Lecture 2 2D Electrons in Excited Landau Levels
|
|
- Warren Bell
- 5 years ago
- Views:
Transcription
1 Lecture 2 2D Electrons in Excited Landau Levels
2 What is the Ground State of an Electron Gas? lower density Wigner
3 Two Dimensional Electrons at High Magnetic Fields E Landau levels N=2 N=1 N= Hartree-Fock prediction: Charge density waves throughout lowest Landau level Fukuyama, Platzman, and Anderson, 1979
4 Hartree-Fock Spectacularly Wrong! lowest Landau level Reality: Fractional Quantum Hall Liquids
5 Low Field Regime lowest Landau level E Landau levels N=2 N=1 N= Excited Landau levels
6 Even-Denominator FQHE in N=1 LL Longitudinal Resistance (Ohm) ν=5/2 2mK Magnetic Field (Tesla)
7 Higher Landau Levels Mobility ~ 1 7 cm 2 /Vs 3 N=2 Landau level 11/2 9/2 T=15mK 5/3 4/3 R xx (Ω) 2 1 5/2 ν= N=1 4 6 B (Tesla) N= 8 1 Structure in R xx in N 2 Landau levels correlations
8 Structure in High Landau Levels 1 R xx (Ω) 5 ν = 9/2 25 mk 5 mk 8 mk 1 mk ν=5 ν= B (Tesla) R xx at half filling increases dramatically below 1mK. Complex structure surrounds the peak. Peak width does not approach zero as T. Not consistent with the localization transition between IQHE states.
9 Anisotropy B <11> <11> T = 2 mk T = 1 mk T = 8 mk T = 25 mk 4 Resistance (Ohms) 2 ν = 9/ Magnetic Field (Tesla)
10 Rapid Onset Below 1mK Longitudinal Resistances (Ω) ν =9/2 <11> <11> 1 Temperature (mk) 2 Low temperature resistance anisotropy is consistently oriented relative to GaAs crystal axes.
11 Anisotropy Widespread in High Landau Levels 12 1 T=25mK ν = 9/2 B <11> R xx & R yy (Ohms) /2 11/2 ν=4 <11> ν = 4 is a boundary between different transport regimes. 2 7/2 5/2 1 2 Magnetic Field (Tesla) N = 2, 3,... N = & 1
12 More Unusual Features in High Landau levels 1 resistances (Ω) magnetic field (Tesla) 5 2 resistances (Ω) Isotropy in flanks of LL New FQHE states? magnetic field (Tesla)
13 Re-entrant Integer Hall Quantization
14 Re-entrant Integer Hall Quantization Integer QHE, localized electrons
15 Re-entrant Integer Hall Quantization no QHE, delocalized electrons
16 Re-entrant Integer Hall Quantization Integer QHE, re-localized electrons
17 Re-entrant Integer Hall Quantization Integer QHE, re-localized electrons RIQHE states must be collective insulators
18 Charge Density Waves in High Landau Levels Koulakov, Fogler, and Shklovskii; Moessner and Chalker 1996 N=5 LL Nodes in high LL wavefunctions soften short range Coulomb repulsion between electrons. Exchange energy favors phase separation.
19 Stripes to Bubbles to Wigner Crystal ν = 4+½ 4+ε
20 Numerical Simulation: N=1 Landau Level ν N = 1/2 stripes ν N = 1/4 bubbles ν N = 1/16 Wigner crystal Koulakov, Fogler, Shklovskii
21 State of the Art Samples N=3 N=2 Longitudinal resistance (Ω) / /2 11/2 2. 9/ /4 1/5 1/6 1/7 Hall resistance (h/e 2 ) Magnetic field (Tesla) A New Class of Collective Phases of 2D Electron Systems
22 Taking a Closer Look What Orients the Resistive Anisotropy? Are the Anisotropic States Nematic Liquid Crystals? Nature of Insulating Phases New Physics in the N=1 Landau Level
23 What Orients the Resistive Anisotropy?
24 Consistent Orientation of Anisotropy longitudinal resistances (Ω) Sample A Sample B B <11> <11> 2 Temperature (mk) 1 Independent of weak, high temperature anisotropies
25 What about Surface Morphology? Sample A <11> Surfaces are typically rough, Δz ~ 1 nm. 2DEG is buried. Sample B <11> Roughness is not isotropic. MBE growth kinetics is anisotropic, wafers can be miscut, etc. 2μm
26 What about Surface Morphology? Sample A <11> <11> Sample B 2μm
27 What about Surface Morphology? Sample A <11> <11> Longitudinal Resistances (Ohms) Magnetic Field (Telsa) Sample B 2μm Longitudinal Resistances (Ohms) QW Magnetic Field (Tesla) No systematic correlation.
28 Crystal Symmetry GaAs has a zinc-blende crystal structure. Ga As S 4 symmetry ensures that band structure ε(k) is 4-fold symmetric.
