Piers Coleman & Onur Erten - University of Cambridge · Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Magnetism

Piers Coleman & Onur ErtenCenter for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK.

Magnetism meets TopologyTopological Kondo Insulators:

Piers Coleman, Rutgers CMT.

Happy Birthday Gil!





Collaborators

Vic Alexandrov, IAS Onur Erten, Rutgers

Maxim Dzero Kent State Kai Sun Michigan Victor Galitski Maryland Vic

Joel Moore, Berkeley Phil Anderson, Princeton Suchitra Sebastian Cambridge Gil Lonzarich Cambridge

Onur



Collaborators

Vic Alexandrov, IAS Onur Erten, Rutgers

Maxim Dzero Kent State Kai Sun Michigan Victor Galitski Maryland Vic

Joel Moore, Berkeley Phil Anderson, Princeton Suchitra Sebastian Cambridge Gil Lonzarich Cambridge

Onur

M. Dzero, K. Sun, V. Galitski, PC Phys. Rev. Lett. 104, 106408 (2010)T. Takimoto, J. Phys. Soc. Jpn. 80, 123710 (2011).

Maxim Dzero, Jing Xia, Victor Galitski, Piers Coleman, Annual Reviews CMP (2016), ArXiv 1506.05635V. Alexandrov, P. Coleman, O. Erten, Phys. Rev. Lett. 114:177202 (2015).



Outline

• SmB6 and the rise of topology• TKIs: a link with superfluid He-3• Is SmB6 topological?• The Magnetic Connection.

Kondo insulators: History

Sm2.7+

B6

SmB6


Sm2.7+

B6

SmB6

Hybridization picture.

Mott Phil Mag, 30,403,1974

kEf

E(k)

H = (|kσ〉Vσα(k)〈α| + H.c)

Maple + Wohlleben, 1972

Allen and Martin, 1979




kEf

E(k)




“In SmB6 and high-pressure SmS a very small gap separates occupied from unoccupied states, this in our view being due to hybridization of 4f and 4d bands.” Mott 1974




kEf

E(k)




In SmB6 and high-pressure SmS a very small gap separates occupied from unoccupied states, this in our view being due to hybridization of 4f and 4d bands.


Cooley, Aronson, et al. 1995

g=0 g=1 g=2 g=3g=genus


14π

∫κdA =

Ω4π

= (1 − g)


Berry v. Klitzing Laughlin Thouless Haldane

von Klitzing, Dorda & Pepper (1980)

Integer Quantum Hall



Integer Quantum Hall

�ak = i∑

n=1,2N

〈un,k|∇k|un,k〉


Kane Mele Zhang Molencamp Hasan Balents Moore Roy Fu


Integer Quantum HallZ2 Topological Insulators

�ak = i∑

n=1,2N

〈un,k|∇k|un,k〉

Conventional band insulator: adiabatic continuation of the vacuum.

Topological insulator

Topological insulator

Gap must close at interface betweentwo different vacua

Metallic surfaces.

: adiabatically disconnected from thevacuum.

Tamm 1932, Shockley, Phys Rev, 56, 317 (1939): 1D TI

1D Topological Insulator

IgorTamm

WilliamShockley


εp -+

-+

++ε-t

tp

V


IgorTamm

WilliamShockley

P=-1

P=+1


εp -+

-+

++ε-t

tp

V


IgorTamm

WilliamShockley

P=-1

P=+1

Open BCs- broken translation symmetry odd/even states mix to form edge states.

Band Crossing of odd and even parity states Yields a Z2 Topological Insulator (Fu, Kane, Mele, 2007)



Topological Texture of Berry Connection


Z2= 1 Z2= -1



Z2 =∏

i

δ(Γi)

Z2= -1Z2= 1


Bi2Se3 , Bi2Te3, Sb2Te3

(Zhang et al ,Xia et al ,Chen et al, Hsieh et al (09))

FIG. 27 ARPES data for Bi2Se3 thin films of thickness (a) 1QL (b)2QL (c) 3QL (d) 5QL (e) 6QL, measured at room temperature (QLstands for quintuple layer). From Zhang et al., 2009.

