Multichannel Majorana Wires
|
|
- Ilene Tyler
- 5 years ago
- Views:
Transcription
1 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 Felix von Oppen Maria-Theresa Rieder Alessandro Romito
2 Excitations in normal metals Sommerfeld model: Electrons can be described as free fermions ε Eigenvalue equation for single-particle energies: ε F =0 Fermi energy Hψ = εψ Ground state: Single-particle states with energy ε < ε F are occupied. wikimedia.org Arnold Sommerfeld
3 Excitations in normal metals Sommerfeld model: Electrons can be described as free fermions ε Eigenvalue equation for single-particle energies: ε F = 0 Hψ = εψ Ground state: Single-particle states with energy ε < ε F are occupied. electron-like excitation hole-like excitation wikimedia.org Arnold Sommerfeld
4 Excitations in normal metals Excitation spectrum: Same as excitations of free fermions ε Eigenvalue equation? ε F = 0 electron-like excitations hole-like excitations Lev Landau
5 Excitations in normal metals Excitation spectrum: Same as excitations of free fermions ε Eigenvalue equation? ε F = 0 electron-like excitations hole-like excitations Electron-like and hole-like excitations both have positive excitation energy
6 Excitations in normal metals Excitation spectrum: Same as excitations of free fermions ε Eigenvalue equation? ε F = 0 Combined spectrum of electron-like and hole-like excitations
7 Excitations in normal metals Excitation spectrum: Same as excitations of free fermions ε Eigenvalue equation? ε F = 0 H 0 0 H electron * u v u = ε v hole Combined spectrum of electron-like and hole-like excitations
8 Excitations in normal metals Excitation spectrum: Same as excitations of free fermions Eigenvalue equation? ε particle-hole conjugation u v* ε F = 0 H 0 0 H electron * u v u = ε v hole Combined spectrum of electron-like and hole-like excitations particle-hole symmetry: eigenvalue spectrum is +/- symmetric one fermionic excitation one pair of eigenvalues ±ε
9 Excitations in superconductors Cooper-pair Superconductor Superconductor = (Macroscopic) superconductors with different numbers of Cooper pairs cannot be distinguished. Leon Cooper Brian Josephson
10 Excitations in superconductors In superconductors one cannot distinguish between electron-like and hole-like excitations Superconductor = Superconductor
11 Excitations in superconductors Excitation spectrum Eigenvalue equation: H Δ u u = ε Δ* H * v v ε F = 0 u: electron v: hole superconducting order parameter Bogoliubov-de Gennes equation particle-hole symmetry: eigenvalue spectrum is +/- symmetric one fermionic excitation two solutions of BdG equation ε particle-hole conjugation u v*
12 Topological superconductors Excitation spectrum Eigenvalue equation: H Δ u u = ε Δ* H * v v ε F = 0 Spectra with and without single level at ε = 0 are topologically distinct. particle-hole symmetry: eigenvalue spectrum is +/- symmetric one fermionic excitation two solutions of BdG equation ε ε particle-hole conjugation u v*
13 Topological superconductors Excitation spectrum Eigenvalue equation: H Δ* Δ H * u v u = ε v ε ε particle-hole conjugation u v* Spectra with and without single level at ε = 0 are topologically distinct. Excitation at ε = 0 is particle-hole symmetric: Majorana state one fermionic excitation two solutions of BdG equation
14 Topological superconductors Excitation spectrum Eigenvalue equation: H Δ* Δ H * u v u = ε v ε ε particle-hole conjugation u v* Spectra with and without single level at ε = 0 are topologically distinct. Excitation at ε = 0 is particle-hole symmetric: Majorana state Excitation at ε = 0 corresponds to ½ fermion: non-abelian statistics
15 Topological superconductors In nature, there are only whole fermions. Majorana states always come in pairs. ε ε particle-hole conjugation u v* In a topological superconductor pairs of Majorana states are spatially well separated. Excitation at ε = 0 is particle-hole symmetric: Majorana state Excitation at ε = 0 corresponds to ½ fermion: non-abelian statistics
