The Story of SmB6 - Quantum Condensed Matter Journal Clubqcmjc/talk_slides/QCMJC... · 10/9/2014 · Quantum Condensed Matter Journal Club Adhip Agarwala Department of Physics Indian

The Story of SmB6Quantum Condensed Matter Journal Club

Adhip Agarwala

Department of PhysicsIndian Institute of Science

[email protected]

October 9, 2014

Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 1 / 32

Why this topic?

(Nature, Dec 2012)


Why this topic?

(Nature, Dec 2012)


About half of these total papers in last 4 years.and about 30 of these in this year !


About half of these total papers in last 4 years.

and about 30 of these in this year !


About half of these total papers in last 4 years.and about 30 of these in this year !


but first things first..

DISCLAIMERThe speaker not an expert!


but first things first..

DISCLAIMERThe speaker not an expert!


Major References

End States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014

Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)


Major References

End States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014

Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)


Major References

End States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)


Outline

The StageI Electronic Configuration and Structure.I The early R vs T Measurement on SmB6

Act II Anderson Impurity ModelI Kondo EffectI Kondo Lattice

Act III 1D Topological Insulator

Act IIII 1D Topological Kondo InsulatorI Some understanding of the experiments.I Comments on 3D TKI.

Conclusions


Outline





Conclusions


Outline





Conclusions


Outline





Conclusions


Outline





Conclusions


Outline





Conclusions


Where exactly are these elements?


Where exactly are these elements?


And..

Electronic ConfigurationSm = [Xe] 4f 6 6s2

B = [He] 2s2 2p1

Sm is in a mixed valence state with valency 2.7+

Review, HasanAdhip Agarwala (IISc) The Story of SmB6 October 9, 2014 9 / 32

R − T MeasurementsFor SmB6

(Allen et al., PRB 20, 12(1979).)

Metal?at ≈ 300KAg ≈ 10−6Ωcm,Hg ≈ 10−4Ωcm

(Ziman, Theory ofTransport in Metals, 1960)

Insulator?at ≈ 20KSi ≈ 104Ωcm,glass ≈ 1012Ωcm

(Fritzsche, J. Phys. Chem.Solids 6 69, 1958)



(Allen et al., PRB 20, 12(1979).)

Metal?

at ≈ 300KAg ≈ 10−6Ωcm,Hg ≈ 10−4Ωcm






(Allen et al., PRB 20, 12(1979).)







(Allen et al., PRB 20, 12(1979).)







(Allen et al., PRB 20, 12(1979).)



Insulator?

at ≈ 20KSi ≈ 104Ωcm,glass ≈ 1012Ωcm




(Allen et al., PRB 20, 12(1979).)







(Allen et al., PRB 20, 12(1979).)






Outline





Conclusions


Towards Kondo Effect..

Now SmB6 has f levels, so how about a single f level in a metal?

















Anderson Impurity Model

Hamiltonian(Bath)

H =∑kσ

εk C†kσCkσ (1)

Impurity Site∑σ

(εf C†fσCfσ) + Un↑n↓ (2)

Hybridization

∑k ,σ

(V√Ω

C†fσCkσ +V√Ω

∗C†kσCfσ) (3)

Anderson(1961)Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 13 / 32


Hamiltonian(Bath)

H =∑kσ

εk C†kσCkσ (1)

Impurity Site∑σ


Hybridization

∑k ,σ

(V√Ω

C†fσCkσ +V√Ω

∗C†kσCfσ) (3)



Hamiltonian(Bath)

H =∑kσ

εk C†kσCkσ (1)

Impurity Site∑σ


Hybridization

∑k ,σ

(V√Ω

C†fσCkσ +V√Ω

∗C†kσCfσ) (3)


Kondo Effect

T TK

low T Hamiltonian

H =∑

kσ ε(k)C†kσCkσ +Js · S

Hewson, The Kondo problem to heavy fermions (CUP), 1997.Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 14 / 32

Kondo Effect

T TK

low T Hamiltonian

H =∑



Kondo Effect

T TK

low T Hamiltonian

H =∑



Kondo Effect

T TK

low T Hamiltonian

H =∑



Kondo Effect

T TK

low T Hamiltonian

H =∑



The Kondo Lattice

Single Impurity(or f level)

at high T → local momentat low T ,→ Js · S.