29 Symmetry of Confinement Potential? Kroemer, ν = 9/2 [11] + [11] AlGaAs GaAs 7/ ν = 9/2 [11] + + [11] AlGaAs GaAs AlGaAs /2 3.5 Does this eliminate all pinning mechanisms based upon lack of inversion symmetry in conventional heterointerfaces?
30 In-plane Magnetic Fields Can Switch Hard and Easy Transport Directions <11> B <11> B Longitudinal Resistance (Ohms) 1 5 ν = 9/2 <11> B = B =.5T B =1.7T <11> Perpendicular Magnetic Field (Tesla) High resistance direction along B
31 Same Effect in Many High Landau Levels 1 5 <11> <11> 9/2 B along <11> Longitudinal Resistance (Ohms) /2 13/ / B (Tesla)
32 Theory of In-Plane Magnetic Field Effect φ <11> <11> E = A cos(2 φ) native symmetry breaker
33 Theory of In-Plane Magnetic Field Effect B λ φ <11> <11> E = A cos(2 φ) + C cos(2 λ) native symmetry breaker field anisotropy energy
34 Theory of In-Plane Magnetic Field Effect Finite thickness of 2D electron layer allows B to distort circular cyclotron orbits: B Jungwirth, MacDonald and Girvin Stanescu and Phillips Shklovskii In agreement with experiment, theory predicts stripes prefer to be perpendicular to B. Estimated native anisotropy energy ~ 1mK/electron at B ~.5 T
35 Dramatic Sensitivity to Direction of B B along <11> B along <11> Longitudinal Resistance (Ohms) <11> <11> B (Tesla) B (Tesla) 11/2 15/2
36 It s not that simple... B along <11> B along <11> Longitudinal Resistance (Ohms) <11> <11> B (Tesla) B (Tesla) 9/2 13/2
37 Lower Density Sample ν = 9/2 12 R xx R yy R (Ω) (T) along [11] B B 2 4 (T) along [11] 6
38 Density-Dependent Interchange of Anisotropy Axes Low Density High Density hard axis <11> hard axis <11> Zhu, et al. 22
39 Piezoelectricity of GaAs <11> Rashba and Sherman 87 Fil <1> <11> [1] <11> <11> U PE θ [1] π/4 π/4
40 Piezoelectricity of GaAs <11> Rashba and Sherman 87 Fil <1> <11> [1] <11> <11> U PE But what lifts the degeneracy? θ [1] π/4 π/4
41 Metastability in Double Well Potential <11> <11> 8 Up up Sweep sweep 13/2 θ = 7 o 8 Down down sweep Sweep θ = 7 o 13/2 15 Field Cooled field cooled 13/2 θ = 7 o R (Ω) R (Ω) R (Ω) B (T) B (T) B (T) 2. <11> <11> <11> <11>
42 Very Slow Approaches to Equilibrium 8 down sweep 13/2 θ = 7 o 15 field cooled 13/2 θ = 7 o R (Ω) R (Ω) B (T) B (T) 2. 8 B = 1.9 T T = 5mK 6 R (Ω) Time (hours) 15
43 Are the Anisotropic States Nematic Liquid Crystals?
44 Liquid Crystal Phases of 2D Electrons Fradkin and Kivelson crystal smectic nematic isotropic
45 A Nematic to Isotropic Phase Transition? Longitudinal Resistances (Ω) ν=9/2 <11> <11> 1 Temperature (mk) 2 Hartree-Fock estimates of stripe formation temperature 2K. Wexler and Dorsey
46 Parallel Field Extends Anisotropy to Higher Temperatures ν=9/2 Resistances (Ω) B = B = 4.3T M Ferromagnet in an External Magnetic Field 2 B= B> T c T Temperature (K)
47 Comparison with classical 2DXY model U = J cos(2[θ i -θ j ]) - h cos(2θ i ) < i j> i ρ hard (kω/ ) 1..5 B = T h/j = M = <cos(2θ)>. 3 T (mk) T/J. 1 Similarity suggests that microscopic stripe moments exist at high temperatures.
48 Scaling B along <11> B along <11> R hard (kω) Temperature (mk) 3 6 Temperature (mk) R hard (kω) T/B (mk/t) 15 3 T/B (mk/t)
49 Nature of Insulating Phases
50 Non-linear I-V Characteristics in Re-Entrant IQHE 1 ν 4+1/4 R xx ( Ω ) 2 RIQHE ν = 9/2 RIQHE V yy (μv) 5 T = 25mK B (T) current (na) 6 Abrupt, hysteretic, and noisy transitions between insulating and conducting states.