16 Overview Spinless superconductors as a habitat for Majorana fermions Disordered multichannel spinless superconducting wires ε -ε
17 Particle-hole symmetric excitation Can one have a particle-hole symmetric excitation in a spinfull superconductor? Superconductor Superconductor =
18 Particle-hole symmetric excitation Can one have a particle-hole symmetric excitation in a spinfull superconductor? Superconductor Superconductor =
19 Particle-hole symmetric excitations Existence of a single particle-hole symmetric excitation: One needs a spinless (or spinpolarized) superconductor. Superconductor Superconductor
20 Particle-hole symmetric excitations Existence of a single particle-hole symmetric excitation: One needs a spinless (or spinpolarized) superconductor. H Δ* Δ H * u v u = ε v Δ is an antisymmetric operator. Without spin: Δ must be an odd function of momentum. p-wave:
21 Spinless p-wave superconductors superconducting order parameter has the form one-dimensional spinless p-wave superconductor spinless p-wave superconductor bulk excitation gap: Δ = Δ p F Majorana fermion end states Kitaev (2001) N p -p r he r eh Δ(p)e iφ(p) S Andreev reflection at NS interface: scattering amplitudes and Andreev (1964) *
22 Spinless p-wave superconductors superconducting order parameter has the form one-dimensional spinless p-wave superconductor spinless p-wave superconductor bulk excitation gap: Δ = Δ p F Majorana fermion end states Kitaev (2001) e iη e -iη N p -p r he r eh Δ(p)e iφ(p) S Bohr-Sommerfeld: Majorana state (i.e., bound state at ε = 0) if Always satisfied if r he =1.
23 Spinless p-wave superconductors superconducting order parameter has the form one-dimensional spinless p-wave superconductor spinless p-wave superconductor bulk excitation gap: Δ = Δ p F Majorana fermion end states Kitaev (2001) e h S ξ = hv F /Δ Argument does not depend on length of normal-metal stub
24 Proposed physical realizations fractional quantum Hall effect at ν=5/2 Moore, Read (1991) unconventional superconductor Sr 2 RuO 4 Das Sarma, Nayak, Tewari (2006) Fermionic atoms near Feshbach resonance Proximity structures with s-wave superconductors, and topological insulators semiconductor quantum well Gurarie, Radzihovsky, Andreev (2005) Cheng and Yip (2005) Fu and Kane (2008) Sau, Lutchyn, Tewari, Das Sarma (2009) Alicea (2010) Lutchyn, Sau, Das Sarma (2010) Oreg, von Oppen, Refael (2010) ferromagnet metal surface states Duckheim, Brouwer (2011) Chung, Zhang, Qi, Zhang (2011) Choy, Edge, Akhmerov, Beenakker (2011) Martin, Morpurgo (2011) Kjaergaard, Woelms, Flensberg (2011) Weng, Xu, Zhang, Zhang, Dai, Fang (2011) Potter, Lee (2010) (and more)
25 Disordered spinless superconductor spinless p-wave superconductor x=0 without disorder: x Majorana end states ε 0 µ = F 2 pf 2m p = k = F mv F
26 Brouwer, Duckheim, Romito, Von Oppen (2011) Disordered spinless superconductor spinless p-wave superconductor x=0 without disorder: with disorder:? x Motrunich, Damle, Huse (2001) Gruzberg, Read, Vishveshwara(2005) µ = F 2 pf 2m p = k = F mv F
27 Disordered spinless superconductor Disordered normal metal spinless p-wave superconductor x=0 without disorder: with disorder:? x Transfer matrix: has eigenvalues
28 Disordered spinless superconductor Disordered normal metal spinless p-wave superconductor x=0 without disorder: with disorder: x Transfer matrix: has eigenvalues topological phase persists for
29 Disordered spinless superconductor spinless p-wave superconductor x=0 without disorder: with disorder: x topological phase persists for
30 Rieder, Brouwer, Adagideli (2013) Multichannel wire with disorder? p+ip? W x=0 x bulk gap: coherence length
31 Multichannel wire with disorder? p+ip? W x=0 x Series of N topological phase transitions at n=1,2,,n 0 disorder strength
