually destroyed; in general: topological Fermi surfaces
nodes protected against gapping can be moved in energy/momentum but not individually destroyed; in general: topological Fermi surfaces physical realization: stacked 2d topological insulators C=1 3d top
Modern Topics in Solid-State Theory: Topological insulators and superconductors
Modern Topics in Solid-State Theory: Topological insulators and superconductors Andreas P. Schnyder Max-Planck-Institut für Festkörperforschung, Stuttgart Universität Stuttgart January 2016 Lecture Four:
Interpolating between Wishart and inverse-wishart distributions
Interpolating between Wishart and inverse-wishart distributions Topological phase transitions in 1D multichannel disordered wires with a chiral symmetry Christophe Texier December 11, 2015 with Aurélien
Workshop on Localization Phenomena in Novel Phases of Condensed Matter May 2010
2144-9 Workshop on Localization Phenomena in Novel Phases of Condensed Matter 17-22 May 2010 Topological Insulators: Disorder, Interaction and Quantum Criticality of Dirac Fermions Alexander D. MIRLIN
Topological quantum criticality of Dirac fermions: From graphene to topological insulators. Alexander D. Mirlin
Topological quantum criticality of Dirac fermions: From graphene to topological insulators Alexander D. Mirlin Karlsruhe Institute of Technology & PNPI St. Petersburg P. Ostrovsky, Karlsruhe Institute
Topological 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
Integer 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.
Dirac-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
Topological 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
Single 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
Exotic Phenomena in Topological Insulators and Superconductors
SPICE Workshop on Spin Dynamics in the Dirac System Schloss Waldthausen, Mainz, 6 June 2017 Exotic Phenomena in Topological Insulators and Superconductors Yoichi Ando Physics Institute II, University of
Universal 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)
Symmetries in Quantum Transport : From Random Matrix Theory to Topological Insulators. Philippe Jacquod. U of Arizona
Symmetries in Quantum Transport : From Random Matrix Theory to Topological Insulators Philippe Jacquod U of Arizona UA Phys colloquium - feb 1, 2013 Continuous symmetries and conservation laws Noether
Multichannel Majorana Wires
Multichannel Majorana Wires Piet Brouwer Frascati, 2014 Dahlem Center for Complex Quantum Systems Physics Department Inanc Adagideli Freie Universität Berlin Mathias Duckheim Dganit Meidan Graham Kells
Topological Defects in the Topological Insulator
Topological Defects in the Topological Insulator Ashvin Vishwanath UC Berkeley arxiv:0810.5121 YING RAN Frank YI ZHANG Quantum Hall States Exotic Band Topology Topological band Insulators (quantum spin
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
Quantum dots and Majorana Fermions Karsten Flensberg
Quantum dots and Majorana Fermions Karsten Flensberg Center for Quantum Devices University of Copenhagen Collaborator: Martin Leijnse and R. Egger M. Kjærgaard K. Wölms Outline: - Introduction to Majorana
Disordered 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
arxiv: v1 [cond-mat.mes-hall] 13 May 2009
![arxiv: v1 [cond-mat.mes-hall] 13 May 2009](/thumbs/80/82315570.jpg "arxiv: v1 [cond-mat.mes-hall] 13 May 2009")
Classification of Topological Insulators and Superconductors arxiv:0905.2029v1 [cond-mat.mes-hall] 13 May 2009 Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig Kavli Institute
Surface 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
Vortex 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
5 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
Symmetry Protected Topological Phases of Matter
Symmetry Protected Topological Phases of Matter T. Senthil (MIT) Review: T. Senthil, Annual Reviews of Condensed Matter Physics, 2015 Topological insulators 1.0 Free electron band theory: distinct insulating
ONLINE SUPPORTING INFORMATION: Interaction-induced criticality in Z 2 topological insulators
ONLINE SUPPORTING INFORMATION: Interaction-induced criticality in Z 2 topological insulators P. M. Ostrovsky, 1,2 I. V. Gornyi, 1,3 1, 4, 5 and A. D. Mirlin 1 Institut für Nanotechnologie, Karlsruhe Institute
