Post on 09-Jul-2020
May, 4 1970 protests LCI - birthplace of
liquid crystal display
Fashion school is in top-3 in USA Clinical Psychology program is
Top-5 in USA
Maxim Dzero
Kent State University (USA)
and
CFIF, Instituto Superior Tecnico (Portugal)
Topological insulators driven by electron spin
Collaborators:
Piers Coleman, Rutgers U.
Victor Galitski, U. of Maryland
Kai Sun, U. Michigan
Victor Alexandrov, CUNY
Bitan Roy, U. of Maryland
Jay Deep Sau, U. of Maryland
Piers
Victor G.Victor A. Kai
Jay Deep
References:MD, K. Sun, V. Galitski & P. Coleman, Phys. Rev. Lett. 104, 106408 (2010)
MD, Europhys. Jour. B 85, 297 (2012)
MD, K. Sun, P. Coleman & V. Galitski, Phys. Rev. B 85, 045703 (2012)
V. Alexandrov, MD & P. Coleman, Phys. Rev. Lett. 111, 206403 (2013)
B. Roy, Jay Deep Sau, MD & V. Galitski, arXiv: 1405.5526 (2014)
MD, M. Vavilov & V. Galitski, preprint (2014)
Maxim Vavilov, U. Wisconsin-M
Maxim
Model Hamiltonian
Special case will be discussed:
Coleman (2002)
increasing localization
incre
asin
g lo
ca
liza
tio
nQuest for topological insulators beyond Bi-based materials
complex materials with d- & f-orbitals
A lot of action takes place on the brink of localization!
Quest for ideal topological insulators
4f-orbitals3d & 4d-orbitals 5d-orbitals 5f-orbitals
complex materials with d- & f-orbitals
Quest for ideal topological insulators
complex materials with d- & f-orbitals
candidates for f-orbital topological insulators
FeSb2, SmB6, YbB12, YbB6 & Ce3Bi4Pt3
f-orbital insulators: Anderson lattice model
2J+
1
2J+
1tetragonal crystal field cubic crystal field
conduction electrons
(s,p,d orbitals)f-electrons
f-orbital insulators: Anderson lattice model
conduction electrons
(s,p,d orbitals)f-electrons
Non-local hybridization
Strong spin-orbit coupling is
encoded in hybridization
• hybridization: matrix element
odd functions of k
Non-interacting limit
• Anderson lattice model: U=0
basis
Hamiltonian (2D)
Equivalent to Bernevig-Hughes-Zhang (BHZ) model
c-f hybridization:
Non-interacting limit
• Anderson lattice model (2D): U=0
Jan Werner and Fakher F. Assaad, PRB 88, 035113
(2013)
Finite-U: local moment formation
P. W. Anderson, Phys. Rev 124, 41, (1961)
local d- or f-electron resonance splits to form a local moment
Electron sea
Heavy Fermion Primer: Kondo impurity
Spin (4f,5f): basic
fabric of heavy
electron physics
2J+
1Curie
Pauli
Spin is screened by
conduction electrons Kondo Temperature
Ce or Sm impurity
total angular
momentum J=5/2
Heavy Fermion Primer
Kondo lattice
coherent heavy fermions
Semiconductors with f-electrons
M. Bat’kova et. al, Physica B 378-380, 618 (2006)
canonical examples: SmB6 & YbB12
P. Canfield et. al, (2003)
Ce3Bi4Pt3
Conductivity remains finite!
exponentialgrowth
Mott’s Hybridization picture N. Mott, Phil. Mag. 30, 403 (1974)
Mott, 1973
Formation of Heavy f-bands: electrons and
localized f doublets hybridize, possibly due to Kondo
effect
Mott’s Hybridization picture N. Mott, Phil. Mag. 30, 403 (1974)
Formation of heavy-fermion insulator
nc+nf=2×integer canonical examples:
SmB6 & YbB12
Interacting electrons: Kondo insulators
• Anderson model: infinite-U limit
Constraint:
Projection (slave-boson) operators:
• infinite-U limit: hamiltonian
mean-field approximation:
Kondo insulators: mean-field theory
• mean-field Hamiltonian:
renormalized
position of the
f-level
• self-consistency equations:
Kondo insulators: mean-field theory
• mean-field Hamiltonian:
renormalized
position of the
f-level
• parity
• time-reversal
P-inversion odd form factor vanishes @ high symmetry
points of the Brillouin zone
L. Fu & C. Kane, PRB 76, 045302 (2007)
Z2 invariants:
jour-ref: Phys. Rev. Lett. 104, 106408 (2010)
tetragonal symmetry: Kramers doublet
10.870.58
WTISTIBI
Strong mixed valence favors strong topological insulator!
Tetragonal Topological Kondo Insulators
“strong”: 3 “weak”:
Q: What factors are important for extending
strong topological insulating state to the local moment regime (nf ≈ 1)?