32 Multichannel spinless p-wave wire? p+ip? W L induced superconductivity is weak: and Without Δ p y : effective time-reversal symmetry, τ 3 Hτ 3 = H* Combine with particle-hole symmetry: chiral symmetry, H anticommutes with τ 2 Tewari, Sau (2012)
33 Periodic Multichannel table of spinless topological p-wave insulators wire? p+ip? IQHE W induced superconductivity is weak: Without Δ p y : effective time-reversal symmetry, τ 3 Hτ 3 = H* Combine with particle-hole symmetry: chiral symmetry, L bulk gap: coherence length 3DTI and QSHE Θ: Time-reversal symmetry Ξ: Particle-hole symmetry Π = ΘΞ: Chiral symmetry H anticommutes with τ 2 Schnyder, Ryu, Furusaki, Ludwig (2008) Tewari, Kitaev Sau (2012) (2009)
34 Periodic Multichannel table of spinless topological p-wave insulators wire? p+ip? IQHE W induced superconductivity is weak: L bulk gap: coherence length 3DTI and QSHE Without Δ p y : effective time-reversal symmetry, τ 3 Hτ 3 = H* Combine with particle-hole symmetry: chiral symmetry, Θ: Time-reversal symmetry Ξ: Particle-hole symmetry Π = ΘΞ: Chiral symmetry H anticommutes with τ 2 Schnyder, Ryu, Furusaki, Ludwig (2008) Tewari, Kitaev Sau (2012) (2009)
35 Multichannel wire with disorder? p+ip? W x=0 x Without Δ y and without disorder: N Majorana end states ψ sin( nπy W ) x / ξ e n=1 n=2 n=3
36 Multichannel wire with disorder Disordered normal metal with N channels? p+ip? W x=0 x Without For N channels, Δ y and without wavefunctions disorder: ψn n increase Majorana exponentially end states at N different rates ψ sin( nπy W ) x / ξ e n=1 n=2 n=3
37 Multichannel wire with disorder Disordered normal metal with N channels? p+ip? W x=0 x Without For N channels, Δ y but with wavefunctions disorder: ψ n increase exponentially at N different rates
38 Multichannel wire with disorder? p+ip? W x=0 x Without Δ y but with disorder: n = N, N-1, N-2,,1 0 N N-1 N-2 N-3 number of Majorana end states disorder strength
39 Series of topological phase transitions? p+ip? W x=0 x # Majorana end states ξ/(n+1)l disorder strength
40 Series of topological phase transitions? p+ip? W x=0 x With Δ y and with disorder: = Topological phase transitions at n = N, N-1, N-2,,1 Δ y /Δ x = 0 disorder strength (N+1)l /ξ disorder strength
41 Series of topological phase transitions? p+ip? W x=0 x With Δ y and with disorder: = Topological phase transitions at n = N, N-1, N-2,,1 Δ y /Δ x = 0 disorder strength (N+1)l /ξ disorder strength
42 Summary One-dimensional superconducting wires come in two topologically distinct classes: with or without a Majorana state at each end. Multiple Majoranas may coexist in the presence of an effective timereversal symmetry. Majorana states may persist in the presence of disorder and with multiple channels. For multichannel p-wave superconductors there is a sequence of disorder-induced topological phase transitions. The last phase transition takes place at l=ξ/(n+1). 0 disorder strength
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
More informationarxiv: v2 [cond-mat.mes-hall] 12 Feb 2013
Reentrant topological phase transitions in a disordered spinless superconducting wire Maria-Theresa Rieder, Piet W. Brouwer Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie niversität
More informationMajorana single-charge transistor. Reinhold Egger Institut für Theoretische Physik
Majorana single-charge transistor Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport through Majorana nanowires: Two-terminal device: Majorana singlecharge
More informationQuantum 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
More informationTopological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires
Topological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires Sumanta Tewari 1, T. D. Stanescu 2, Jay D. Sau 3, and S. Das Sarma 4 1 Department of Physics and Astronomy,
More informationManipulation of Majorana fermions via single charge control
