Kondo vs. Hubbard superlatticesnqs2014.ws/archive/Presen...Kondo superlattice Hubbard superlattice...

Kondo vs. Hubbard superlattices

Norio KawakamiKyoto University

NQS2014 KyotoNov.4-Dec.2, 2014

Kyoto University

京都

R. Peters(RIKEN)

Y. Tada(ISSP, Tokyo)

Collaborators

S. Ueda(Kyoto)

Kyoto University

京都

LaVO3/SrVO3 superlattice

LaVO3: Mott insulator

SrVO3: metal

CeIn3/LaIn3 superlattice

New platform

Heavy-fermion systems Transition-metal systems

Artificially-madecorrelated superlattices electron correlations

Kondo superlattice Hubbard superlattice

Novel phenomena different from ordinary bulk ones

Shishido et al. (2010) A. David et. al., Appl. 2011

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Outline

How correlated electrons behavein superlattices ?

(1) Kondo superlattice

(2) Hubbard superlattice

Similarity / difference

Kondo superlattice

Artificially-layered heavy-fermion systems


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“Heavy fermions”Correlated metalKondo insulatorsExotic superconductorsAntiferromagnetismFerromagnetism

Kondo Lattice Model

Kondo screening vs RKKY

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RKKY and Kondo effect

Local Kondo couplingfavoring a singlet state:

Kondo insulator at half filling

Magnetic long-range interactionfavoring a magnetic state:

Neel state at half fillingSuperconductor away from half filling

etc

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f-electron superlattices

Shishido et al. Science 327, 980 (2010)Mizukami et al. Nature Phys. 7, 849 (2011)Goh et al. Phys. Rev. Lett. 109, 157006 (2012)

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Shishido et al. Science 327, 980 (2010)Mizukami et al. Nature Phys. 7, 849 (2011)Goh et al. Phys. Rev. Lett. 109, 157006 (2012)

SuperconductivityAntiferromagnetism

f-electron superlattices

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How heavy fermions behave in the superlattice ?

Proximity of the Kondo effect

(1) Heavy fermions(2) Application to STM experiments

Model and Method


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f-electron layer(Kondo-lattice)

non-interacting layerSuperlattice:

Kondo lattice layers (f- layers)noninteracting layers.

n Kondo lattice layers (KLL) m non-interacting layers (NIL)

(n;m) KLL(n)/NIL(m)

Heavy f-electron layersKondo lattice model

Model and Method

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Dynamical Mean Field TheoryMetzner-Vollhardt, Georges- Kotliar et al., etc

Effective bath

c

c

NRG

Model and Method

Single Kondo layer embedded in a 3D metal

Warm up!


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What happens, if a single Kondo lattice is inserted into a 3D metal ?

Single Kondo-layer in 3D

Mixed dimensions

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Kondo lattice gap changes

Inter-layer hoppingGap size decreases

Gap shows a power-lawρ(ω) ～ ω2

Density of States

Inter-layerHopping tz

Kondo-layerMixed dimensions T=0

J/W=0.5


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Layer-dependent DOS

◇ f-electron layer forms the Kondo gap◇ 2kF oscillation of the resonance

Proximity ofKondo effect

T=0


Kondo superlattice

Paramagnetic state


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◇ Peak in the NIL is strongly enhanced

constructiveinterference

◇ f-electron layer forms the Kondo gap

Kondo layer non-Kondo layer

1 Kondo lattice layer 1 non-interacting layer

(1,1)

Paramagnetic state in Kondo superlattice

t = tz

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DOS at the Fermi energy Kondo temperature

1 Kondo lattice layer 1 non-interacting layer

(1,1)

Kondo layer

non-Kondo layer


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1 Kondo lattice layer 2 non-interacting layers

Peak in the NIL is completely suppressed

destructiveinterference

Kondo layer non-Kondo layer(1,2)


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(1,3)-superlatticeresonances at the Fermi energy