Strong Topological Kondo Insulators
A: Degeneracy = high symmetry (cubic!)
10.870.58
WTISTIBI
Topological Kondo Insulators: Large-N theory
SU(2) -> SP(2N): time-reversal symmetry is preserved
control parameter: 1/2N
M. Dzero, Europhys. Jour. B 85, 297 (2012)
Replicate Kramers doublet N times: SU(2) -> SP(2N)
T. Takimoto, Jour. Phys. Soc. Jpn. 80, 123710 (2011)
V. Alexandrov, M. Dzero, P. Coleman, Phys. Rev. Lett. 111, 206403 (2013)
Cubic Topological Kondo Insulators
4d 5f
Antonov,Harmon,Yaresko, PRB (2006)
Cubic symmetry (quartet): SmB6
Bands must invert either @ X or M high symmetry points
V. Alexandrov, M. Dzero, P. Coleman, Phys. Rev. Lett. 111, 206403 (2013)
Cubic Topological Kondo Insulators
Cubic symmetry (quartet): SmB6
Cubic symmetry protects strong topological insulator!
0.56
STI
1
BI
4d
5f
V. Alexandrov, M. Dzero, P. Coleman, Phys. Rev. Lett. 111, 206403 (2013))
Mean-field theory for SmB6: is N=1/4 small enough?
• integrated spectral weight of the gap: T-dependence
Nyhus, Cooper, Fisk, Sarrao,
PRB 55, 12488 (1997)
Mean-field-like onset of the insulating gap!
• full insulating gap: dependence on pressure
Derr et al. PRB 77, 193107 (2008)
Cubic Topological Kondo Insulators: surface states
• Bulk Hamiltonian:
Assumption: boundary has little effect on the bulk parameters,
i.e. mean-field theory in the bulk still holds with open boundaries
Cubic Topological Kondo Insulators: surface states
• effective surface Hamiltonian:
Fermi velocities are small: surface electrons are heavy
Cubic Topological Kondo Insulators: surface states
three Dirac cones: one @ Gamma point, other two @ X points
Surface potential has two effects:
no surface potential
• band bending: surface carriers are light!
• Dirac point moves into the valence band: confirmed by ARPES experiments!
What makes topological Kondo insulators special?
Q: Are topological Kondo insulators adiabatically connected to
topological band insulators?
A: NO! Gap closes as the strength of U gradually increases
Jan Werner and Fakher F. Assaad, PRB 88, 035113
(2013)
SmB6: potential candidate for correlated TI
SmB6: experiments
Q: Can we establish that SmB6 hosts
helical surface states with Dirac spectrum while relying on experimental data only?
(1) transport is limited to the surface
(2) time-reversal symmetry breaking
leads to localization
(3) strong spin-orbit coupling = helicity(4) Dirac spectrum
@ T < 5K transport comes from the surface ONLY!
S. Wolgast et al.,
PRB 88, 180405 ® (2013)
surface transport bulk transport
Idea: pass the current and measure voltage drop
D. J. Kim, J. Xia & Z. Fisk, Nat. Comm. (2014)
Idea: Ohm’s law
in ideal topo insultor
resistivity is independent
of sample’s thickness:
surface transport
Resistivity ratio
Thickness independent!
SmB6: transport experiments
Non-magnetic ions (Y) on the surface:
time-reversal symmetry is preserved
Kim, Xia & Fisk, arXiv:1307.0448
ee
X
Localization
ee
No backscattering
Magnetic ions (Gd) on the surface:
time-reversal symmetry is broken
SmB6: quantum oscillations experiments
G. Li et al. (Li Lu group Ann Arbor) arXiv:1306.5221
very light
effective
mass: 0.07-0.1me
Strong surface potential!
Idea: zero-energy Landau level exists for Dirac electrons:
Experimental
consequence:
shift in Landau
index n must be
observed – only
E0=0 contributes at
infinite magnetic
field!
SmB6: weak anti-localization (WAL)
Weak SO coupling -> WL
Strong SO coupling -> WAL
SmB6: weak anti-localization
S. Thomas et al. arXiv:1307.4133
*diffusion (classical) conductivity is field-independent
Conclusion & open questions
• Topological Kondo insulators from artificial structures?
[Can we increase the temperature @ which only surface is conducting?]
Role of correlations?
• Why all Kondo insulators have cubic symmetry?
[Kondo semimetals have tetragonal symmetry]
• surface conductance & insulating bulk below 5K SmB6 is a correlated
topological insulator • quantum oscillations experiments confirm Dirac
Dirac spectrum of surface electrons
• weak anti-localization: strong SO coupling
• effect magnetic vs. non-magnetic doping on
the magnitude of surface conductivity
• Pressure- or chemical substitution-driven superconductivity?