Manipulation of Majorana fermions via single charge control Karsten Flensberg Niels Bohr Institute University of Copenhagen Superconducting hybrids: from conventional to exotic, Villard de Lans, France,
More informationTopological 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
More informationarxiv: v2 [cond-mat.mes-hall] 29 Oct 2013
Topological invariant for generic 1D time reversal symmetric superconductors in class DIII Jan Carl Budich, Eddy Ardonne Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden Dated:
More informationarxiv: v1 [cond-mat.mes-hall] 5 Jan 2015
Equivalence of topological mirror and chiral superconductivity in one dimension Eugene Dumitrescu 1, Girish Sharma 1, Jay D. Sau 2, and Sumanta Tewari 1 1 Department of Physics and Astronomy, Clemson University,
More informationdisordered 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
More informationMajorana 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)
More informationLecture notes on topological insulators
Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan Dated: May 8, 07 I. D p-wave SUPERCONDUCTOR Here we study p-wave SC in D
More informationarxiv: v3 [cond-mat.mes-hall] 17 Feb 2014
Andreev reflection from a topological superconductor with chiral symmetry M. Diez, J. P. Dahlhaus, M. Wimmer, and C. W. J. Beenakker Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden,
More informationTransport through interacting Majorana devices. Reinhold Egger Institut für Theoretische Physik
Transport through interacting Maorana devices Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport through Maorana nanowires: Two-terminal device: Maorana
More informationMajoranas in semiconductor nanowires Leo Kouwenhoven
Majoranas in semiconductor nanowires Leo Kouwenhoven Önder Gül, Hao Zhang, Michiel de Moor, Fokko de Vries, Jasper van Veen David van Woerkom, Kun Zuo, Vincent Mourik, Srijit Goswami, Maja Cassidy, AHla
More informationTopological Kondo effect in Majorana devices. Reinhold Egger Institut für Theoretische Physik
Topological Kondo effect in Maorana devices Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport in a Maorana device: Topological Kondo effect with stable
More informationMajorana Fermions and Topological Quantum Information Processing. Liang Jiang Yale University & IIIS. QIP 2013, Beijing
Majorana Fermions and Topological Quantum Information Processing Liang Jiang Yale University & IIIS QIP 2013, Beijing 2013.1.21 Conventional Quantum Systems Local degrees of freedom E.g., spins, photons,
More informationA 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
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 informationInterpolating 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
More informationDetecting 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
More informationReducing 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,
More informationBell-like non-locality from Majorana end-states
Bell-like non-locality from Majorana end-states Alessandro Romito with Yuval Gefen (WIS) 07.09.2016, Daejeon, Workshop on Anderson Localiation in Topological Insulators Outline Topological superconductors
More informationarxiv: v1 [cond-mat.mes-hall] 16 Feb 2013
Proposal for Manipulation of Majorana Fermions in Nano-Patterned Semiconductor-Superconductor Heterostructure arxiv:1302.3947v1 [cond-mat.mes-hall] 16 Feb 2013 Abstract Long-Hua Wu,, Qi-Feng Liang, Zhi
More informationExotic 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
More informationQuantum Transport through a Triple Quantum Dot System in the Presence of Majorana Bound States
Commun. Theor. Phys. 65 (016) 6 68 Vol. 65, No. 5, May 1, 016 Quantum Transport through a Triple Quantum Dot System in the Presence of Majorana Bound States Zhao-Tan Jiang ( ), Zhi-Yuan Cao ( ì ), and
More informationMagneto-Josephson effects and Majorana bound states in quantum wires