51 CDW Depinning due to Hall Electric Field? E x I y V yy
52 Discontinuous I-V curves found only within the RIQHE 2.15 ν = 4 IQHE Magnetic Field (T) Magnetic Field (T) V yy yy RIQHE RIQHE R yy (Ohms) R yy (Ω) 5 μv I dc (na) I dc (μa)
53 And only at very low temperatures 65 mk 6 mk V yy 55 mk 45 mk 25 mk 2 μv I dc (na)
54 Narrow Band Noise in Insulating Phases R xx ( Ω) 2 RIQHE ν = 9/2 RIQHE B (T) I dc V dc B = 2.83 T V dc (μ V) V ac V ac 5μV..5 I dc 1. (μa) milliseconds 8 1
55 Spectral Analysis Noise in V ac 1 nv/(hz) 1/2.63μA.84μA.99μA 1 2 ƒ (khz) 3 4 V dc (mv).3 3 ƒ (khz) (μa) I dc
56 Noise confined to RIQHE Resistance (Ω) ν = 9/2 2.7 B (T) rms noise (μv) 8 rms noise (μv) T (mk) 15
57 Origin of Noise a Washboard noise? ƒ wb ~ J a / e ~ 1 MHz for 2nA/mm Frequencies generally increase with current, but ƒ exp ~ 1 khz Iceberg or droplet noise? Do low frequencies point to 1μm-size objects? Avalanche heating? Why restricted to RIQHE at mk temperatures? Circuit oscillations? Insensitive to external circuit. Local variations observed.
58 New Physics in the N=1 Landau Level
59 First Excited Landau Level Longitudinal Resistance (Ω) 1 5 CDW N > 1 N = 1 FQHE N = Magnetic Field (T) 5 6
60 Robust 5/2 States 8 T=2, 4, 1mK Longitudinal Resistance (Ohms) /2 7/ Magnetic Field (T) 5.
61 A Role for Spin? 1/3 state Ψ ~ i,.., n ( z z )... i j 3 Ψ ~ i,.., n ( z z )... i j 2 5/2 state?
62 A Role for Spin? 1/3 state Ψ ~ i,.., n ( z z )... i j 3 Ψ ~ i,.., n ( z z )... i j 2 5/2 state? but perhaps spins are not polarized... Haldane-Rezayi Hollow Core Model 1988
63 1988: Tilt Sample to Increase Zeeman Energy θ B TOT Tilting destroys 5/2 state? Ground state contains reversed spins.
64 Today s Theory 1/2 state: Composite Fermion Fermi Liquid - No QHE Jain Halperin-Lee-Read 5/2 state: BCS-like p-wave paired CF Liquid - QHE Moore-Read Rezayi-Haldane Both are spin polarized states.
65 1999: Revisit 5/2 State in Tilted Fields B = B =7.7T along <11> Resistance (Ω) <11> <11> B (Tesla) B (Tesla) 5. Tilting destroys 5/2 and 7/2 FQHE states and produces strongly anisotropic transport Rezayi and Haldane: Stripe state close in energy to paired FQHE state at B =.
66 Re-Entrant Integer Hall Quantization.35 5mK 15mK h/3e 2 Integer Hall quantization near ν 3 2/7, 3/7, 4/7, and 5/7 R xy (h/e 2 ).3 ν = 7/2 3+1/5 3+4/5 New Collective Insulators: Bubbles?.25 h/4e 2 Wigner Crystals? Magnetic Field (Tesla)
67 Similar near 5/2 Δ 5/2 ~ 3mK
68 5/2 State Quasiparticles May Be Non-Abelian
69 Conclusion A new class of collective phases of 2D electron systems in high LLs. Impressive overlap with HF theory of stripe and bubble phases. N=1 LL is borderline; has FQHE and stripes and bubbles.
New Physics in High Landau Levels
New Physics in High Landau Levels J.P. Eisenstein 1, M.P. Lilly 1, K.B. Cooper 1, L.N. Pfeiffer 2 and K.W. West 2 1 California Institute of Technology, Pasadena, CA 91125 2 Bell Laboratories, Lucent Technologies,
More informationBeyond the Quantum Hall Effect
Beyond the Quantum Hall Effect Jim Eisenstein California Institute of Technology School on Low Dimensional Nanoscopic Systems Harish-chandra Research Institute January February 2008 Outline of the Lectures
More informationNew Phases of Two-Dimensional Electrons in Excited Landau Levels
i New Phases of Two-Dimensional Electrons in Excited Landau Levels Thesis by Ken B. Cooper In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology
More informationCorrelated 2D Electron Aspects of the Quantum Hall Effect
Correlated 2D Electron Aspects of the Quantum Hall Effect Magnetic field spectrum of the correlated 2D electron system: Electron interactions lead to a range of manifestations 10? = 4? = 2 Resistance (arb.
