Experimental reconstruction of the Berry curvature in a topological Bloch band
|
|
- Austen Pitts
- 5 years ago
- Views:
Transcription
1 Experimental reconstruction of the Berry curvature in a topological Bloch band Christof Weitenberg Workshop Geometry and Quantum Dynamics Natal arxiv: (2015)
2 Topological Insulators Topology of the bulk leads to chiral edge states Experimental access is mostly limited to the edge states Solid State Model systems Quantum Hall effect, Von Klitzing, PRL (1980). Helical waveguides Rechtsman, Nature 496, 196 (2013). Silicon photonics Hafezi,Nat. Photon. 7, 1001 (2013). Unidirectional backscattering in Polariton system Wang, Nature 461, 772 (2009). Topological RF circuit Ningyuan, PRX 5, (2015). Mechanical topological insulator Süsstrunk, Science 349, 47 (2015).
3 Wavefunction microscope To see the bulk topology, we need a wavefunction microscope! Experiments with cold atoms might provide new insight Our wavefunction microscope See also work with superconducting qubits Roushan, Nature (2014)
4 Topological bands are a hot topic in cold atom research! Theory Experiments/Lattice Engineering of topological bands: Jaksch, Zoller, New J. Phys. 5, 56 (2003). Kitagawa et al. PRB 82, (2010). Dalibard et al. Rev. Mod. Phys. 83, 1523 (2011). Cooper, PRL 106, (2011). Rudner et al. PRX 3, (2013). Goldman, Dalibard, PRX 4, (2014). Baur et al. PRA 89, (R) (2014). Bukov et al. Adv. Phys. 64, 139 (2015). Detection of topology: Alba et al. PRL 107, (2011). Price, Cooper, PRA 85, (2012). Goldman et al. PRL 108, (2012). Dauphin, Goldman, PRL 110, (2013). Wang et al. PRL 110, (2013). Goldman et al. PNAS 110, 6736 (2013). Price, Cooper, PRL 111, (2013). Hauke et al. PRL 113, (2014). Non-Abelian Gauge fields: Osterloh et al. PRL 95, (2005). Nayak et al. Rev. Mod. Phys. 80, 1083 (2008). Goldman et al. PRL 103, (2009). Hauke et al. PRL 109, (2012). Topology and Interactions: Raghu et al. PRL 100, (2008). Rachel, Le Hur, PRB 82, (2010). Neupert et al. PRL 106, (2011). Cooper, Dalibard, PRL 110, (2013). Bergholtz et al. Intern. J. Mod. Phys. B 27, (2013). Grushin et al. PRL 112, (2014). Soltan-Panahi et al., Nat. Phys (2011). Soltan-Panahi et al., Nat. Phys (2012). Jo et al., PRL 108, (2012). Struck et al. PRL 108, (2012). Cheuk et al. PRL 109, (2012). Struck et al. Nature Phys. 9, 738 (2013). Parker et al. Nature Phys. 9, 769 (2013). Atala et al. Nature Phys. 9, 795 (2013). Aidelsburger et al. PRL 111, (2013). Miyake et al. PRL 111, (2013). Jotzu et al. Nature 515, 237 (2014). Atala et al. Nature Phys. 10, 588 (2014). Aidelsburger et al. Nature Phys. 11, 162 (2015). Kennedy et al. Nature Phys. (2015). Stuhl et al., Science (2015). Mancini et al., Science (2015). Jotzu et al. PRL 115, (2015). Duca et al. Science 347, 288 (2015). Li et al. arxiv: (2015). Taie et al. arxiv: (2015). Nakajima et al. arxiv: (2015). Lohse et al. arxiv: (2015). Lu et al. arxiv: (2015).
