M. IMADA

November 20, 2014, Kyoto

Superconducting mechanisms of

iron-based and cuprate superconductors

Masatoshi ImadaCollaborator: Takahiro Misawa

Shiro Sakai

Marcello Civelli

M. IMADA

Topological states in iridium oxides

A2Ir2O7

Weak topological

insulator:

Protected metallic

state at domain wall

Edge state of 1D weak Chern insulator

⇒ controllability

Na2IrO3

Ab initio study

Zig-zag order in agreement with experiment

How can we approach Kitaev spin liquid?

Yamaji, Nomura, Kurita, Ryotaro Arita, Imada

Phys. Rev. Lett. 113, 107201 (2014)

Yamaji, Imada, Phys. Rev. X 4, 021035 (2014)

M. IMADA

Outline

1. Introduction

2. How to identify the mechanism of high-Tc?

Hidden fermion theory for the cupratesarXiv:1411.4365

3. Ab initio studies on iron-based superconductors

arXiv:1409.6536

Phys. Rev. Lett. 108, 177007 (2012)

4. Mechanism of superconductivity for 2D Hubbard

Phys. Rev. B 90, 115137 (2014)

5. Outlook

M. IMADA

Introduction

M. IMADA

High-Tc superconductors

© Kitagawa &Kittaka

© Atsushi Fujimori

© Y. Kamihara et al.

Superconductivity above 50K

2D anisotropy, square lattice

close to antiferromagnetic order

cuprates, iron-based superconductors

M. IMADA

Outline

1. Introduction

Ab initio Approach

2. How to identify the mechanism of high-Tc?

Hidden fermion theory for the cuprates

arXiv:1411.4365

3. Mechanism of superconductivity for 2D Hubbard

4. Ab initio studies on iron-based superconductors

5. Outlook

M. IMADA

How was the mechanism of the conventional BCS electron-phonon superconductivity solved?

strong-coupling superconductivity

McMillan-Rowell

1965, 1969

N(E

)

E

Eliashberg

eq. α2F

(E)

Emeasured phonon

density of states

neutron scattering

data

anomalous

self-energy

D (E)

S

Pb

dI/

dE

Bosonic (phonon)

glue makes peaks

M. IMADA

Similar peak of anomalous self-energy & gap functionin cuprate models

Maier, Poilblanc,Scalapino

PRL 100, 237001 (2008)

Σano

Origin of peaks is not clear

Le Tacon et al.

Nat. Phys. 7, 725 (2011)

cf. Spin fluctuation scenariot-J model

Gap function

D(w) = z Σano

Kyung et al(08), Civelli(09)

cluster DMFT

2x2 cluster

exact

diagonalization

for T > 0

Hubbard model

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Peak indeed generates high Tc

0

2 Im ( , ')Re ( , 0) '

'd

ww w

w

DD = =

kk

0

2 Im ( , ')( , ) '

Re ( , 0) 'I d

ww

w w

D =

D = k

kk

cf. Maier, Poiblanc,

Scalapino, PRL’08

I(kAN,=0.5)=0.8: 80% of the gap is attributed to the peak!

Gap function

What makes this peak?

Gap function

D(w) = z Σano

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Poles of Snor and Sano

n=0.95

Perfect agreement

Peak in Im Sano comes from

the pole of Sano

arXiv:1411.4365

ImS nor and ImS ano are peaked at the same energy!

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Pole cancellation between Snor and Sano

If the peak directly comes from

bosonic excitations such as

spin fluctuations,

the cancellation cannot happen.

U=8t t’=-0.2tn=0.95T=0.01k=kAN

Poles of Snor/ano are

invisible in A(k,w).

1nor

ano 2

nor *

( , ) ( , ) ( , )

( , )( , )

( , )

G W

W

w w w w

ww

w w

= S

S=

S

k

k

k k k

kk

k

Snor cancels with W !