Kondo layer non-Kondo layer

1 Kondo lattice layer 3 non-interacting layers

(1,3)


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doping away from half filling

Hole doped systems:Kondo proximity effects are visible: Dip-Peak structure Asymmetric shape

(1,2)Noninteracting

Kondo

T=0


STM experimentsCeCoIn5

Applications

Natural superlattice


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STM ExperimentsVisualizing heavy fermions emerging in a quantum critical Kondo lattice

P Aynajian et al.NATURE 286, 201(2012)

CeCoIn5

Ce-In

Ce layer theory

Co layer theory

Kyoto University

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Two-channel Cotunneling Model

PRL 103, 206402 (2009).M.Maltseva, M. Dzero, and P. Coleman

Interference between two tunneling processesFano-type asymmetric resonance

Serious drawback

tf > tc

large tf at Co siteCeCoIn5

Extrinsic effect

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Our Model

Proximity of Kondo effect

Intrinsic effect !

Superlattice structure

R. Peters and NK (2014)

Tunneling tc into conduction electrons( tf should be small )

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Peters-NK, 2014

CeCoIn5

Temperature dependent LDOS

TK=50K

Ce surface

Co surface

Superlattice structureProximity of Kondo effectIntrinsic phenomenon

ExplainSTM of CeCoIn5

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How heavy fermions behave in the superlattice ?

Summary Part I

Proximity of the Kondo effect

(1) Heavy fermionsconstructive/destructive

(2) Application to experimentsCeCoIn5STM: new mechanism: intrinsic

Hubbard Superlattices

Transition-metal interlayer compounds

S. Ueda(Kyoto)


Kyoto University

京都


SrVO3: metal

……

Superlattice： periodically alignedLaVO3 and SrVO3


Unit cell

ex.) (3Mott, 1metal)

# of Mott, Metal layers

Peak position depends on # of metal layers

U. Lüders et al. J Phys Chem Solids 75 (2014)

Resistiv

ity (Ω

cm） # of Mott layers=6

# of Metal layers

A. David et. al., Appl. Phys. Lett. 98, 212106 2011Temperature

Peak structure in resistivity

Resistance (μΩ)

Recent experiments

T2

logT6 Mott1 metal

logT plot

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SrVO3: metal

……

Superlattice： periodically alignedLaVO3 and SrVO3

Unit cell

ex.) (LaVO3)3/(SrVO3)1

# of LaVO3, SrVO3

What are roles of electron correlations?

‐ Electron interaction U‐ Periodicity of superlattice

Key words

Metal‐insulator transition

Resistiv

ity

# of Mott layer

# of Metal layer=1

W.C.Sheets, et. al. Appl. Phys. Lett. (2007)

Recent experiments


Kondo vs Hubbard

Insulator m≧5

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Mott Ins.

Metal

……

Mott insulator/metal superlattice

Mott insulator：Ui=U=18t Metal：Ui=0

Model

‐Unit cell U U・・・・・・

N M

Mott metal

‐ Extended Hubbard model

Method Dynamical mean‐field＋IPT

U U・・・・・・

N M

Mott metal

Unit cell

Lattice Problem

U U・・・

N

Single‐impurity Problems

Model and Method

‐ Half‐filled paramagnetic case

Results 1 Mott insulator embedded

in a 3D metal


Mixed dimensions

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1 Mott layer in 3D metal

What happens ?・・・

Mott

Metal

・・・

‐ A Mott layer behaves as a barrier‐Metal layers show 2kF oscillation.Common for metal with boundary How “Mott physics” manifests itself ?

Charge gapGapless spin excitationMott insulator

Mott Metal

Distance from Mott layer

Layer dependent DOS

High temperatures

Peak PeakDip

cf Kondo

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What happens ?・・・

Mott

Metal

・・・

Mott Metal

Distance from Mott layerLow temperatures

DipPeak

Dip

1 Mott layer: a resonance peak at ω=02 Metal layers: dip‐peak structures3 Constant DOS at Fermi level: Fermi liquid

Layer dependent DOS

1 Mott layer in 3D metal

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‐Dip‐peak structure

・・・

Mott

Metal

・・・Mott Metal

What are roles of Mott layers?