5 Experiments with topological bands (I) Hofstadter model Haldane model Cyclotron orbits in Hofstadter Model Aidelsburger, PRL (2013) Bloch group Chern number of Hofstadter bands Aidelsburger, Nature Phys. (2015) Bloch group Condensation in Hofstadter Model Kennedy, Nature Phys. (2015) Ketterle group Chern number in Haldane Model Jotzu, Nature (2014) Esslinger group Chiral edge states Chiral edge states Stuhl, Science (2015) Spielman group Chiral edge states Mancini, Science (2015) Inguscio group Meissner effect Atala, Nature Phys. (2014) Bloch group
6 Experiments with topological bands (II) Magnetism via lattice driving 1D Gauge potentials Ising XY spin-models Struck, Nature Phys. (2013) Sengstock group Ferromagnetic domains Parker, Nature Phys. (2013) Chin group 1D Gauge potential Struck, PRL (2012) Sengstock group Spin-dependent driving Jotzu, PRL (2015) Esslinger group Spin-orbit coupled lattice Zak and Berry phase Spin-orbit coupled lattice Cheuk, PRL (2012) Zwierlein group Zak phase Atala, Nature Phys. (2013) Bloch group Aharonov-Bohm interferometer Duca, Science (2015) Bloch group Wilson lines Li, arxiv (2015) Bloch group
7 ,Berry-ology * But how are all the different properties related to one-another? Berry connection: NOT gauge invariant Berry curvature: Berry phase Chern Number Would be nice to see this Berry curvature * Fuchs et al., EPJB 77, 351 (2010)
8 Calculated Berry Curvature for different systems Boron nitride (tight-binding model) Fuchs et al., Euro Phys. J B 77, 351 (2010) Ferromagnetic bcc Fe Yao et al., Phys. Rev. Lett. 92, (2004) Strained graphene Guinea et al., Nature Phys. 6, 30 (2009) Monolayer MoS 2 Feng et al., Phys. Rev. B 86, (2012)
9 Map of the full Berry curvature Fläschner et al., arxiv: (2015) related work: Li et al. arxiv: (2015)
10 How do we do it? Tunable hexagonal lattice for fermionic 40 K See: Soltan-Panahi et al.,nat.phys 7, 434 (2011) Baur et al., PRA 89, (R) (2014). Offset between A and B Boron-nitride Massive Dirac points A B Well separated flat s-bands Tomography Berry curvature flattens out
11 Floquet engineering of dressed bands Quasi-energy Circular shaking Breaks time-reversal symmetry k-dependent coupling Berry curvature engineering Dirac point at K annihilated Dirac point at Γ created Three-fold symmetry
12 Eigenstates in Bloch sphere representation Two-band Hamiltonian allows for a Bloch sphere representation States of flat bands lie at the north- and south-pole For each k, the ground state is given by: k is given by:
13 Eigenstate reconstruction We follow the proposal by P. Hauke, M. Lewenstein, A.Eckardt, PRL 113, (2014): Related proposal Alba et al., PRL 107, (2011)
14
15 Reconstruction of full Hamiltonian The oscillations become visible in k-space after time-of-flight Momentum space density Fitting the oscillations gives and for each momentum (pixel)
16 Berry curvature Now we can reconstruct the Berry curvature using:
17 Amplitude + Phase = Berry curvature N. Fläschner, B. Rem, M. Tarnowski, D. Vogel, D. Lühmann, K. Sengstock., C. Weitenberg, arxiv: (2015)
18 Engineering of Berry Curvature Berry curvature (1/ b ²) Increasing amplitude 200 nm 100 nm
19 Conclusion Full state tomography Full measurement of Berry curvature Allows us to determine Chern number Engineering of Berry curvature Annihilation and creation of Dirac points Localization
20 Outlook What next? A B We want to further explore topological bands Study interacting Fermions, Bosons, or mixtures in these bands How can we prepare a Floquet topological Insulator? What can we learn from quenches into the nontrivial regime? We still have the spin degree of freedom: study high-spin systems or engineer additional spin-orbit-coupling Explore other interesting geometries using the tunable lattice
21 The BFM-team Barcelona Dresden Hamburg In collaboration with Ludwig Mathey Klaus Sengstock Christof Weitenberg Benno Rem Dirk-Sören Lühmann Matthias Tarnowski Nick Fläschner Dominik Vogel André Eckardt Maciej Lewenstein
Experimental 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 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 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 informationSpontaneous Loop Currents and Emergent Gauge Fields in Optical Lattices
IASTU Condensed Matter Seminar July, 2015 Spontaneous Loop Currents and Emergent Gauge Fields in Optical Lattices Xiaopeng Li ( 李晓鹏 ) CMTC/JQI University of Maryland [Figure from JQI website] Gauge fields
More informationMagnetic fields and lattice systems
Magnetic fields and lattice systems Harper-Hofstadter Hamiltonian Landau gauge A = (0, B x, 0) (homogeneous B-field). Transition amplitude along x gains y-dependence: J x J x e i a2 B e y = J x e i Φy
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 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 informationLaboratoire Kastler Brossel Collège de France, ENS, UPMC, CNRS. Artificial gauge potentials for neutral atoms
Laboratoire Kastler Brossel Collège de France, ENS, UPMC, CNRS Artificial gauge potentials for neutral atoms Fabrice Gerbier Workshop Hadrons and Nuclear Physics meet ultracold atoms, IHP, Paris January