Time 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
Quantum 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
Conference on Superconductor-Insulator Transitions May 2009
2035-10 Conference on Superconductor-Insulator Transitions 18-23 May 2009 Phase transitions in strongly disordered magnets and superconductors on Bethe lattice L. Ioffe Rutgers, the State University of
Matrix product states for the fractional quantum Hall effect
Matrix product states for the fractional quantum Hall effect Roger Mong (California Institute of Technology) University of Virginia Feb 24, 2014 Collaborators Michael Zaletel UC Berkeley (Stanford/Station
Electron transport in disordered graphene. Alexander D. Mirlin
Electron transport in disordered graphene Alexander D. Mirlin Research Center Karslruhe & University Karlsruhe & PNPI St. Petersburg P. Ostrovsky, Research Center Karlsruhe & Landau Inst., Chernogolovka
From Luttinger Liquid to Non-Abelian Quantum Hall States
From Luttinger Liquid to Non-Abelian Quantum Hall States Jeffrey Teo and C.L. Kane KITP workshop, Nov 11 arxiv:1111.2617v1 Outline Introduction to FQHE Bulk-edge correspondence Abelian Quantum Hall States
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
Topological delocalization of two-dimensional massless fermions
- CMP Meets HEP at IPMU Kashiwa /10/010 - Topoloical delocalization of two-dimensional massless fermions Kentaro Nomura (Tohoku University) collaborators Shinsei Ryu (Berkeley) Mikito Koshino (Titech)
(Effective) Field Theory and Emergence in Condensed Matter
(Effective) Field Theory and Emergence in Condensed Matter T. Senthil (MIT) Effective field theory in condensed matter physics Microscopic models (e.g, Hubbard/t-J, lattice spin Hamiltonians, etc) `Low
Topology driven quantum phase transitions
Topology driven quantum phase transitions Dresden July 2009 Simon Trebst Microsoft Station Q UC Santa Barbara Charlotte Gils Alexei Kitaev Andreas Ludwig Matthias Troyer Zhenghan Wang Topological quantum
Effective 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
Studying Topological Insulators. Roni Ilan UC Berkeley
Studying Topological Insulators via time reversal symmetry breaking and proximity effect Roni Ilan UC Berkeley Joel Moore, Jens Bardarson, Jerome Cayssol, Heung-Sun Sim Topological phases Insulating phases
Chiral spin liquids. Bela Bauer
Chiral spin liquids Bela Bauer Based on work with: Lukasz Cinco & Guifre Vidal (Perimeter Institute) Andreas Ludwig & Brendan Keller (UCSB) Simon Trebst (U Cologne) Michele Dolfi (ETH Zurich) Nature Communications
Non-Abelian Anyons in the Quantum Hall Effect
Non-Abelian Anyons in the Quantum Hall Effect Andrea Cappelli (INFN and Physics Dept., Florence) with L. Georgiev (Sofia), G. Zemba (Buenos Aires), G. Viola (Florence) Outline Incompressible Hall fluids:
Detecting and using Majorana fermions in superconductors
Detecting and using Majorana fermions in superconductors Anton Akhmerov with Carlo Beenakker, Jan Dahlhaus, Fabian Hassler, and Michael Wimmer New J. Phys. 13, 053016 (2011) and arxiv:1105.0315 Superconductor
Topological 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
Majorana Fermions in Superconducting Chains
16 th December 2015 Majorana Fermions in Superconducting Chains Matilda Peruzzo Fermions (I) Quantum many-body theory: Fermions Bosons Fermions (II) Properties Pauli exclusion principle Fermions (II)
Valence Bonds in Random Quantum Magnets
Valence Bonds in Random Quantum Magnets theory and application to YbMgGaO 4 Yukawa Institute, Kyoto, November 2017 Itamar Kimchi I.K., Adam Nahum, T. Senthil, arxiv:1710.06860 Valence Bonds in Random Quantum
Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea
Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets In collaboration with: Olexei Motrunich & Jason Alicea I. Background Outline Avoiding conventional symmetry-breaking in s=1/2 AF Topological
team 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
Weyl semimetals from chiral anomaly to fractional chiral metal
Weyl semimetals from chiral anomaly to fractional chiral metal Jens Hjörleifur Bárðarson Max Planck Institute for the Physics of Complex Systems, Dresden KTH Royal Institute of Technology, Stockholm J.