1( , ) Im ( , )A Gw w

= k k

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Two-component fermion

†

1

1

2

22

[ ( ) ( )( . ) '( ) ]

'1( )

' ( )( ')

' 1

( )( ')( )

'

k k k k k k

k

cc

H k c c k c d h c k d d

G H

G

w w w

w w w w

w

w w w

w

=

= = =

= =

† † †

S=

w

1G

2

'w

S =

mutually hybridizing

c and d fermions

c d

origin of mean field gap

of CDW, SDW(AF), ....

hybridization gap =

zero of Gc = pole of Sc= pole of Gd

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Two-component fermion II

† † † †

[ ( ) ( )( . ) ( )

+ H.c.]

c k k k k d k k

k

c k k d k k

H k c c k c d h c k d d

c c d d

=

D D

† † †

for Λ=0

becomes complicated, but

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Zeros of Green’s function

Poles of Σcnor and Vc completely cancel

⇒ G does not have zeros at the poles of the self-energy!

This cancellation disappears in the pseudogap phase

⇒ Zeros of the quasiparticle Green’s function emerge

at the poles of d-fermion Green’s function

= pseudogap

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Origin of pseudogap

pole of hidden fermion

→ pole of Snor

Below Tc it disappears

because of the cancellation by Sano

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Excellent agreement between CDMFT and TCFT

U=8t’=-0.2n=0.96T=0.01

( ) ~ ( ), ( , ).f c =k k Q Q

-A(k,w): d-wave

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What is the hidden fermion d ?

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Candidate: Quasiparticle vs. Composite fermion

quasiparticle:

kinetic energy gain interaction energy gain

life time

hybridization composite fermion:

Yamaji & Imada

PRL101 (2011) 016404

PRB 83 (2011) 214522

natural extension of exciton

† † 11

(1 ), mi i i im m

d c n m n

( )† † †(1 ) (1 ) 1(1 ) 1

4 2(1 2 ) 2 1 2

m m m m m mUn n U c d d c U d d U n

m m

=

cf. L. Zhu & J.-X. Zhu PRB (2013) hybridizatoin

incoherent part of fermion

d and f satisfy fermion anticommutation approximately

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Origin of high Tc

Peak of Im D = pole of hidden fermion (composite fermion)

Nearly localized incoherent electron

acquire local large binding energy

of pair

hybridization

proximity to quasiparticle

not boson but fermion

boosts up Tc

M. IMADA

Outline

1. Introduction

Ab initio Approach

2. How to identify the mechanism of high-Tc?

Hidden fermion theory for the cuprates

3. Ab initio studies on iron-based superconductors

arXiv:1409.6536,

Phys. Rev. Lett. 108, 177007 (2012)

4. Mechanism of superconductivity for 2D Hubbard

5. Outlook

M. IMADA

Experimental Discovery

Ln = La, Pr, Sm, …

Tc ~ 26K-55K

Kamihara et al, JACS

130, 3296 (2008)

Antiferro-

magnetic

metal

LnFeAs(O1-xFx)

Mukuda et al. PRB

89 (2013) 064511

Zhao et al. Nat .Mat.

7,963 (2008)

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downfolding;

Fe 3d 5 band models

(d model)

First Principles Approach

dimensional

downfolding

→ 2 D effective model

Review: Imada, Miyake:

J. Phys. Soc. Jpn. 79 (2010) 112001

MACEtarget bands

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Ab initio derivation of U by constrained RPA

U / t :d model dp model

LaFePO 8 20

LaFeAsO 9 20

FeTe 11 26

FeSe 14 30 Miyake, Nakamura, Arita, Imada

JPSJ 79 (2010) 044705

smaller size of Wannier

⇒ larger bare Coulomb

smaller covalency

⇒ poor screening

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Variational Monte Carlo Tahara, MI

JPSJ 77 (2008)

114701

fij : pair-dependent variational parameter

optimization of 1000-10000 variables to overcome bias

Gutzwiller factor

quantum number

projection

Gros

Sorella et al.