More informationTakuya 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 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 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 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 informationEngineering Synthetic Gauge Fields, Weyl Semimetals, and Anyons
Engineering Synthetic Gauge Fields, Weyl Semimetals, and Anyons Φ q Φ q Φ q T. Dubček 1, M. Todorić 1, B. Klajn 1, C. J. Kennedy 2, L. Lu 2, R. Pezer 5, D. Radić 1, D. Jukić 4, W. Ketterle 2, M. Soljačić
More informationSynthetic topology and manybody physics in synthetic lattices
Synthetic topology and manybody physics in synthetic lattices Alessio Celi EU STREP EQuaM May 16th, 2017 Atomtronics - Benasque Plan Integer Quantum Hall systems and Edge states Cold atom realizations:
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 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 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 informationteam Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber
title 1 team 2 Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber motivation: topological states of matter 3 fermions non-interacting, filled band (single particle physics) topological
More informationQuantum simulation with SU(N) fermions: orbital magnetism and synthetic dimensions. Leonardo Fallani
Quantum simulation with SU(N) fermions: orbital magnetism and synthetic dimensions Frontiers in Quantum Simulation with Cold Atoms, Seattle, April 1 st 2015 Leonardo Fallani Department of Physics and Astronomy
More informationPhases of strongly-interacting bosons on a two-leg ladder
Phases of strongly-interacting bosons on a two-leg ladder Marie Piraud Arnold Sommerfeld Center for Theoretical Physics, LMU, Munich April 20, 2015 M. Piraud Phases of strongly-interacting bosons on a
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 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 informationExploring topological states with cold atoms and photons
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
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 informationSynthetic Creutz-Hubbard model: interacting topological insulators with ultracold atoms
interacting topological insulators Matteo Rizzi Johannes Gutenberg Universität Mainz J. Jünemann, et al., -- accepted on PRX ICTP Trieste, 14 September 2017 Motivation Topological phases of matter: academic
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 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 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 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 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 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 informationarxiv: v1 [cond-mat.quant-gas] 5 Dec 2018
Measuring the topological phase transition via the single-particle density matrix arxiv:1812.01991v1 [cond-mat.quant-gas] 5 Dec 2018 Jun-Hui Zheng, 1 Bernhard Irsigler, 1 Lijia Jiang, 2 Christof Weitenberg,
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 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 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 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 Bandstructures for Ultracold Atoms
Topological Bandstructures for Ultracold Atoms Nigel Cooper Cavendish Laboratory, University of Cambridge New quantum states of matter in and out of equilibrium GGI, Florence, 12 April 2012 NRC, PRL 106,
More informationCurriculum Vitae Dr. Christof Weitenberg
Curriculum Vitae Dr. Christof Weitenberg Name: Christof Weitenberg Email: cweitenb@physnet.uni-hamburg.de Research Interests Ultracold quantum gases, Optical lattices, Quantum many-body systems, Quantum
More informationarxiv: v2 [cond-mat.quant-gas] 14 Jul 2014
Simulation of non-abelian lattice gauge fields with a single component gas arxiv:1403.1221v2 [cond-mat.quant-gas] 14 Jul 2014 Arkadiusz Kosior 1 and Krzysztof Sacha 1, 2 1 Instytut Fizyki imienia Mariana
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 informationInterplay of micromotion and interactions
Interplay of micromotion and interactions in fractional Floquet Chern insulators Egidijus Anisimovas and André Eckardt Vilnius University and Max-Planck Institut Dresden Quantum Technologies VI Warsaw
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 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 informationMatrix 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
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 informationEngineering and Probing Topological Bloch Bands in Optical Lattices
Engineering and Probing Topological Bloch Bands in Optical Lattices Monika Aidelsburger, Marcos Atala, Michael Lohse, Christian Schweizer, Julio Barreiro Christian Gross, Stefan Kuhr, Manuel Endres, Marc
More informationShuichi Murakami Department of Physics, Tokyo Institute of Technology
EQPCM, ISSP, U. Tokyo June, 2013 Berry curvature and topological phases for magnons Shuichi Murakami Department of Physics, Tokyo Institute of Technology Collaborators: R. Shindou (Tokyo Tech. Peking Univ.)
