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!

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

Magnetism meets TopologyTopological Kondo Insulators:

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

Magnetism meets TopologyTopological Kondo Insulators:

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

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

Magnetism meets TopologyTopological Kondo Insulators:

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).

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

Magnetism meets TopologyTopological Kondo Insulators:

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

Kondo insulators: History

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

Kondo insulators: History

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

“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

Kondo insulators: History

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

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.

Kondo insulators: History

Cooley, Aronson, et al. 1995

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

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

14π

∫κdA =

Ω4π

= (1 − g)

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

Berry v. Klitzing Laughlin Thouless Haldane

von Klitzing, Dorda & Pepper (1980)

Integer Quantum Hall

Berry v. Klitzing Laughlin Thouless Haldane

von Klitzing, Dorda & Pepper (1980)

Integer Quantum Hall

�ak = i∑

n=1,2N

〈un,k|∇k|un,k〉

Berry v. Klitzing Laughlin Thouless Haldane

Kane Mele Zhang Molencamp Hasan Balents Moore Roy Fu

von Klitzing, Dorda & Pepper (1980)

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

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

εp -+

-+

++ε-t

tp

V

1D Topological Insulator

IgorTamm

WilliamShockley

P=-1

P=+1

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

εp -+

-+

++ε-t

tp

V

1D Topological Insulator

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)

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

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

Topological Texture of Berry Connection

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

Z2= 1 Z2= -1

Topological Texture of Berry Connection

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

Z2 =∏

i

δ(Γi)

Z2= -1Z2= 1

Topological Texture of Berry Connection

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)

Are Kondo insulators topological?

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

Are Kondo insulators topological?

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

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

Are Kondo insulators topological?

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

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

Many Body Localized

Are Kondo insulators topological?

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

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

Many Body Delocalization

Many Body Localized

Are Kondo insulators topological?

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

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

Many Body Delocalization

Many Body Localized

Are Kondo insulators topological?

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

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).

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

Many Body Delocalization

Many Body Localized

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

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

Three crossings: THREE DIRAC CONESON SURFACE.

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

Three crossings: THREE DIRAC CONESON SURFACE.

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

Three crossings: THREE DIRAC CONESON SURFACE.

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

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.

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

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.

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

=3

H(k) =(

εk V sk · �σV sk · �σ ε f k

)

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.

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

=3

H(k) =(

εk V sk · �σV sk · �σ ε f k

)Like He-3B: an adaptive insulator.

sk = (sin kx, sin ky, sin kz) ∼ k

d(k) = ks(k) = k

X

Vαβ(k) = Vsk · �σαβ

(a)

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

Three crossings: THREE DIRAC CONESON SURFACE.

Is SmB6 a topological Kondo insulator?

SmB6 Surface Conductivity

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.

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.

Large Vertical Resistance indicatesconductivity is from the surface.

SmB6 Surface Conductivity Bulk Insulator

Surface Conductivity

Robustness/Sensitivity to potential/magnetic scattering.

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.

Large Vertical Resistance indicatesconductivity is from the surface.

SmB6 TKI Check List.

SmB6 TKI Check List.

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

SmB6 TKI Check List.

5d-band

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

SmB6 TKI Check List.

5d-band

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

SmB6 TKI Check List.

5d-band

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

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

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)

Bulkf states

�

� Γ

M

X

_

__ kx

ky

Low

FHigh

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)

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

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

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

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

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

Kondo Breakdown at surface.

Lower co-ordinationat surface dramaticallysuppresses the Kondotemperature

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

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

ARPES: vs~ 220-300 meVA

10x too small! AFS/(2π)2 = Δnf

Theory: vs~ 30-50 meVA

Kondo Breakdown at surface.

Lower co-ordinationat surface dramaticallysuppresses the Kondotemperature

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

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

ARPES: vs~ 220-300 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

Kondo Breakdown at surface.

Lower co-ordinationat surface dramaticallysuppresses the Kondotemperature

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

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

I. Kondo Breakdown

AFS/(2π)2 = Δnf

Kondo Breakdown at surface.

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

Phys. Rev. Lett. 114:177202 2015.

I. Kondo Breakdown

AFS/(2π)2 = Δnf

Kondo Breakdown at surface.

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

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

Phys. Rev. Lett. 114:177202 2015.

I. Kondo Breakdown

AFS/(2π)2 = Δnf

Kondo Breakdown at surface.

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

Surface Kondo physics? Magnetism, QCP even superconductivity.

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

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

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

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

IV. Field effect

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

• 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!