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variational Monte Carlo; accuracy

Capello et al. PRB 72(2005) 085121

Tomonaga Luttinger liquid

S(0)S(r)∝(logr)1/21/r1+Kρ

R. Kaneko, S. Morita, MI

algebraic decay

∝1/r

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Solution of low-energy solver

ordered magnetic moment

see also Yin Haule Kotliar Nat. Mat. (2011)

Misawa et al.

JPSJ 80 (2011) 023704

PRL 108 (2012) 177007near magnetic quantum critical point

VMC result for

ab initio models of

mother compounds

★ experiment

◇ ab initio model

● λ scaled model

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Detailed Study on Doping Effect

Orbital Selective Mottnessand

Charge Inhomogeneity

arXiv:1409.6536, Nat. Commun. in press

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dx2-y2 Mottness and Stripe Order

Orbital selective Mott insulator

Ishida, Liebsch

Misawa, Imada

2 2X Yd

stays at half filling

for δ<0.05

2 2X Yd

Stripe order

driven by

high-spin to low-spin transition by JH

⇒ strong first order transition

two first-order transitions of

stripe order cf. nematic

LAF

SAF

order

LAF

SAF

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Phase Separation

Phase separation necessarily

appears around the first-order

transitions

0.1 < δ < 0.16

Takeshita, Kadono

New J. Phys. 11 (2009) 1367.

Charnukha et al. PRL 109, 017003 (2012)

Lang et al. PRL 104, 097001 (2010)

Park et al. PRL 102 (2009) 117006

Inosov et al. PRB 79, 224503 (2009)

Lang et al.

Maxwell

construction

NQR

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Superconducting Mechanism

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Superconductivity

s±symmetry （3s）orbital gives

dominant contribution

2 2X Yd

2 2 2 23 , 3 ,lim ( )

s X Y s X YrP r

D =

2 2X Yd

0.08<d<0.32;

SC, N

two local minima

governs magnetism

& superconductivity

⇒ similarity to cuprates

0.2 < d < 0.32

SC ground state

Superconducting order has domes

near first-order jumps

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Role of Electron Correlation

λ

λ = 0.95

Sensitive dependence

on λ

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Phase Diagram

λ～0.96 ⇔ experiment

Possible small role of

electron phonon int.

LaFeAsO1-xHx

Yamaura et al.

QCP

LaFePO

Nomura et al. (2013)

0.4 eV attraction within 0.02 eV

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Smoking Gun of Superconducting Mechanism

and -d2E/dδ2 show

same peak structure:

One-to-one correspondence

2 23 ,s X YD

Superconductivity around

1st order trans. and PS

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Summary

1. Ab intio electronic model shows s± superconducting phase

by electron doping into stripe AF phase of LaFeAsO.

Agreement with experiment

2. Orbital selective Mottness of dx2-y2 orbital holds an underlying

key for the emergence of the high-Tc superconductivity.

Major role for both magnetism and superconductivity.

3. Superconductivity emerges because of the charge instability

accompanied by the PS caused by the strong 1st order

AF/nematic transition.

Smoking gun is found in one-to-one correspondence between

charge compressibility and superconductivity in various cases.

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Single band Hubbard modelMisawa & Imada

Phys. Rev. B 90, 115137 (2014)

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Single band Hubbard model Misawa & Imada

Phys. Rev. B 90, 115137 (2014)

Charge fluctuation

has one-to-one

correspondence to SC

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Conclusion

1. “Hidden fermion” boosts up D and hence Tc

2. Cancellation of Snor and Sano in A(k,w)

3. Hidden fermion may represent incoherent

and excitonic electron ⇔ large gap

proximity to QP

4. Iron-based SC emerges from density fluct.

5. Hubbard model has a similar origin of SC

M. IMADA

Thank you