More informationAnisotropic transport of unidirectional lateral superlattice around half filling of N 1 Landau levels
Anisotropic transport of unidirectional lateral superlattice around half filling of N 1 Landau levels A Endo and Y Iye Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba, -51 Japan
More informationZooming in on the Quantum Hall Effect
Zooming in on the Quantum Hall Effect Cristiane MORAIS SMITH Institute for Theoretical Physics, Utrecht University, The Netherlands Capri Spring School p.1/31 Experimental Motivation Historical Summary:
More informationEffects of Interactions in Suspended Graphene
Effects of Interactions in Suspended Graphene Ben Feldman, Andrei Levin, Amir Yacoby, Harvard University Broken and unbroken symmetries in the lowest LL: spin and valley symmetries. FQHE Discussions with
More informationQuantum numbers and collective phases of composite fermions
Quantum numbers and collective phases of composite fermions Quantum numbers Effective magnetic field Mass Magnetic moment Charge Statistics Fermi wave vector Vorticity (vortex charge) Effective magnetic
More informationThe Quantum Hall Effects
The Quantum Hall Effects Integer and Fractional Michael Adler July 1, 2010 1 / 20 Outline 1 Introduction Experiment Prerequisites 2 Integer Quantum Hall Effect Quantization of Conductance Edge States 3
More informationRecent results in microwave and rf spectroscopy of two-dimensional electron solids
J. Phys. IV France 131 (2005) 241 245 C EDP Sciences, Les Ulis DOI: 10.1051/jp4:2005131061 Recent results in microwave and rf spectroscopy of two-dimensional electron solids R.M. Lewis 1,2, Y.P. Chen 1,2,
More informationProbing Wigner Crystals in the 2DEG using Microwaves
Probing Wigner Crystals in the 2DEG using Microwaves G. Steele CMX Journal Club Talk 9 September 2003 Based on work from the groups of: L. W. Engel (NHMFL), D. C. Tsui (Princeton), and collaborators. CMX
More informationPINNING MODES OF THE STRIPE PHASES OF 2D ELECTRON SYSTEMS IN HIGHER LANDAU LEVELS
International Journal of Modern Physics B Vol. 23, Nos. 12 & 13 (2009) 2628 2633 c World Scientific Publishing Company PINNING MODES OF THE STRIPE PHASES OF 2D ELECTRON SYSTEMS IN HIGHER LANDAU LEVELS
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 informationObservation of neutral modes in the fractional quantum hall effect regime. Aveek Bid
Observation of neutral modes in the fractional quantum hall effect regime Aveek Bid Department of Physics, Indian Institute of Science, Bangalore Nature 585 466 (2010) Quantum Hall Effect Magnetic field
More informationCorrelated 2D Electron Aspects of the Quantum Hall Effect
Correlated 2D Electron Aspects of the Quantum Hall Effect Outline: I. Introduction: materials, transport, Hall effects II. III. IV. Composite particles FQHE, statistical transformations Quasiparticle charge
More informationFractional quantum Hall effect and duality. Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017
Fractional quantum Hall effect and duality Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017 Plan Plan General prologue: Fractional Quantum Hall Effect (FQHE) Plan General
More informationNematic Order and Geometry in Fractional Quantum Hall Fluids
Nematic Order and Geometry in Fractional Quantum Hall Fluids Eduardo Fradkin Department of Physics and Institute for Condensed Matter Theory University of Illinois, Urbana, Illinois, USA Joint Condensed
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationLuttinger Liquid at the Edge of a Graphene Vacuum
Luttinger Liquid at the Edge of a Graphene Vacuum H.A. Fertig, Indiana University Luis Brey, CSIC, Madrid I. Introduction: Graphene Edge States (Non-Interacting) II. III. Quantum Hall Ferromagnetism and
More informationTopological Phases under Strong Magnetic Fields
Topological Phases under Strong Magnetic Fields Mark O. Goerbig ITAP, Turunç, July 2013 Historical Introduction What is the common point between graphene, quantum Hall effects and topological insulators?...
More informationPseudospin Soliton in the ν=1 Bilayer Quantum Hall State. A. Sawada. Research Center for Low Temperature and Materials Sciences Kyoto University
YKIS2007, Sawada Pseudospin Soliton in the ν=1 Bilayer Quantum Hall State A. Sawada Research Center for Low Temperature and Materials Sciences Kyoto University Collaborators Fukuda (Kyoto Univ.) K. Iwata
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son GGI conference Gauge/gravity duality 2015 Ref.: 1502.03446 Plan Plan Fractional quantum Hall effect Plan Fractional quantum Hall effect Composite fermion
More informationarxiv: v1 [cond-mat.str-el] 3 Apr 2017
Anisotropic magnetoresistance and piezoelectric effect in GaAs Hall samples Orion Ciftja Department of Physics, Prairie View A&M University, Prairie View, Texas 77446, USA (Dated: April 5, 2017) arxiv:1704.00815v1
More informationPhysics of Semiconductors
Physics of Semiconductors 13 th 2016.7.11 Shingo Katsumoto Department of Physics and Institute for Solid State Physics University of Tokyo Outline today Laughlin s justification Spintronics Two current
More informationLandau quantization, Localization, and Insulator-quantum. Hall Transition at Low Magnetic Fields
Landau quantization, Localization, and Insulator-quantum Hall Transition at Low Magnetic Fields Tsai-Yu Huang a, C.-T. Liang a, Gil-Ho Kim b, C.F. Huang c, C.P. Huang a and D.A. Ritchie d a Department
More informationThe 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
More informationSpin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
More informationTHE CASES OF ν = 5/2 AND ν = 12/5. Reminder re QHE:
LECTURE 6 THE FRACTIONAL QUANTUM HALL EFFECT : THE CASES OF ν = 5/2 AND ν = 12/5 Reminder re QHE: Occurs in (effectively) 2D electron system ( 2DES ) (e.g. inversion layer in GaAs - GaAlAs heterostructure)
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
More informationConformal 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.