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 informationArtificial magnetism and optical flux lattices for ultra cold atoms
Artificial magnetism and optical flux lattices for ultra cold atoms Gediminas Juzeliūnas Institute of Theoretical Physics and Astronomy,Vilnius University, Vilnius, Lithuania Kraków, QTC, 31 August 2011
More informationQuantum simulation of an extra dimension
Quantum simulation of an extra dimension Alessio Celi based on PRL 108, 133001 (2012), with O. Boada, J.I. Latorre, M. Lewenstein, Quantum Technologies Conference III QTC III, Warzsawa, 14/09/2012 p. 1/14
More informationTopological 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
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 informationProtection of the surface states of a topological insulator: Berry phase perspective
Protection of the surface states of a topological insulator: Berry phase perspective Ken-Ichiro Imura Hiroshima University collaborators: Yositake Takane Tomi Ohtsuki Koji Kobayashi Igor Herbut Takahiro
More informationTutorial: Berry phase and Berry curvature in solids
Tutorial: Berry phase and Berry curvature in solids Justin Song Division of Physics, Nanyang Technological University (Singapore) & Institute of High Performance Computing (Singapore) Funding: (Singapore)
More informationKonstantin Y. Bliokh, Daria Smirnova, Franco Nori. Center for Emergent Matter Science, RIKEN, Japan. Science 348, 1448 (2015)
Konstantin Y. Bliokh, Daria Smirnova, Franco Nori Center for Emergent Matter Science, RIKEN, Japan Science 348, 1448 (2015) QSHE and topological insulators The quantum spin Hall effect means the presence
More informationKouki Nakata. University of Basel. KN, S. K. Kim (UCLA), J. Klinovaja, D. Loss (2017) arxiv:
Magnon Transport Both in Ferromagnetic and Antiferromagnetic Insulating Magnets Kouki Nakata University of Basel KN, S. K. Kim (UCLA), J. Klinovaja, D. Loss (2017) arxiv:1707.07427 See also review article
More informationWeyl fermions and the Anomalous Hall Effect
Weyl fermions and the Anomalous Hall Effect Anton Burkov CAP congress, Montreal, May 29, 2013 Outline Introduction: Weyl fermions in condensed matter, Weyl semimetals. Anomalous Hall Effect in ferromagnets
More informationSynthetic gauge fields in Bose-Einstein Condensates 1. Alexander Fetter Stanford University. University of Hannover, May 2015
Synthetic gauge fields in Bose-Einstein Condensates 1 Alexander Fetter Stanford University University of Hannover, May 2015 1. Two-component trapped spin-orbit coupled Bose-Einstein condensate (BEC) 2.
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 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 informationSimulation of Quantum Many-Body Systems
Numerical Quantum Simulation of Matteo Rizzi - KOMET 337 - JGU Mainz Vorstellung der Arbeitsgruppen WS 14-15 QMBS: An interdisciplinary topic entanglement structure of relevant states anyons for q-memory
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 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 informationMesoscopic physics: From low-energy nuclear [1] to relativistic [2] high-energy analogies
Mesoscopic physics: From low-energy nuclear [1] to relativistic [2] high-energy analogies Constantine Yannouleas and Uzi Landman School of Physics, Georgia Institute of Technology [1] Ch. 4 in Metal Clusters,
More informationTOPOLOGICAL SUPERFLUIDS IN OPTICAL LATTICES
TOPOLOGICAL SUPERFLUIDS IN OPTICAL LATTICES Pietro Massignan Quantum Optics Theory Institute of Photonic Sciences Barcelona QuaGATUA (Lewenstein) 1 in collaboration with Maciej Lewenstein Anna Kubasiak
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 informationPart 1. March 5, 2014 Quantum Hadron Physics Laboratory, RIKEN, Wako, Japan 2
MAR 5, 2014 Part 1 March 5, 2014 Quantum Hadron Physics Laboratory, RIKEN, Wako, Japan 2 ! Examples of relativistic matter Electrons, protons, quarks inside compact stars (white dwarfs, neutron, hybrid
More informationIs 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)
More informationCorrelated Phases of Bosons in the Flat Lowest Band of the Dice Lattice
Correlated Phases of Bosons in the Flat Lowest Band of the Dice Lattice Gunnar Möller & Nigel R Cooper Cavendish Laboratory, University of Cambridge Physical Review Letters 108, 043506 (2012) LPTHE / LPTMC
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 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 informationTopological insulators. Pavel Buividovich (Regensburg)
