Interacting topological insulators out of equilibrium . Dimitrie Culcer. D. Culcer, PRB 84, 235411 (2011) D. Culcer, Physica E 44, 860 (2012) – review on TI transport . Outline. Introduction to topological insulators
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Interacting topological insulators out of equilibrium
Dimitrie Culcer
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, Physica E 44, 860 (2012) – review on TI transport
D. Culcer, Physica E 44, 860 (2012) – review on TI transport
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, E. H. Hwang, T. D. Stanescu, S. Das Sarma, PRB 82, 155457 (2010)
C.L. Kane & E.J. Mele, Physical Review Letters 95 (2005) 226801.
M.Z. Hasan& C.L. Kane, Reviews of Modern Physics 82 (2010) 3045.
X.-L. Qi & S.-C. Zhang, Reviews of Modern Physics 83 (2011) 1057.
X.-L. Qi, T.L. Hughes & S.-C. Zhang, Physical Review B 78 (2008) 195424.
Boring semiconductor
Bulk conduction
Eg
Bulk valence
Bulk conduction
Surface
states
Bulk valence
Zhang et al, Nature Physics 5, 438 (2009)
Zhang et al, Nature Physics 5, 438 (2009)
Zhang et al, PRL 103, 266803 (2009)
Alpichshev et al, PRL 104, 016401 (2010)
Exotic phases with correlations cf. talk by Kou Su-Peng this morning
流光溢彩
See also Greg Fiete, Physica E 44, 844 (2012) review on spin liquid in TI + ee
Bulk conduction
εF
Surface
states
Bulk valence
Semiconductor with SO
Effective magnetic field
ky
Spin
kx
General picture at each k
Out of equilibrium the spin may deviate slightly from the direction of the effective magnetic field
Spin-momentum locking
Equilibrium picture
Driving term due to the electric field
Spin precession
Scattering
Scattering in
Scattering out
Effective magnetic field
Spin
Conserved spin
Non-conserved spin
Culcer, Hwang, Stanescu, Das Sarma, PRB 82, 155457 (2010)
ζ contains the angular dependence of the scattering potential.
W is the strength of the scattering potential.
Momentum relaxation time
Conducting edge
Insulating bulk
ky
ky
kx
kx
E // x
No E
D. Culcer, PRB 84, 235411 (2011)
DOS
EF
Minority
Majority
D. Culcer, PRB 84, 235411 (2011)
This is just the band Hamiltonian – Dirac
This is the Coulomb interaction term
Plane wave states
This is just the electron-electron Coulomb potential
D. Culcer, PRB 84, 235411 (2011)
Culcer, Hwang, Stanescu, Das Sarma, PRB 82, 155457 (2010)
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
ky
ky
kx
kx
Non-interacting
Interacting
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
Majority spin subband, spins save energy. Polarization enhanced.
Polarization reduced.
TI is like minority spin subband.
Spins gain energy by lining up with the field.
TI
Rashba
Minority spin subband, spins gain energy. Polarization reduced.
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, PRB 84, 235411 (2011)
εF
Wei-Zhe Liu, A. H. MacDonald, and D. Culcer (2012)
Wei-Zhe Liu, A. H. MacDonald, and D. Culcer (2012)
Wei-Zhe Liu, A. H. MacDonald, and D. Culcer (2012)
D. Culcer, PRB 84, 235411 (2011)
D. Culcer, Physica E 44, 860 (2012) – review on TI transport
Wei-Zhe Liu, A. H. MacDonald, and D. Culcer (2012)