Home Search Collections Journals About Contact us My IOPscience Magneto-Josephson effects and Majorana bound states in quantum wires This content has been downloaded from IOPscience. Please scroll down
More informationNovel topologies in superconducting junctions
Novel topologies in superconducting junctions Yuli V. Nazarov Delft University of Technology The Capri Spring School on Transport in Nanostructures 2018, Anacapri IT, April 15-22 2018 Overview of 3 lectures
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 informationSymmetries 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
More informationField 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
More informationSymmetric 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
More informationTopological protection, disorder, and interactions: Life and death at the surface of a topological superconductor
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),
More informationTOPOLOGY IN CONDENSED MATTER SYSTEMS: MAJORANA MODES AND WEYL SEMIMETALS. Jan 23, 2012, University of Illinois, Urbana-Chamapaign
TOPOLOGY IN CONDENSED MATTER SYSTEMS: MAJORANA MODES AND WEYL SEMIMETALS Pavan Hosur UC Berkeley Jan 23, 2012, University of Illinois, Urbana-Chamapaign Acknowledgements Advisor: Ashvin Vishwanath UC Berkeley
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 informationMajorana-type quasiparticles in nanoscopic systems
Kraków, 20 IV 2015 Majorana-type quasiparticles in nanoscopic systems Tadeusz Domański / UMCS, Lublin / Kraków, 20 IV 2015 Majorana-type quasiparticles in nanoscopic systems Tadeusz Domański / UMCS, Lublin
More informationSingle particle Green s functions and interacting topological insulators
1 Single particle Green s functions and interacting topological insulators Victor Gurarie Nordita, Jan 2011 Topological insulators are free fermion systems characterized by topological invariants. 2 In
More informationMAJORANAFERMIONS IN CONDENSED MATTER PHYSICS
MAJORANAFERMIONS IN CONDENSED MATTER PHYSICS A. J. Leggett University of Illinois at Urbana Champaign based in part on joint work with Yiruo Lin Memorial meeting for Nobel Laureate Professor Abdus Salam
More informationarxiv: v2 [cond-mat.mes-hall] 12 Apr 2012
Search for Majorana fermions in superconductors C. W. J. Beenakker Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands (Dated: April 2012) arxiv:1112.1950v2 [cond-mat.mes-hall]
More informationMajorana modes in topological superconductors
Majorana modes in topological superconductors Roman Lutchyn Microsoft Station Q Introduction to topological quantum computing Physical realizations of Majorana modes in topological superconductors Experimental
More informationarxiv: v2 [quant-ph] 24 Aug 2018
Maximal distant entanglement in Kitaev tube P. Wang 1, S. Lin 1, G. Zhang 1,2, and Z. Song 1,* arxiv:1709.05086v2 [quant-ph] 24 Aug 2018 1 School of Physics, ankai University, Tianjin 300071, China 2 College
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 informationarxiv: v2 [cond-mat.supr-con] 3 Aug 2013
Time-Reversal-Invariant Topological Superconductivity and Majorana Kramers Pairs Fan Zhang, C. L. Kane, and E. J. Mele Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA
More informationMultichannel Kondo dynamics and Surface Code from Majorana bound states
Multichannel Kondo dynamics and Surface Code from Maorana bound states Reinhold Egger Institut für Theoretische Physik Dresden workshop 14-18 Sept. 2015 Overview Brief introduction to Maorana bound states
More informationarxiv: v1 [cond-mat.supr-con] 17 Dec 2009
Odd-Parity Topological Superconductors: Theory and Application to Cu x Bi Se 3 Liang Fu and Erez Berg Department of Physics, Harvard University, Cambridge, MA 0138 arxiv:091.394v1 [cond-mat.supr-con] 17
More informationarxiv: v2 [cond-mat.supr-con] 18 Dec 2012
Majorana Kramers Doublets in dx2 y2 -wave Superconductors with Rashba Spin-Orbit Coupling Chris L. M. Wong, K. T. Law arxiv:1211.0338v2 [cond-mat.supr-con] 18 Dec 2012 Department of Physics, Hong Kong