‐Mott layer at boundary ⇒ develop coherence

DipPeak

Coherent

3 Mott layers in 3D metal

Layer dependent DOS

Incoherent

Decreasing temperature

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Additional fine structures

・・・

Mott

Metal

・・・Mott Metal

What are roles of Mott layers?

Fermi liquid metal realizes

DipPeak

Dip Peak

Dip

# of fine structures = # of Mott layers

Layer dependent DOS

Further decreasing temperature

3 Mott layers in 3D metal

Results 2

Superlattice


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1 Mott layer 1 Metal layer

Mott Metal

MottMetal

(1Mott,1metal)

Unit cellLayer dependent DOS

decreasin

g T

Decreasing temperature

Mott layer: barrier ⇒ correlated metalMetal layer: dip structure is visible

What is a role of superlattice periodicity?

Similar to “Mott layers in 3D metal”

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TMottMetal

Mott

Metal

(1Mott,1metal)

(1Mott,2metal)(1Mott,4metal)

Mott

Metal

(1Mott,3metal)

Mott

Metal1neighbor 2neighbor

1neighbor 2neighbor

Dip‐peak structure is visible for all SLs

Its magnitude shows even‐odd dependenceIntrinsic to Mott/metal interface

T

1 Mott layer m Metal layer

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Odd # of metal layers

(1Mott,1metal)

MetalMott

・・・

Dip Peak Dip ・・・

Dip Peak Dip

Dip Peak Dip

◇ Superlattice

◇ Single Mott layer in 3D metal

Enhanced dip‐peak structure

Constructive interference

Dip‐peak structure &Superlattice periodicity

Cooperative

Commensurate


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Even # of metal layers

MetalMott

・・・

Dip Peak Dip ・・・

◇ Superlattice

◇ Single Mott layer in 3D metal

Suppressed dip‐peak structure

(1Mott,2metal)

Dip Peak DipPeak

Dip Peak DipPeak

Incommensurate

Destructive interference

Dip‐peak structure &Superlattice periodicity

Uncooperative

Even‐odd dependence creates a feedback on the Mott layer


Results 3 ‐Resistivity

comparison with experients


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Electrical resistivity

Peak position T*

Temperature T/t

In‐plane resistivity

Temperature T/t

Out‐of‐plane resistivity

(Mott, Metal)

Both ρXX and ρZZ are in proportion to T2

ρXX shows peak structure at T=T*

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Comparison with experiments

Resistiv

ity

Temperature

1. Peak structure in resistivity

2. Peak‐position of ρXX depends on superlattice structure

Resistiv

ity

Temperature

YES/NO‐ Reconstruction of metallic DOS‐ But even‐odd dependence is opposite

Resistiv

ity3. Metal‐insulator transition YES(1Mott,1metal): conducting(n>1Mott,1metal): insulating

Qualitatively consistent with experiment

‐ Kondo screening ‐ Formation of heavy electron

YES

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Hubbard model within DMFT＋IPT

Summary of part IIWhat happens in superlattices of a Mott insulator ?

1. Density of states in superlattice

2. Resistivity, metal‐insulator nature・ Peak structure in ρXX(T)

・Metal‐insulator transition

3. Comparison with experiments

Superlattice periodicity causesstrong/weak reconstruction

・ Dip‐peak structure in metal layers・ Resonance peak in Mott layers

Problem of Mott reconstruction

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Summary

How correlated electrons behave in the superlattice ?

(1) Kondo superlattice

(2) Hubbard superlattice

Kondo vs. Hubbard superlatticesnqs2014.ws/archive/Presen...Kondo superlattice Hubbard superlattice...

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