More informationLecture 20: Semiconductor Structures Kittel Ch 17, p , extra material in the class notes
Lecture 20: Semiconductor Structures Kittel Ch 17, p 494-503, 507-511 + extra material in the class notes MOS Structure Layer Structure metal Oxide insulator Semiconductor Semiconductor Large-gap Semiconductor
More informationLaughlin quasiparticle interferometer: Observation of Aharonov-Bohm superperiod and fractional statistics
Laughlin quasiparticle interferometer: Observation of Aharonov-Bohm superperiod and fractional statistics F.E. Camino, W. Zhou and V.J. Goldman Stony Brook University Outline Exchange statistics in 2D,
More informationThe Quantum Hall Effect
The Quantum Hall Effect David Tong (And why these three guys won last week s Nobel prize) Trinity Mathematical Society, October 2016 Electron in a Magnetic Field B mẍ = eẋ B x = v cos!t! y = v sin!t!!
More informationTopological insulator part I: Phenomena
Phys60.nb 5 Topological insulator part I: Phenomena (Part II and Part III discusses how to understand a topological insluator based band-structure theory and gauge theory) (Part IV discusses more complicated
More informationRICE UNIVERSITY. 5/2 State in High Electron Density GaAs/AlGaAs Quantum Well. by Chi Zhang
RICE UNIVERSITY 5/2 State in High Electron Density GaAs/AlGaAs Quantum Well by Chi Zhang A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE Master of Science APPROVED, THESIS
More informationEvolution of the Second Lowest Extended State as a Function of the Effective Magnetic Field in the Fractional Quantum Hall Regime
CHINESE JOURNAL OF PHYSICS VOL. 42, NO. 3 JUNE 2004 Evolution of the Second Lowest Extended State as a Function of the Effective Magnetic Field in the Fractional Quantum Hall Regime Tse-Ming Chen, 1 C.-T.
More informationNuclear spin spectroscopy for semiconductor hetero and nano structures
(Interaction and Nanostructural Effects in Low-Dimensional Systems) November 16th, Kyoto, Japan Nuclear spin spectroscopy for semiconductor hetero and nano structures Yoshiro Hirayama Tohoku University
More informationSpins and spin-orbit coupling in semiconductors, metals, and nanostructures
B. Halperin Spin lecture 1 Spins and spin-orbit coupling in semiconductors, metals, and nanostructures Behavior of non-equilibrium spin populations. Spin relaxation and spin transport. How does one produce
More informationQuantum Hall Effect in Graphene p-n Junctions
Quantum Hall Effect in Graphene p-n Junctions Dima Abanin (MIT) Collaboration: Leonid Levitov, Patrick Lee, Harvard and Columbia groups UIUC January 14, 2008 Electron transport in graphene monolayer New
More informationQuantum theory of quantum Hall smectics
PHYSICAL REVIEW B VOLUME 61, NUMBER 8 Quantum theory of quantum Hall smectics 15 FEBRUARY 2000-II A. H. MacDonald Department of Physics, Indiana University, Bloomington, Indiana 47405-4202 and Institute
More informationThe quantum Hall effect under the influence of a top-gate and integrating AC lock-in measurements
The quantum Hall effect under the influence of a top-gate and integrating AC lock-in measurements TOBIAS KRAMER 1,2, ERIC J. HELLER 2,3, AND ROBERT E. PARROTT 4 arxiv:95.3286v1 [cond-mat.mes-hall] 2 May
More informationThermoelectric response of fractional quantized Hall and re-entrant insulating states in the N=1 Landau level
Thermoelectric response of fractional quantized Hall and re-entrant insulating states in the N= Landau level W.E. Chickering, J.P. Eisenstein, L.N. Pfeiffer, and K.W. West Condensed Matter Physics, California
More informationTunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime
Tunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime The Harvard community has made this article openly available. Please share how this access benefits you. Your
More informationSpin-orbit Effects in Semiconductor Spintronics. Laurens Molenkamp Physikalisches Institut (EP3) University of Würzburg
Spin-orbit Effects in Semiconductor Spintronics Laurens Molenkamp Physikalisches Institut (EP3) University of Würzburg Collaborators Hartmut Buhmann, Charlie Becker, Volker Daumer, Yongshen Gui Matthias
More informationBroken Symmetry States and Divergent Resistance in Suspended Bilayer Graphene
Broken Symmetry States and Divergent Resistance in Suspended Bilayer Graphene The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
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 informationarxiv:cond-mat/ v1 22 Dec 1993
Hund s Rule for Composite Fermions J.K. Jain and X.G. Wu Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3800 arxiv:cond-mat/931090v1 Dec 1993 (October 18,
More informationPhase transitions in Bi-layer quantum Hall systems
Phase transitions in Bi-layer quantum Hall systems Ming-Che Chang Department of Physics Taiwan Normal University Min-Fong Yang Departmant of Physics Tung-Hai University Landau levels Ferromagnetism near
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 informationQuantum Hall Effect in Vanishing Magnetic Fields
Quantum Hall Effect in Vanishing Magnetic Fields Wei Pan Sandia National Labs Sandia is a multi-mission laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department
More informationc Copyright by Michael J. Lawler. All rights reserved.
