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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
Kyoto University
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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
NQS2014 KyotoNov.4-Dec.2, 2014
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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)
Kyoto University
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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
Kyoto University
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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
NQS2014 KyotoNov.4-Dec.2, 2014
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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!
NQS2014 KyotoNov.4-Dec.2, 2014
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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
Single Kondo-layer in 3D
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Layer-dependent DOS
◇ f-electron layer forms the Kondo gap◇ 2kF oscillation of the resonance
Proximity ofKondo effect
T=0
Single Kondo-layer in 3D
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
Paramagnetic state in Kondo superlattice
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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)
Paramagnetic state in Kondo superlattice
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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)
Paramagnetic state in Kondo superlattice
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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
Paramagnetic state in Kondo superlattice
STM experimentsCeCoIn5
Applications
Natural superlattice
NQS2014 KyotoNov.4-Dec.2, 2014
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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)
NQS2014 KyotoNov.4-Dec.2, 2014
Kyoto University
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LaVO3: Mott insulator
SrVO3: metal
……
Superlattice: periodically alignedLaVO3 and SrVO3
LaVO3/SrVO3 superlattice
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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LaVO3: Mott insulator
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
LaVO3/SrVO3 superlattice
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
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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
1 Mott layer m Metal layer
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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
1 Mott layer m Metal 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