More informationComposite 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)
More informationFrom single magnetic adatoms to coupled chains on a superconductor
From single magnetic adatoms to coupled chains on a superconductor Michael Ruby, Benjamin Heinrich, Yang Peng, Falko Pientka, Felix von Oppen, Katharina Franke Magnetic adatoms on a superconductor Sample
More informationChiral Majorana edge state in a quantum anomalous Hall insulatorsuperconductor
Chiral Majorana edge state in a quantum anomalous Hall insulatorsuperconductor structure Qing Lin He 1 *, Lei Pan 1, Alexander L. Stern 2, Edward Burks 3, Xiaoyu Che 1, Gen Yin 1, Jing Wang 4,5, Biao Lian
More informationarxiv: v2 [cond-mat.mes-hall] 16 Nov 2012
TOPICAL REVIEW arxiv:1206.1736v2 [cond-mat.mes-hall] 16 Nov 2012 Introduction to topological superconductivity and Majorana fermions 1. Introduction Martin Leijnse and Karsten Flensberg Center for Quantum
More informationTopological invariants for 1-dimensional superconductors
Topological invariants for 1-dimensional superconductors Eddy Ardonne Jan Budich 1306.4459 1308.soon SPORE 13 2013-07-31 Intro: Transverse field Ising model H TFI = L 1 i=0 hσ z i + σ x i σ x i+1 σ s:
More informationField 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
More informationStudying 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
More informationarxiv: v1 [cond-mat.mes-hall] 25 Nov 2011
Coulomb-assisted braiding of Majorana fermions in a Josephson junction array arxiv:.6v [cond-mat.mes-hall] 25 Nov 2 B. van Heck, A. R. Akhmerov, F. Hassler, 2 M. Burrello, and C. W. J. Beenakker Instituut-Lorentz,
More informationMajorana bound states in spatially inhomogeneous nanowires
Master Thesis Majorana bound states in spatially inhomogeneous nanowires Author: Johan Ekström Supervisor: Assoc. Prof. Martin Leijnse Division of Solid State Physics Faculty of Engineering November 2016
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 informationMassive Dirac Fermion on the Surface of a magnetically doped Topological Insulator
SLAC-PUB-14357 Massive Dirac Fermion on the Surface of a magnetically doped Topological Insulator Y. L. Chen 1,2,3, J.-H. Chu 1,2, J. G. Analytis 1,2, Z. K. Liu 1,2, K. Igarashi 4, H.-H. Kuo 1,2, X. L.
More informationSplitting of a Cooper pair by a pair of Majorana bound states
Chapter 7 Splitting of a Cooper pair by a pair of Majorana bound states 7.1 Introduction Majorana bound states are coherent superpositions of electron and hole excitations of zero energy, trapped in the
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 informationarxiv: v2 [cond-mat.supr-con] 13 Aug 2010
Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures Roman M. Lutchyn, Jay D. Sau, and S. Das Sarma Joint Quantum Institute and Condensed Matter Theory
More informationQuenched 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
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 informationarxiv: v1 [cond-mat.supr-con] 15 Dec 2011
Topological Protection of Majorana Qubits arxiv:1112.3662v1 [cond-mat.supr-con] 15 Dec 2011 Meng Cheng, 1, 2, 3 Roman M. Lutchyn, 1 and S. Das Sarma 2 1 Station Q, Microsoft Research, Santa Barbara, CA
More informationarxiv: v1 [cond-mat.mes-hall] 29 Apr 2018
Noise signatures for determining chiral Majorana fermion modes arxiv:184.1872v1 [cond-mat.mes-hall] 29 Apr 218 Yu-Hang Li, 1 Jie Liu, 2 Haiwen Liu, 3 Hua Jiang, 4, Qing-Feng Sun, 1,5,6 and X. C. Xie 1,5,6,
More informationTopological 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
More informationSuperconductivity at nanoscale
Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and
More informationTopological superconducting phase and Majorana bound states in Shiba chains