What has this to do with SmB6?There is no impurity there, eachSm atom has a f level...okay! So, put a f level at each site!and at low T

Kondo Lattice HamiltonianH =

∑k εk c†k ck +

∑i JK Si · si +JH

∑i,j Si · Sj


The Kondo Lattice

Single Impurity(or f level)at high T → local moment

at low T ,→ Js · S.



∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice

Single Impurity(or f level)at high T → local momentat low T ,→ Js · S.



∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice


What has this to do with SmB6?

There is no impurity there, eachSm atom has a f level...okay! So, put a f level at each site!and at low T


∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice


What has this to do with SmB6?There is no impurity there, eachSm atom has a f level.

..okay! So, put a f level at each site!and at low T


∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice


What has this to do with SmB6?There is no impurity there, eachSm atom has a f level...

okay! So, put a f level at each site!and at low T


∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice


What has this to do with SmB6?There is no impurity there, eachSm atom has a f level...okay! So, put a f level at each site!

and at low T


∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice




∑k εk c†k ck +


∑i,j Si · Sj


The Kondo Lattice



Kondo Lattice Hamiltonian

H =∑

k εk c†k ck +∑

i JK Si · si +JH∑

i,j Si · Sj


The Kondo Lattice




∑k εk c†k ck

+∑


i,j Si · Sj


The Kondo Lattice




∑k εk c†k ck +

∑i JK Si · si

+JH∑

i,j Si · Sj


The Kondo Lattice




∑k εk c†k ck +


∑i,j Si · Sj


Outline





Conclusions


1− D Topological Insulator!

t1 t1 t1 t1t2 t2 t2 t2

Tight binding dispersion(0 h(k)

h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy

Semi Infinite Chain?

t1 t1t2 t2t2

An edge state exists if t2 > t1!And we can see this from the bulkdispersion,

x

iy

hyt2 > t1

t2 < t1

hx

Shockley(1939), Pershoguba et al.(PRB 86, 075304)(2012)Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 17 / 32


t1 t1 t1 t1t2 t2 t2 t2

Tight binding dispersion

(0 h(k)

h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2

An edge state exists if t2 > t1!

And we can see this from the bulkdispersion,

x

iy

hyt2 > t1

t2 < t1

hx



t1 t1 t1 t1t2 t2 t2 t2


h∗(k) 0

)h(k) = t1 + t2eik

h(k) = (t1 + t2 cos(k)) + it2 sin(k)

x

iy

hx

hy


t1 t1t2 t2t2


x

iy

hyt2 > t1

t2 < t1

hx


And the Story Ahead..

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉h(k) = (t1 + t2 cos(k)) + it2 sin(k)

Lower eigenvector, u(k) =

1√2

(ei tan−1(hy/hx )

−1

)hx = t1 + t2 cos(k)

hy = t2 sin(k)

take derivative and the innerproductand integrate,

0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1

P=0/1, trivial/non-trivial

t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉

h(k) = (t1 + t2 cos(k)) + it2 sin(k)


1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)

take derivative and the innerproduct

and integrate,

0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2



P = e2π

∫BZ A(k)dk



1√2

(ei tan−1(hy/hx )

−1


hy = t2 sin(k)


0.5 1.0 1.5 2.0t2

0.1

0.2

0.3

0.4

0.5

P

t1=1


t1 t1 t1 t1t2 t2 t2 t2


Reality Check!

You told about a single impurity in a metal

I and some low energy system of JS.sI also something about Kondo Lattice..I Hamiltonian

H =∑

k εk c†k ck +


∑i,j Si · Sj

and then 1D topological insulator,

t1 t1 t1 t1t2 t2 t2 t2

I and about a quantity polarization PI and edge states? etc.

..And the title of your talk is SmB6?


Reality Check!

You told about a single impurity in a metalI and some low energy system of JS.s

I also something about Kondo Lattice..I Hamiltonian

H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!

You told about a single impurity in a metalI and some low energy system of JS.sI also something about Kondo Lattice..

I HamiltonianH =

∑k εk c†

k ck +∑


i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!

You told about a single impurity in a metalI and some low energy system of JS.sI also something about Kondo Lattice..I Hamiltonian

H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2

I and about a quantity polarization P

I and edge states? etc.



Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




Reality Check!


H =∑

k εk c†k ck +


∑i,j Si · Sj


t1 t1 t1 t1t2 t2 t2 t2




A Closer Look!


A Closer Look!


Outline





Conclusions


1D Topological Kondo Insulator

HamiltonianH = Hc + HH + HK

Hc = −t∑

j,σ(c†j+1σcjσ + H.c)

HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)

2 Sj ·p†j,ασαβpj,β

pj,σ ≡ cj+1,σ − cj−1σ.

Alexandrov et al. arXiv:1403.6819v1, PRB 90, 115147(2014)Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 22 / 32



Hc = −t∑


HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)






Hc = −t∑


HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)






Hc = −t∑


HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)






Hc = −t∑


HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)






Hc = −t∑


HH = JH∑

i Sj · Sj+1

HK =∑

j,αβJK (j)




Equation Overdose

H = Hc + HH + HK

H = −t∑

j,σ(c†j+1σcjσ + H.c) + JH∑

i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f

†jσσσσ′ fjσ′ ; nf ,j = 1

HH =−JH

∑j,αβ(f †j+1,αfjα)(f †j,β fj+1β)

HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f

†jσσσσ′ fjσ′ ;

nf ,j = 1

HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)

+∑j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+

∑j λj (nf ,j − 1)


Equation Overdose

H = Hc + HH + HK

H = −t∑


i Sj · Sj+1 +∑

j,αβJK(j)


Sj =∑σσ′ f


HH =−JH


HK =

−JK∑

j,αβ

(f †j,αpjα

)(p†j,β fjβ

)

H →Hc +

∑j,σ

(∆j f†j+1,σfj,σ + H.c +

|∆j |2JH

)+∑

j,σ

(Vj (c† j+1σ − c† j−1σ)fjσ + H.c +

|Vj |2JK (j)

)+∑

j λj (nf ,j − 1)


Insulator in Kondo Lattice?

HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑

jσ V (C† j+1,σ −C† j−1,σ)fjσ + h.c +∑jσ ∆(f † j+1,σfj,σ + h.c) +

∑j λnf ,j

New fermions

Sj · σαβpj,β ≡(

2VJK

)fj,α

p† j,βσβα · Sj ≡(

2VJK

)f † j,α

HTB =∑

k (c†kσ, f†kσ)(

−2t cos k −2i V sin k2iV sin k 2∆ cos k + λ

)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.)

+∑jσ V (C† j+1,σ −C† j−1,σ)fjσ + h.c +∑jσ ∆(f † j+1,σfj,σ + h.c) +

∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑

jσ V (C† j+1,σ −C† j−1,σ)fjσ + h.c

+∑jσ ∆(f † j+1,σfj,σ + h.c) +

∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑


∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑


∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑


∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑


∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)



HamiltonianH = −t

∑jσ(C† j+1,σCj,σ + h.c.) +∑


∑j λnf ,j

New fermions


2VJK

)fj,α


2VJK

)f † j,α

HTB =∑



)(ckσfkσ

)


Understanding R vs TT TK

Js · STTK

(Allen et al., PRB 20, 12(1979).)



Js · STTK

(Allen et al., PRB 20, 12(1979).)



Js · STTK

(Allen et al., PRB 20, 12(1979).)



Js · S

TTK

(Allen et al., PRB 20, 12(1979).)



Js · S

TTK

(Allen et al., PRB 20, 12(1979).)



Js · S

TTK

(Allen et al., PRB 20, 12(1979).)



Js · S

TTK

(Allen et al., PRB 20, 12(1979).)



Js · STTK

(Allen et al., PRB 20, 12(1979).)


Topology?

HTB =∑



)(ckσfkσ

)

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉t = ∆ = Vu(k) =

1√2

(cos(k/2)eik/2

−isin(k/2)eik/2

)

P = e/2! non − trivial


Topology?

HTB =∑



)(ckσfkσ

)

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉t = ∆ = Vu(k) =

1√2

(cos(k/2)eik/2

−isin(k/2)eik/2

)



Topology?

HTB =∑



)(ckσfkσ

)

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉

t = ∆ = Vu(k) =

1√2

(cos(k/2)eik/2

−isin(k/2)eik/2

)



Topology?