c Copyright by Michael J. Lawler. All rights reserved. QUANTUM ELECTRONIC LIQUID CRYSTALS BY MICHAEL J. LAWLER B.Eng., Queen s University, 1999 DISSERTATION Submitted in partial fulfillment of the requirements
More informationThe BTE with a High B-field
ECE 656: Electronic Transport in Semiconductors Fall 2017 The BTE with a High B-field Mark Lundstrom Electrical and Computer Engineering Purdue University West Lafayette, IN USA 10/11/17 Outline 1) Introduction
More informationFractional quantum Hall effect and duality. Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017
Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017 Plan Fractional quantum Hall effect Halperin-Lee-Read (HLR) theory Problem
More informationLandau-level crossing in two-subband systems in a tilted magnetic field
PHYSICAL REVIEW B 76, 075346 2007 Landau-level crossing in two-subband systems in a tilted magnetic field C. A. Duarte, G. M. Gusev, A. A. Quivy, T. E. Lamas, and A. K. Bakarov* Instituto de Física da
More informationDetermining the Order Parameter of Unconventional Superconductors by Josephson Interferometry
The Josephson Effect Half-Centennial Symposium University of Cambridge --- June 23, 212 Determining the Order Parameter of Unconventional Superconductors by Josephson Interferometry - - Dale J. Van Harlingen
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 informationGraphite, graphene and relativistic electrons
Graphite, graphene and relativistic electrons Introduction Physics of E. graphene Y. Andrei Experiments Rutgers University Transport electric field effect Quantum Hall Effect chiral fermions STM Dirac
More informationWhat is Quantum Transport?
What is Quantum Transport? Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. http://www.physics.udel.edu/~bnikolic Semiclassical Transport (is boring!) Bloch-Boltzmann
More informationElectron interactions in graphene in a strong magnetic field
Electron interactions in graphene in a strong magnetic field Benoit Douçot Mark O. Goerbig Roderich Moessner K = K K CNRS and ENS Paris VI+XI cond-mat/0604554 Overview Recent experiments: integer QHE in
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 15 Feb 2000
Stripes in Quantum Hall Double Layer Systems L. Brey Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Cantoblanco, Madrid, Spain. arxiv:cond-mat/000228v [cond-mat.mes-hall] 5 Feb 2000 H.A. Fertig
More informationPHY331 Magnetism. Lecture 8
PHY331 Magnetism Lecture 8 Last week. We discussed domain theory of Ferromagnetism. We saw there is a motion of domain walls with applied magnetic field. Stabilization of domain walls due to competition
More informationNeutral Fermions and Skyrmions in the Moore-Read state at ν =5/2
Neutral Fermions and Skyrmions in the Moore-Read state at ν =5/2 Gunnar Möller Cavendish Laboratory, University of Cambridge Collaborators: Arkadiusz Wójs, Nigel R. Cooper Cavendish Laboratory, University
More informationExchange Mechanisms. Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich. lecture notes:
Exchange Mechanisms Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich lecture notes: www.cond-mat.de/events/correl Magnetism is Quantum Mechanical QUANTUM MECHANICS THE KEY TO UNDERSTANDING
More informationSECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS
2753 SECOND PUBLIC EXAMINATION Honour School of Physics Part C: 4 Year Course Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS TRINITY TERM 2011 Wednesday, 22 June, 9.30 am 12.30
More informationLow-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator
Low-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator M. Shayegan, 1,2 K. Karrai, 1 Y. P. Shkolnikov, 2 K. Vakili, 2 E. P. De Poortere, 2 and S.