Home Search Collections Journals About Contact us My IOPscience Topological superconducting phase and Maorana bound states in Shiba chains This content has been downloaded from IOPscience. Please scroll
More informationModern 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:
More informationTopological Superconductivity and Superfluidity
Topological Superconductivity and Superfluidity SLAC-PUB-13926 Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang Department of Physics, McCullough Building, Stanford University, Stanford,
More informationMajorana fermions in a tunable semiconductor device
Selected for a Viewpoint in Physics Majorana fermions in a tunable semiconductor device Jason Alicea Department of Physics, California Institute of Technology, Pasadena, California 91125, USA Received
More informationarxiv: v3 [cond-mat.mes-hall] 3 Apr 2015
Random-matrix theory of Majorana fermions and topological superconductors C. W. J. Beenakker Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands (Dated: February 2015)
More informationJoel Röntynen and Teemu Ojanen Tuning topological superconductivity in helical Shiba chains by supercurrent
Powered by TCPDF (www.tcpdf.org) This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Joel Röntynen and
More informationTopological insulator (TI)
Topological insulator (TI) Haldane model: QHE without Landau level Quantized spin Hall effect: 2D topological insulators: Kane-Mele model for graphene HgTe quantum well InAs/GaSb quantum well 3D topological
More informationWiring 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
More informationarxiv: v2 [cond-mat.mes-hall] 13 Jan 2014
Signatures of tunable Majorana-fermion edge states arxiv:1401.1636v2 [cond-mat.mes-hall] 13 Jan 2014 Rakesh P. Tiwari 1, U. Zülicke 2 and C. Bruder 1 1 Department of Physics, University of Basel, Klingelbergstrasse
More informationQuantum disordering magnetic order in insulators, metals, and superconductors
Quantum disordering magnetic order in insulators, metals, and superconductors Perimeter Institute, Waterloo, May 29, 2010 Talk online: sachdev.physics.harvard.edu HARVARD Cenke Xu, Harvard arxiv:1004.5431
More informationQuantum Hall effect. Quantization of Hall resistance is incredibly precise: good to 1 part in I believe. WHY?? G xy = N e2 h.
Quantum Hall effect V1 V2 R L I I x = N e2 h V y V x =0 G xy = N e2 h n.b. h/e 2 = 25 kohms Quantization of Hall resistance is incredibly precise: good to 1 part in 10 10 I believe. WHY?? Robustness Why
More informationThe Quantum Anomalous Hall Majorana Platform
The Quantum Anomalous Hall Majorana Platform doped Bi Se 3 thin films in which proximitized superconductivity has already been demonstrated [5, 6] experimentally, and which are close to the MTI s QAH insulator/normal
More informationarxiv: v1 [cond-mat.str-el] 26 Feb 2014
Realiing Majorana Zero Modes by Proximity Effect between Topological Insulators and d-wave High-Temperature Superconductors Zi-Xiang Li, Cheung Chan, and Hong Yao Institute for Advanced Study, Tsinghua
More informationThe experimental realization of a quantum computer ranks
ARTICLES PUBLISHED ONLINE: 3 FEBRUARY 0 DOI: 0.038/NPHYS95 Non-Abelian statistics and topological quantum information processing in D wire networks Jason Alicea *, Yuval Oreg, Gil Refael 3, Felix von Oppen
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 informationTopological properties of superconducting chains
Bachelor's thesis Theoretical Physics Topological properties of superconducting chains Kim Pöyhönen 213 Advisor: Supervisor: Teemu Ojanen Tommy Ahlgren Helsinki University Department of Physics Postbox
More informationarxiv: v2 [quant-ph] 13 Mar 2018
arxiv:1712.6413v2 [quant-ph] 13 Mar 218 Distinguishing Majorana bound states and Andreev bound states with microwave spectra Zhen-Tao Zhang School of Physics Science and Information Technology, Shandong
More informationTopological Insulators and Superconductors. Tokyo 2010 Shoucheng Zhang, Stanford University