arxiv:cond-mat/ v1 [cond-mat.supr-con] 4 Dec 2001
![arxiv:cond-mat/ v1 [cond-mat.supr-con] 4 Dec 2001](/thumbs/94/120833242.jpg "arxiv:cond-mat/ v1 [cond-mat.supr-con] 4 Dec 2001")
Interaction effects on quasiparticle localization in dirty superconductors arxiv:cond-mat/0112044v1 [cond-mat.supr-con] 4 Dec 2001 M. Jeng 1, A. W. W. Ludwig 1, T. Senthil 2, C. Chamon 3 1 Dept. of Physics,
Topological Kondo Insulators!
Topological Kondo Insulators! Maxim Dzero, University of Maryland Collaborators: Kai Sun, University of Maryland Victor Galitski, University of Maryland Piers Coleman, Rutgers University Main idea Kondo
The Dirac composite fermions in fractional quantum Hall effect. Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016
The Dirac composite fermions in fractional quantum Hall effect Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016 A story of a symmetry lost and recovered Dam Thanh Son (University
2015 Summer School on Emergent Phenomena in Quantum Materials. Program Overview
Emergent Phenomena in Quantum Materials Program Overview Each talk to be 45min with 15min Q&A. Monday 8/3 8:00AM Registration & Breakfast 9:00-9:10 Welcoming Remarks 9:10-10:10 Eugene Demler Harvard University
Introduction 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,
Conformal Field Theory of Composite Fermions in the QHE
Conformal Field Theory of Composite Fermions in the QHE Andrea Cappelli (INFN and Physics Dept., Florence) Outline Introduction: wave functions, edge excitations and CFT CFT for Jain wfs: Hansson et al.
Ashvin Vishwanath UC Berkeley
TOPOLOGY + LOCALIZATION: QUANTUM COHERENCE IN HOT MATTER Ashvin Vishwanath UC Berkeley arxiv:1307.4092 (to appear in Nature Comm.) Thanks to David Huse for inspiring discussions Yasaman Bahri (Berkeley)
Superconductivities of doped Weyl semimetals
UIUC, Feb 5 th (2013) Superconductivities of doped Weyl semimetals Phys. Rev. B. 86, 214514 (2012) - Editors suggestion Gil Young Cho UC Berkeley Jens H Bardarson Yuan-Ming Lu Joel E Moore Plan. Part 1
Composite Dirac liquids
Composite Dirac liquids Composite Fermi liquid non-interacting 3D TI surface Interactions Composite Dirac liquid ~ Jason Alicea, Caltech David Mross, Andrew Essin, & JA, Physical Review X 5, 011011 (2015)
Topological Phases in One Dimension
Topological Phases in One Dimension Lukasz Fidkowski and Alexei Kitaev arxiv:1008.4138 Topological phases in 2 dimensions: - Integer quantum Hall effect - quantized σ xy - robust chiral edge modes - Fractional
Which Spin Liquid Is It?
Which Spin Liquid Is It? Some results concerning the character and stability of various spin liquid phases, and Some speculations concerning candidate spin-liquid phases as the explanation of the peculiar
Topological nonsymmorphic crystalline superconductors
UIUC, 10/26/2015 Topological nonsymmorphic crystalline superconductors Chaoxing Liu Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA Chao-Xing Liu, Rui-Xing
KITP miniprogram, Dec. 11, 2008
1. Magnetoelectric polarizability in 3D insulators and experiments! 2. Topological insulators with interactions (3. Critical Majorana fermion chain at the QSH edge) KITP miniprogram, Dec. 11, 2008 Joel
Braid 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)
SPT: a window into highly entangled phases
SPT: a window into highly entangled phases T. Senthil (MIT) Collaborators: Chong Wang, A. Potter Why study SPT? 1. Because it may be there... Focus on electronic systems with realistic symmetries in d
Is the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son (University of Chicago) Cold atoms meet QFT, 2015 Ref.: 1502.03446 Plan Plan Composite fermion: quasiparticle of Fractional Quantum Hall Effect (FQHE)
Ψ({z i }) = i<j(z i z j ) m e P i z i 2 /4, q = ± e m.