More informationInteger quantum Hall effect for bosons: A physical realization
Integer quantum Hall effect for bosons: A physical realization T. Senthil (MIT) and Michael Levin (UMCP). (arxiv:1206.1604) Thanks: Xie Chen, Zhengchen Liu, Zhengcheng Gu, Xiao-gang Wen, and Ashvin Vishwanath.
More informationFractional charge in the fractional quantum hall system
Fractional charge in the fractional quantum hall system Ting-Pong Choy 1, 1 Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801-3080, USA (Dated: May
More informationCarbon based Nanoscale Electronics
Carbon based Nanoscale Electronics 09 02 200802 2008 ME class Outline driving force for the carbon nanomaterial electronic properties of fullerene exploration of electronic carbon nanotube gold rush of
More informationHigh-mobility electron transport on cylindrical surfaces
High-mobility electron transport on cylindrical surfaces Klaus-Jürgen Friedland Paul-Drude-nstitute for Solid State Electronics, Berlin, Germany Concept to create high mobility electron gases on free standing
More informationEdge Transport in Quantum Hall Systems
Lectures on Mesoscopic Physics and Quantum Transport, June 15, 018 Edge Transport in Quantum Hall Systems Xin Wan Zhejiang University xinwan@zju.edu.cn Outline Theory of edge states in IQHE Edge excitations
More informationLectures: Condensed Matter II 1 Electronic Transport in Quantum dots 2 Kondo effect: Intro/theory. 3 Kondo effect in nanostructures
Lectures: Condensed Matter II 1 Electronic Transport in Quantum dots 2 Kondo effect: Intro/theory. 3 Kondo effect in nanostructures Luis Dias UT/ORNL Lectures: Condensed Matter II 1 Electronic Transport
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION DOI: 10.1038/NNANO.2014.16 Electrical detection of charge current-induced spin polarization due to spin-momentum locking in Bi 2 Se 3 by C.H. Li, O.M.J. van t Erve, J.T. Robinson,
More informationFractional Charge. Particles with charge e/3 and e/5 have been observed experimentally......and they re not quarks.
Fractional Charge Particles with charge e/3 and e/5 have been observed experimentally......and they re not quarks. 1 Outline: 1. What is fractional charge? 2. Observing fractional charge in the fractional
More information3D topological insulators and half- Heusler compounds
3D topological insulators and half- Heusler compounds Ram Seshadri Materials Department, and Department of Chemistry and Biochemistry Materials Research Laboratory University of California, Santa Barbara
More informationConductance fluctuations at the integer quantum Hall plateau transition
PHYSICAL REVIEW B VOLUME 55, NUMBER 3 15 JANUARY 1997-I Conductance fluctuations at the integer quantum Hall plateau transition Sora Cho Department of Physics, University of California, Santa Barbara,
More informationFatih Balli Department of Physics, University of South Carolina 11/6/2015. Fatih Balli, Department of Physics UofSC
Fatih Balli Department of Physics, University of South Carolina 11/6/2015 1 Timeline and Motivation Hall Effect Landau Problem on Planar System Quantum Hall Effect Incompressibility and Multiparticle Wavefunction
More informationOrbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to (ET)2Cu2(CN)3
Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to (ET)2Cu2(CN)3 Olexei Motrunich (KITP) PRB 72, 045105 (2005); PRB 73, 155115 (2006) with many thanks to T.Senthil
More informationExchange statistics. Basic concepts. University of Oxford April, Jon Magne Leinaas Department of Physics University of Oslo
University of Oxford 12-15 April, 2016 Exchange statistics Basic concepts Jon Magne Leinaas Department of Physics University of Oslo Outline * configuration space with identifications * from permutations
More informationCommensurability-dependent transport of a Wigner crystal in a nanoconstriction
NPCQS2012, OIST Commensurability-dependent transport of a Wigner crystal in a nanoconstriction David Rees, RIKEN, Japan Kimitoshi Kono (RIKEN) Paul Leiderer (University of Konstanz) Hiroo Totsuji (Okayama
More informationCondensed matter theory Lecture notes and problem sets 2012/2013
Condensed matter theory Lecture notes and problem sets 2012/2013 Dmitri Ivanov Recommended books and lecture notes: [AM] N. W. Ashcroft and N. D. Mermin, Solid State Physics. [Mar] M. P. Marder, Condensed
More information=
.52.5.48.46.44.42 =..22 2 x 3 4 Application of DMRG to 2D systems L y L x Unit cell Periodic boundary conditions for both x and y directions k y = 2n/L y = X n / l 2 Initial basis states (Landau gauge)
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 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 informationSpin Interactions. Giuseppe Pileio 24/10/2006
Spin Interactions Giuseppe Pileio 24/10/2006 Magnetic moment µ = " I ˆ µ = " h I(I +1) " = g# h Spin interactions overview Zeeman Interaction Zeeman interaction Interaction with the static magnetic field
More informationChapter 2 The Two-Dimensional Electron System
Chapter 2 The Two-Dimensional Electron System At the heart of this thesis are the properties of high-quality two-dimensional electron systems when being exposed to strong magnetic fields and low temperatures.