HTB =∑



)(ckσfkσ

)

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉t = ∆ = Vu(k) =

1√2

(cos(k/2)eik/2

−isin(k/2)eik/2

)



Topology?

HTB =∑



)(ckσfkσ

)

P = e2π

∫BZ A(k)dk

..A(k) = −i〈u(k)|∇k |u(k)〉t = ∆ = Vu(k) =

1√2

(cos(k/2)eik/2

−isin(k/2)eik/2

)



But SmB6 is not a 1D system!

3D topological insulators have a different story..

and to characterize them we have four integers νo, ν1, ν2, ν3

which tells us about the kind of surface states etc.

SmB6 has a BCC lattice..In a series of papers, in which spin orbit coupling is included in thehopping elements..It was predicted that SmB6 may be a Topological Kondo Insulator whichhas robust surface states.These conclusions are drawn from a mean field calculation of the Kondolattice hamiltonian similar in spirit to what we saw for 1D problem.Look at experiments now..

Dzero et al. PRL 104,106408(2010), PRB 85, 045130 (2012)Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 27 / 32


3D topological insulators have a different story..and to characterize them we have four integers νo, ν1, ν2, ν3












SmB6 has a BCC lattice..

In a series of papers, in which spin orbit coupling is included in thehopping elements..It was predicted that SmB6 may be a Topological Kondo Insulator whichhas robust surface states.These conclusions are drawn from a mean field calculation of the Kondolattice hamiltonian similar in spirit to what we saw for 1D problem.Look at experiments now..





SmB6 has a BCC lattice..In a series of papers, in which spin orbit coupling is included in thehopping elements..

It was predicted that SmB6 may be a Topological Kondo Insulator whichhas robust surface states.These conclusions are drawn from a mean field calculation of the Kondolattice hamiltonian similar in spirit to what we saw for 1D problem.Look at experiments now..





SmB6 has a BCC lattice..In a series of papers, in which spin orbit coupling is included in thehopping elements..It was predicted that SmB6 may be a Topological Kondo Insulator whichhas robust surface states.

These conclusions are drawn from a mean field calculation of the Kondolattice hamiltonian similar in spirit to what we saw for 1D problem.Look at experiments now..





SmB6 has a BCC lattice..In a series of papers, in which spin orbit coupling is included in thehopping elements..It was predicted that SmB6 may be a Topological Kondo Insulator whichhas robust surface states.These conclusions are drawn from a mean field calculation of the Kondolattice hamiltonian similar in spirit to what we saw for 1D problem.

Look at experiments now..







Understanding R vs T again

Why does this saturate?Wolgast(2013)



Why does this saturate?

Wolgast(2013)



Why does this saturate?

Wolgast(2013)



Why does this saturate?Wolgast(2013)


Another Experiment

(Kim et al. 2013)


Outline





Conclusions


Conclusions and Open questions?

Evidence of surface transport in SmB6 is there. Attempted a qualitativeunderstanding of experiments using a toy 1D model. Deeperunderstading needs us to go to 3D TKI.

To prove conclusively that SmB6 is indeed a TKI requires many morechecks!These include robustness against scattering, disorder etc. (Kim et al.Paglione Group)and ARPES studies to check the actual dispersion etc. Some of thesehave been done. (Hasan, Review)There are still some unsettled issues.(Coleman, APS Talk 2014)

SmB6 belongs to the field of heavy fermions, which has variety of kinds ofsuperconductivity, magnetic phases, fermi and non fermi liquids etc.Many of the theories regarding these involve reaching a mean fieldhamiltonian.Can these material systems be test beds for variety of models innon-interacting systems involving topology etc.



Evidence of surface transport in SmB6 is there. Attempted a qualitativeunderstanding of experiments using a toy 1D model. Deeperunderstading needs us to go to 3D TKI.To prove conclusively that SmB6 is indeed a TKI requires many morechecks!