Fractionalization of charge and statistics in graphene and related structures M. Franz University of British Columbia franz@physics.ubc.ca January 5, 2008 In collaboration with: C. Weeks, G. Rosenberg,
Classification of topological quantum matter with reflection symmetries
Classification of topological quantum matter with reflection symmetries Andreas P. Schnyder Max Planck Institute for Solid State Research, Stuttgart June 14th, 2016 SPICE Workshop on New Paradigms in Dirac-Weyl
From 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
Bosonic Symmetry Protected Topological States: Theory, Numerics, And Experimental Platform. Zhen Bi University of California, Santa Barbara
Bosonic Symmetry Protected Topological States: Theory, Numerics, And Experimental Platform Zhen Bi University of California, Santa Barbara Acknowledgements Collaborators from UCSB: Cenke Xu, Leon Balents,
Topological 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)
Fully 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)
Electronic transport in topological insulators
Electronic transport in topological insulators Reinhold Egger Institut für Theoretische Physik, Düsseldorf Alex Zazunov, Alfredo Levy Yeyati Trieste, November 011 To the memory of my dear friend Please
Topological Field Theory and Conformal Quantum Critical Points
Topological Field Theory and Conformal Quantum Critical Points One might expect that the quasiparticles over a Fermi sea have quantum numbers (charge, spin) of an electron. This is not always true! Charge
Loop 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
Wiring Topological Phases
1 Wiring Topological Phases Quantum Condensed Matter Journal Club Adhip Agarwala Department of Physics Indian Institute of Science adhip@physics.iisc.ernet.in February 4, 2016 So you are interested in
Two-dimensional heavy fermions in Kondo topological insulators
Two-dimensional heavy fermions in Kondo topological insulators Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University Rice University, August 28, 2014 Acknowledgments
arxiv: v1 [math-ph] 31 Jan 2016
![arxiv: v1 [math-ph] 31 Jan 2016](/thumbs/78/78601167.jpg "arxiv: v1 [math-ph] 31 Jan 2016")
February 2, 2016 1:43 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in ProdanICMP2015 page 1 1 Topological Insulators at Strong Disorder Emil Prodan Physics Department, Yeshiva University, New York,
Defects in topologically ordered states. Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014
Defects in topologically ordered states Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014 References Maissam Barkeshli & XLQ, PRX, 2, 031013 (2012) Maissam Barkeshli, Chaoming Jian, XLQ,
Spin liquids on ladders and in 2d
Spin liquids on ladders and in 2d MPA Fisher (with O. Motrunich) Minnesota, FTPI, 5/3/08 Interest: Quantum Spin liquid phases of 2d Mott insulators Background: Three classes of 2d Spin liquids a) Topological
Quantum transport in disordered systems: Part III. Alexander D. Mirlin
Quantum transport in disordered systems: Part III Alexander D. Mirlin Research Center Karslruhe & University Karlsruhe & PNPI St. Petersburg http://www-tkm.physik.uni-karlsruhe.de/ mirlin/ Evers, ADM Anderson
Properties of monopole operators in 3d gauge theories
Properties of monopole operators in 3d gauge theories Silviu S. Pufu Princeton University Based on: arxiv:1303.6125 arxiv:1309.1160 (with Ethan Dyer and Mark Mezei) work in progress with Ethan Dyer, Mark
Three Applications of Topology to Physics
Three Applications of Topology to Physics Dan Freed University of Texas at Austin January 12, 2018 Problem 1: Invertible Phases of Matter Fix discrete parameters for quantum system: dimension, symmetry
Topological 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.