Topological insulators Pavel Buividovich (Regensburg) Hall effect Classical treatment Dissipative motion for point-like particles (Drude theory) Steady motion Classical Hall effect Cyclotron frequency
More informationTopological 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 informationOptical Flux Lattices for Cold Atom Gases
for Cold Atom Gases Nigel Cooper Cavendish Laboratory, University of Cambridge Artificial Magnetism for Cold Atom Gases Collège de France, 11 June 2014 Jean Dalibard (Collège de France) Roderich Moessner
More informationPhilipp T. Ernst, Sören Götze, Jannes Heinze, Jasper Krauser, Christoph Becker & Klaus Sengstock. Project within FerMix collaboration
Analysis ofbose Bose-Fermi Mixturesin in Optical Lattices Philipp T. Ernst, Sören Götze, Jannes Heinze, Jasper Krauser, Christoph Becker & Klaus Sengstock Project within FerMix collaboration Motivation
More informationSupplementary Figure 3: Interaction effects in the proposed state preparation with Bloch oscillations. The numerical results are obtained by
Supplementary Figure : Bandstructure of the spin-dependent hexagonal lattice. The lattice depth used here is V 0 = E rec, E rec the single photon recoil energy. In a and b, we choose the spin dependence
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 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 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 information3.14. The model of Haldane on a honeycomb lattice
4 Phys60.n..7. Marginal case: 4 t Dirac points at k=(,). Not an insulator. No topological index...8. case IV: 4 t All the four special points has z 0. We just use u I for the whole BZ. No singularity.
More informationMagnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases
Magnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases Leonardo Mazza Scuola Normale Superiore, Pisa Seattle March 24, 2015 Leonardo Mazza (SNS) Exotic Phases in Alkaline-Earth Fermi
More informationInteraction-induced Symmetry Protected Topological Phase in Harper-Hofstadter models
Interaction-induced Symmetry Protected Topological Phase in Harper-Hofstadter models arxiv:1609.03760 Lode Pollet Dario Hügel Hugo Strand, Philipp Werner (Uni Fribourg) Algorithmic developments diagrammatic
More informationClassification 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)
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 informationInti Sodemann (MIT) Séptima Escuela de Física Matemática, Universidad de Los Andes, Bogotá, Mayo 25, 2015
Inti Sodemann (MIT) Séptima Escuela de Física Matemática, Universidad de Los Andes, Bogotá, Mayo 25, 2015 Contents Why are the fractional quantum Hall liquids amazing! Abelian quantum Hall liquids: Laughlin
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 informationAditi Mitra New York University
Superconductivity following a quantum quench Aditi Mitra New York University Supported by DOE-BES and NSF- DMR 1 Initially system of free electrons. Quench involves turning on attractive pairing interactions.
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 informationWeyl 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.
More informationDesign and realization of exotic quantum phases in atomic gases
Design and realization of exotic quantum phases in atomic gases H.P. Büchler and P. Zoller Theoretische Physik, Universität Innsbruck, Austria Institut für Quantenoptik und Quanteninformation der Österreichischen
More informationCooperative Phenomena
Cooperative Phenomena Frankfurt am Main Kaiserslautern Mainz B1, B2, B4, B6, B13N A7, A9, A12 A10, B5, B8 Materials Design - Synthesis & Modelling A3, A8, B1, B2, B4, B6, B9, B11, B13N A5, A7, A9, A12,
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 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 informationTopology 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
More informationlattice that you cannot do with graphene! or... Antonio H. Castro Neto
Theoretical Aspects What you can do with cold atomsof on agraphene honeycomb lattice that you cannot do with graphene! or... Antonio H. Castro Neto 2 Outline 1. Graphene for beginners 2. Fermion-Fermion
More informationIdentifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data Benno S. Rem 1,2, Niklas Käming 1, Matthias Tarnowski 1,2, Luca Asteria 1, Nick Fläschner 1, Christoph Becker
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 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 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 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 information