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?