Topological Insulators and Superconductors Tokyo 2010 Shoucheng Zhang, Stanford University Colloborators Stanford group: Xiaoliang Qi, Andrei Bernevig, Congjun Wu, Chaoxing Liu, Taylor Hughes, Sri Raghu,
More informationTopological Insulators
Topological Insulators A new state of matter with three dimensional topological electronic order L. Andrew Wray Lawrence Berkeley National Lab Princeton University Surface States (Topological Order in
More 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 informationInAs/GaSb A New Quantum Spin Hall Insulator
InAs/GaSb A New Quantum Spin Hall Insulator Rui-Rui Du Rice University 1. Old Material for New Physics 2. Quantized Edge Modes 3. Andreev Reflection 4. Summary KITP Workshop on Topological Insulator/Superconductor
More informationUnconventional pairing in three-dimensional topological insulators with warped surface state Andrey Vasenko
Unconventional pairing in three-dimensional topological insulators with warped surface state Andrey Vasenko Moscow Institute of Electronics and Mathematics, Higher School of Economics Collaborators Alexander
More informationHarish-Chandra Spherical Functions, Topology & Mesoscopics
Harish-Chandra Spherical Functions, Topology & Mesoscopics Dmitry Bagrets A. Altland, DB,, A. Kamenev,, L. Fritz, H. Schmiedt,, PRL 11, 0660 A. Altland, DB,, A. Kamenev, arxiv: : 1411.599, to appear in
More informationTopological Quantum Computation with Majorana Zero Modes. Roman Lutchyn. Microsoft Station
Topological Quantum Computation with Majorana Zero Modes Roman Lutchyn Microsoft Station IPAM, 08/28/2018 Outline Majorana zero modes in proximitized nanowires Experimental and material science progress
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 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 informationAndreev transport in 2D topological insulators
Andreev transport in 2D topological insulators Jérôme Cayssol Bordeaux University Visiting researcher UC Berkeley (2010-2012) Villard de Lans Workshop 09/07/2011 1 General idea - Topological insulators
More informationCurrent noise in topological Josephson junctions
Current noise in topological Josephson junctions Julia S. Meyer with Driss Badiane, Leonid Glazman, and Manuel Houzet INT Seattle Workshop on Quantum Noise May 29, 2013 Motivation active search for Majorana
More informationIntroductory lecture on topological insulators. Reza Asgari
Introductory lecture on topological insulators Reza Asgari Workshop on graphene and topological insulators, IPM. 19-20 Oct. 2011 Outlines -Introduction New phases of materials, Insulators -Theory quantum
More informationarxiv: v1 [cond-mat.supr-con] 5 Sep 2015
Converting a topologically trivial superconductor into a topological superconductor via magnetic doping arxiv:59.666v [cond-mat.supr-con] 5 Sep 5 Wei Qin, Di Xiao, Kai Chang, 3 Shun-Qing Shen, 4 and Zhenyu
More informationInterferometric and noise signatures of Majorana fermion edge states in transport experiments
Interferometric and noise signatures of ajorana fermion edge states in transport experiments Grégory Strübi, Wolfgang Belzig, ahn-soo Choi, and C. Bruder Department of Physics, University of Basel, CH-056
More informationTopological Physics in Band Insulators. Gene Mele Department of Physics University of Pennsylvania
Topological Physics in Band Insulators Gene Mele Department of Physics University of Pennsylvania A Brief History of Topological Insulators What they are How they were discovered Why they are important
More informationDefects 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,
More informationTopological states of matter in correlated electron systems
Seminar @ Tsinghua, Dec.5/2012 Topological states of matter in correlated electron systems Qiang-Hua Wang National Lab of Solid State Microstructures, Nanjing University, Nanjing 210093, China Collaborators:Dunghai
More information