These include robustness against scattering, disorder etc. (Kim et al.Paglione Group)and ARPES studies to check the actual dispersion etc. Some of thesehave been done. (Hasan, Review)There are still some unsettled issues.(Coleman, APS Talk 2014)




Evidence of surface transport in SmB6 is there. Attempted a qualitativeunderstanding of experiments using a toy 1D model. Deeperunderstading needs us to go to 3D TKI.To prove conclusively that SmB6 is indeed a TKI requires many morechecks!These include robustness against scattering, disorder etc. (Kim et al.Paglione Group)

and ARPES studies to check the actual dispersion etc. Some of thesehave been done. (Hasan, Review)There are still some unsettled issues.(Coleman, APS Talk 2014)




Evidence of surface transport in SmB6 is there. Attempted a qualitativeunderstanding of experiments using a toy 1D model. Deeperunderstading needs us to go to 3D TKI.To prove conclusively that SmB6 is indeed a TKI requires many morechecks!These include robustness against scattering, disorder etc. (Kim et al.Paglione Group)and ARPES studies to check the actual dispersion etc. Some of thesehave been done. (Hasan, Review)

There are still some unsettled issues.(Coleman, APS Talk 2014)




Evidence of surface transport in SmB6 is there. Attempted a qualitativeunderstanding of experiments using a toy 1D model. Deeperunderstading needs us to go to 3D TKI.To prove conclusively that SmB6 is indeed a TKI requires many morechecks!These include robustness against scattering, disorder etc. (Kim et al.Paglione Group)and ARPES studies to check the actual dispersion etc. Some of thesehave been done. (Hasan, Review)There are still some unsettled issues.(Coleman, APS Talk 2014)





SmB6 belongs to the field of heavy fermions, which has variety of kinds ofsuperconductivity, magnetic phases, fermi and non fermi liquids etc.

Many of the theories regarding these involve reaching a mean fieldhamiltonian.Can these material systems be test beds for variety of models innon-interacting systems involving topology etc.




SmB6 belongs to the field of heavy fermions, which has variety of kinds ofsuperconductivity, magnetic phases, fermi and non fermi liquids etc.Many of the theories regarding these involve reaching a mean fieldhamiltonian.

Can these material systems be test beds for variety of models innon-interacting systems involving topology etc.










The End

ReferencesEnd States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014 PRB 90,115147(2014)

Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)Hewson, Alexander Cyril. The Kondo Problem to Heavy Fermions. No. 2.Cambridge university press, 1997.

AcknowledgmentsThanks to Vijay and Aveek for many discussions. Special thanks to Sangramfor references on the experiments. Thanks to many friends for discussions.

Thank you :)


The End

ReferencesEnd States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014 PRB 90,115147(2014)Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014

Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)Hewson, Alexander Cyril. The Kondo Problem to Heavy Fermions. No. 2.Cambridge university press, 1997.


Thank you :)


The End

ReferencesEnd States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014 PRB 90,115147(2014)Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)

Hewson, Alexander Cyril. The Kondo Problem to Heavy Fermions. No. 2.Cambridge university press, 1997.


Thank you :)


The End

ReferencesEnd States in a 1D topological Kondo insulator.Alexandrov et al. arXiv:1403.6819v1 26th March,2014 PRB 90,115147(2014)Topological Insulators, Topological Crystalline Insulators, and TopologicalKondo Insulators (Review Article)M. Zahid Hasan et al. arXiv:1406.1040 2nd June,2014Chapter 17 and 18, Introduction to Many Body Physics.Piers Coleman, unpublished preprint on his webpage, available onrequest (2014)Hewson, Alexander Cyril. The Kondo Problem to Heavy Fermions. No. 2.Cambridge university press, 1997.


Thank you :)


The End


AcknowledgmentsThanks to Vijay and Aveek for many discussions.

Special thanks to Sangramfor references on the experiments. Thanks to many friends for discussions.

Thank you :)


The End


AcknowledgmentsThanks to Vijay and Aveek for many discussions. Special thanks to Sangramfor references on the experiments.

Thanks to many friends for discussions.

Thank you :)


The End



Thank you :)


The End



Thank you :)Adhip Agarwala (IISc) The Story of SmB6 October 9, 2014 32 / 32

Links to References

TheoryI 1D TKII 1D TII 3D TKI 2010I 3D TKI 2012I PC Lecture HF

ExperimentI R vs T 1979I R vs T Surface 2013I Hall 2013I Hasan Review

NotesI Vijay KondoI Vijay TI


Documents

The Story of SmB6 - Quantum Condensed Matter Journal Clubqcmjc/talk_slides/QCMJC... · 10/9/2014 · Quantum Condensed Matter Journal Club Adhip Agarwala Department of Physics Indian