More informationElectromagnetism II. Instructor: Andrei Sirenko Spring 2013 Thursdays 1 pm 4 pm. Spring 2013, NJIT 1
Electromagnetism II Instructor: Andrei Sirenko sirenko@njit.edu Spring 013 Thursdays 1 pm 4 pm Spring 013, NJIT 1 PROBLEMS for CH. 6 http://web.njit.edu/~sirenko/phys433/phys433eandm013.htm Can obtain
More informationMagnetoresistance in a High Mobility Two- Dimensional Electron System as a Function of Sample Geometry
Journal of Physics: Conference Series OPEN ACCESS Magnetoresistance in a High Mobility Two- Dimensional Electron System as a Function of Sample Geometry To cite this article: L Bockhorn et al 213 J. Phys.:
More informationSUPPLEMENTARY INFORMATION
doi:1.138/nature12186 S1. WANNIER DIAGRAM B 1 1 a φ/φ O 1/2 1/3 1/4 1/5 1 E φ/φ O n/n O 1 FIG. S1: Left is a cartoon image of an electron subjected to both a magnetic field, and a square periodic lattice.
More informationInterplay of interactions and disorder in two dimensions
Interplay of interactions and disorder in two dimensions Sergey Kravchenko in collaboration with: S. Anissimova, V.T. Dolgopolov, A. M. Finkelstein, T.M. Klapwijk, A. Punnoose, A.A. Shashkin Outline Scaling
More informationStudies of Exciton Condensation and Transport in Quantum Hall Bilayers
Studies of Exciton Condensation and Transport in Quantum Hall Bilayers Thesis by Aaron David Kiyoshi Finck In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute
More informationTHERMOPOWER AND MAGNETORESISTANCE STUDIES IN A TWO-DIMENSIONAL ELECTRON GAS
THERMOPOWER AND MAGNETORESISTANCE STUDIES IN A TWO-DIMENSIONAL ELECTRON GAS by Jian Zhang A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for
More informationScanning gate microscopy and individual control of edge-state transmission through a quantum point contact
Scanning gate microscopy and individual control of edge-state transmission through a quantum point contact Stefan Heun NEST, CNR-INFM and Scuola Normale Superiore, Pisa, Italy Coworkers NEST, Pisa, Italy:
More informationEffects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in 2D Fermi Gases
Effects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in D Fermi Gases Carlos A. R. Sa de Melo Georgia Institute of Technology QMath13 Mathematical Results in Quantum
More informationScreening Model of Magnetotransport Hysteresis Observed in arxiv:cond-mat/ v1 [cond-mat.mes-hall] 27 Jul Bilayer Quantum Hall Systems
, Screening Model of Magnetotransport Hysteresis Observed in arxiv:cond-mat/0607724v1 [cond-mat.mes-hall] 27 Jul 2006 Bilayer Quantum Hall Systems Afif Siddiki, Stefan Kraus, and Rolf R. Gerhardts Max-Planck-Institut
More informationWhat is a topological insulator? Ming-Che Chang Dept of Physics, NTNU
What is a topological insulator? Ming-Che Chang Dept of Physics, NTNU A mini course on topology extrinsic curvature K vs intrinsic (Gaussian) curvature G K 0 G 0 G>0 G=0 K 0 G=0 G
More informationLecture 20 - Semiconductor Structures
Lecture 0: Structures Kittel Ch 17, p 494-503, 507-511 + extra material in the class notes MOS Structure metal Layer Structure Physics 460 F 006 Lect 0 1 Outline What is a semiconductor Structure? Created
More informationPhysics of Semiconductors (Problems for report)
Physics of Semiconductors (Problems for report) Shingo Katsumoto Institute for Solid State Physics, University of Tokyo July, 0 Choose two from the following eight problems and solve them. I. Fundamentals
More informationLecture 19: Building Atoms and Molecules
Lecture 19: Building Atoms and Molecules +e r n = 3 n = 2 n = 1 +e +e r ψ even Lecture 19, p 1 Today Nuclear Magnetic Resonance Using RF photons to drive transitions between nuclear spin orientations in
More informationLecture 2: Deconfined quantum criticality
Lecture 2: Deconfined quantum criticality T. Senthil (MIT) General theoretical questions Fate of Landau-Ginzburg-Wilson ideas at quantum phase transitions? (More precise) Could Landau order parameters
More informationLecture 19: Building Atoms and Molecules
Lecture 19: Building Atoms and Molecules +e r n = 3 n = 2 n = 1 +e +e r y even Lecture 19, p 1 Today Nuclear Magnetic Resonance Using RF photons to drive transitions between nuclear spin orientations in
More information