FIG. 25 ARPES data for the dispersion of the surface states ofBi2Se3, along directions (a) Γ − M and (b) Γ − K in the surfaceBrillioun zone. Spin-resolved ARPES data is shown along Γ−M fora fixed energy in (d), from which the spin polarization in momentumspace (c) can be extracted. From Xia et al., 2009 and Hsieh et al.,2009.

Bi2Se3 , Bi2Te3, Sb2Te3

(Zhang et al ,Xia et al ,Chen et al, Hsieh et al (09))

FIG. 27 ARPES data for Bi2Se3 thin films of thickness (a) 1QL (b)2QL (c) 3QL (d) 5QL (e) 6QL, measured at room temperature (QLstands for quintuple layer). From Zhang et al., 2009.

FIG. 25 ARPES data for the dispersion of the surface states ofBi2Se3, along directions (a) Γ − M and (b) Γ − K in the surfaceBrillioun zone. Spin-resolved ARPES data is shown along Γ−M fora fixed energy in (d), from which the spin polarization in momentumspace (c) can be extracted. From Xia et al., 2009 and Hsieh et al.,2009.

Are Kondo insulators topological?

R. Martin & J. Allen, J. Applied Physics, 50,7561 (1979)




Dzero, Sun, Galitski, PC Phys. Rev. Lett. 104, 106408 (2010)





Many Body Localized




Many Body Delocalization

Many Body Localized





Many Body Localized



Band Theory SmB6: T. Takimoto, J. Phys. Soc. Jpn. 80, 123710 (2011).

Maxim Dzero, Kai Sun, Piers Coleman and Victor Galitski, Phys. Rev. B 85 , 045130-045140 (2012).

Victor Alexandrov, Maxim Dzero and Piers Coleman PRL (2013).

Gutzwiller + Band Theory F. Lu, J. Zhao, H. Weng, Z. Fang and X. Dai, Phys. Rev. Lett. 110, 096401 (2013).



Many Body Localized

Dzero et al, Annual Reviews of Condensed Matter Physics (2016), arXiv 1506.05635


Three crossings: THREE DIRAC CONESON SURFACE.






sk = (sin kx, sin ky, sin kz) ∼ k

d(k) = ks(k) = k

X

Vαβ(k) = Vsk · �σαβ

Three crossings: THREE DIRAC CONESON SURFACE.Hybridization of f (P=+) and d (P=-) vanishes at X point.



d(k) = ks(k) = k

X




=3

H(k) =(

εk V sk · �σV sk · �σ ε f k

)


d(k) = ks(k) = k

X




=3

H(k) =(

εk V sk · �σV sk · �σ ε f k

)Like He-3B: an adaptive insulator.


d(k) = ks(k) = k

X


(a)

F. Lu, et al., Phys. Rev. Lett. 110:096401 (2013)Gutzwiller + DFT


Is SmB6 a topological Kondo insulator?

SmB6 Surface Conductivity


RVert

RLat u

Wolgast et al, Phys Rev B, 88, 180405 (2013)D. J. Kim et al, Scientific Reports 3, 3150 (2013)

Hall constant derives from the Surface.


RVert

RLat u



Large Vertical Resistance indicatesconductivity is from the surface.

SmB6 Surface Conductivity Bulk Insulator

Surface Conductivity

Robustness/Sensitivity to potential/magnetic scattering.

RVert

RLat u



Large Vertical Resistance indicatesconductivity is from the surface.

SmB6 TKI Check List.


4f j=5/2, 7/2Multiplets


5d-band



5d-band



5d-band


Odd number (3) of Surface FS (ARPES, dHVA, STM).

d-band crossing at X points

Nan Xu , X. Shi , P. Biswas , C. Matt , R. Dhaka , Y. Huang , N. Plumb , M. Radovic , J. Dil , E. Pomjakushina , K. Conder , A. Amato , Z. Salman , D. Paul , J. Mesot , Hong Ding , Ming Shi

Spin Resolved ARPES

Nature Communications Volume: 5, 4566 (2014)

Low

FHigh


Spin Resolved ARPES


Bulkf states

�

� Γ

M

X

_

__ kx

ky

Low

FHigh


Spin Resolved ARPES


Bulkf states

�

� Γ

M

X

_

__ kx

ky

Low

FHigh

But no consensus yet!

arxiv/1502.01542

Phys. Rev. Lett. 111, 216402 (2013)

I. Kondo BreakdownII. Pressure:AFMIII. Neutrons: ExcitonIV. Field: dHvA and Quantum Criticality.

V. Alexandrov, P. Coleman, O. Erten,

Phys. Rev. Lett. 114:177202 2015.I. Kondo Breakdown

ARPES: vs~ 220-300 meVA




10x too small!Theory: vs~ 30-50 meVA





Lower co-ordinationat surface dramaticallysuppresses the Kondotemperature










Kondo Breakdown at surface.





