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IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Topological Insulators
Yize Jin, Lu Zheng
Department of Physics, Fudan University, China
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Topology
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Genus
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Topological Insulators
Topological insulator is insulator in bulk but conductor only onedge.
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Hall Effect
|u(~k)〉 is an eigenstate of the Hamiltonian, the Berry’sphase of this is Am = i〈um|∇k |um〉 this may be expressedas a surface integral of the Berry flux
Fm = ∇× Am
The first chern number of each state of an electron
nm =1
2π
∫d2~kFm
The first chern number of an electron
n =∑
m
nm
Hall conductivityσxy = Ne2/~
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Quantum Spin Hall Effect
The conditions of QHE(Quantum Hall Effect) are strongmagnetic field and low temperature ,which are hard toorealize.QHE =⇒ QSHE(Quantum Spin Hall Effect):no magneticfield
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Quantum Spin Hall Effect
Electronic current =⇒ Spin current
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Quantum Spin Hall Effect
Edge-states electrons in QSHE are immune to impurityscattering
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Quantum Spin Hall Effect
In figure (a), reflected light from upper edge and bottomedge interfere with each other destructively.In figure (b),the upper electron is scattered clockwise(π)while the lower counterclockwise(−π).Since an electron is a spin-1/2 particle, a 2π(= π − (−π))rotation difference will cause a phase difference of -1,resulting in destructive interference.
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Band Structure
Topologically Inequivalent
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Band Structure
Why are they topologically inequivalent?=⇒ Theintersections of trivial insulators can be seperated, but nottopological insulators.Why can’t the intersections of topological insulators beseperated?=⇒ Kramers theoremWhat is Kramers theorem?=⇒The energy levels ofsystems with an odd total number of fermions remain atleast doubly degenerate in the presence of purely electricfields.In topological insulators, the red line(edge states) doesn’tcome back to valence band like trivial insulators. =⇒Bandinversion.
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Outline
1 Introduction
2 Quantum Hall Effect
3 Topological InsulatorsQuantum Spin Hall EffectBand StructureThe First Found Topological Insulators
4 Application
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
Forecast
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
HgTe: Eg < 0 ⇐⇒ p orbital band is above the s orbitalband.CdTe: Eg > 0 ⇐⇒ s orbital band is above the p orbitalband.Make a sandwich=⇒band inversion=⇒topologicalinsulator?
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Quantum Spin Hall EffectBand StructureThe First Found Topological Insulators
The First Found Topological Insulator
E1 is the s-likeconduction subbandand H1 is p-likevalence subband.dc = 6.5nmThick quantum wellhas a quantizedresistance plateau at
R =h
2e2
due to the conductingedge states
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Possible Application
SuperconductorTopological Quantum ComputationAnomalous Quantum Hall EffectMajorana Fermion,,
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
Spintronic Devices
Impurity scattering =⇒ Heat dissipationSolution:QSHE
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
References
X.-L Qi,S.-C Zhang, Phys. Today 63(1), 33(2010).B.A. Bernevig, T. L. Hughes, S.-C. Zhang, Science 314,1757(2006).M.König et al., Science 318, 766 (2007).M.Z.Hasan, and C.L.Kane (2010), e-print arXiv:1002.3895.
Yize Jin,Lu Zheng Topological Insulators
IntroductionQuantum Hall Effect
Topological InsulatorsApplication
THANK YOU!
Yize Jin,Lu Zheng Topological Insulators