10x too small! AFS/(2π)2 = Δnf

Theory: vs~ 30-50 meVA






10x too small! AFS/(2π)2 = Δnf

Breakdown of Kondo effect at surface causes surface Dirac cones to dope,submerging the Dirac point and considerably enhancing the Fermi velocity.

Theory: vs~ 30-50 meVA





I. Kondo Breakdown

AFS/(2π)2 = Δnf



Phys. Rev. Lett. 114:177202 2015.

I. Kondo Breakdown

AFS/(2π)2 = Δnf


Local moments on the surface form a 2D Kondo lattice with spin-orbit locked conduction bands.


Phys. Rev. Lett. 114:177202 2015.

I. Kondo Breakdown

AFS/(2π)2 = Δnf


Local moments on the surface form a 2D Kondo lattice with spin-orbit locked conduction bands.

Surface Kondo physics? Magnetism, QCP even superconductivity.


Phys. Rev. Lett. 114:177202 2015.

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

AFM?

Sm

B6

SmB6

A. Barla et al, PRL 94, 2005

II. The effect of Pressure: AFM

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

Fuhrman et al, PRL 114, 036401 (2015)

III. Magnetic Fluctuations

AFM Fluctuations

Fuhrman et al, PRL 114, 036401 (2015)

RPATheory

AFM Fluctuations

III. Magnetic Fluctuations

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

IV. Field effect

H

Cooley et al, 1999

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

IV. Field effect

H

Cooley et al, 1999

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

?

IV. Field effect

H

Cooley et al, 1999

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

6GPaQC

?

Hc

>160T?

IV. Field effect

H

Cooley et al, 1999

T

P

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

6GPaQC

?

L=5, S=5/2, J=5/2, g~0.2-0.3Field effect is ORBITALHc

>160T?

IV. Field effect

H

T

P

H

50KGap opens

0.3-4K plateau

6GPaQCP?

FM, AFM?

6GPaQC

Hc

>160T?

IV. Field effect

2D fluctuations:

G. Li et al, Science 346, 1208 (2014).

IV. Field effect

2D surface states:

G. Li et al, Science 346, 1208 (2014).

Tan et al, Science (2015).

IV. Field effect

2D surface states:

G. Li et al, Science 346, 1208 (2014).

Tan et al, Science (2015).

IV. Field effect

2D surface states:

G. Li et al, Science 346, 1208 (2014).

Tan et al, Science (2015). 3D orbits!

IV. Field effect

2D surface states:

G. Li et al, Science 346, 1208 (2014).

Tan et al, Science (2015). 3D orbits!

IV. Field effect

2D surface states:

G. Li et al, Science 346, 1208 (2014).

Tan et al, Science (2015). 3D orbits! 6x Rise in N(0)*: Q Criticality?

IV. Field effect

Tan et al, Science (2015). 3D orbits! 6x Rise in N(0)*: Q Criticality?

IV. Field effect

Tan et al, Science (2015). 3D orbits! 6x Rise in N(0)*: Q Criticality? • 3D FS in a bulk insulator !

IV. Field effect


• ωc ≳ V ? (Knolle &Cooper arXiv 1507.00885)

IV. Field effect


• ωc ≳ V ? (Knolle &Cooper arXiv 1507.00885)

• Majorana FS? Are KI gapless? ( Baskaran arXiv 1507 to appear;

Miranda, PC, Tsvelik, Physica B, 186-188, 362, 1993)

• Quantum Criitcal phase separation?

Piers Coleman, Rutgers CMT.

Congratulations Gil!

Piers Coleman & Onur Erten - University of Cambridge · Piers Coleman & Onur Erten Center for Materials Theory, Rutgers U, USA Royal Holloway, University of London, UK. Magnetism

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