Smaller is different and more: Low dimensional superconductivity for new physics and applications - PowerPoint Presentation

Slide1

Smaller is different and more: Low dimensional superconductivity for new physics and applications

Antonio M. García-García Cavendish Laboratory, Cambridge University

Pedro Ribeiro Lisbon

Bermudez

Cambridge

C

azalilla Tsinghua

MayohCambridge

Endo Paris, ENS

Paul

Chesler

Harvard

Tezuka

Kyoto

Hong Liu MIT

Lobos Maryland

Naidon

RIKENSlide2

Mavericks

MgB2 39K 2001 Akimitsu Cuprates ~100K 1986 Mueller & Bednorz

FeSC ~50K 2006 Hotsono

Quantum critical points ©

Superconductivity For Happiness

Trial and errorSlide3

LibrariansControl

Pb ~7K Al ~1K Sn ~3.7K Nb ~9.3K Thinner

Cleaner

Smaller

BCS + (weak) disorder, interactions..Thin films

Josephson Junctions

Nanowires

DFTSlide4

Enhancement of superconductivity? Mavericks meet Librarians

Theory does not driftExperimental ControlConventional SC in low dimensions Artificial

hetero,nano-

structures

Novel Interfaces FeSe

/STO, LAO/STO

True Design of Materials!

A revolution is going onSlide5

Abeles, Cohen, Cullen, Phys. Rev.

Lett., 17, 632 (1966) A.M. Goldman, Dynes, Tinkham…Thin Films?Crow, Parks, Douglass, Jensen,

Giaver, Zeller.... Slide6

Shape Resonances

Blatt, Thompson, Phys. Lett. 5, 6 (1963) Thin FilmsFluctuations?Charge neutrality?

Substrate?

>10Tc!

Bermudez, AGG, Phys. Rev. B 89, 064508 (2014) 89, 024510 (2014)

Yu, et al.,Rev

. B 14, 996 (1976)Slide7

A.M. Goldman et al.

PRL 62 2180 (1989)PRB 47 5931 (1993)

Smoother

Thinner

Disordered

Transition

BKT

(anti)Vortex unbindingSlide8

Xue et al., Science 306, 1915 (2004)

Shih et al., Science 324, 1314 (2009)2000 Atomic scale control

Pb

Size effects but not higher TcSlide9

STM

Epitaxial growthImpurities?

Xue

TsinghuaSlide10

LaAlO3

/SrTiO3 interfaceTriscone et al. , Nature 456 624 (2008)Control

Mannhart

et al., Nature 502, 528 (2013)

Tunability

Localization

Exotic Quantum Matter

TopologySlide11

Cuprates high Tc Heterostructures

Bozovic et al., Nature 455, 782 (2008) Higher Tc!! Slide12

Nature Comm. 3, 931 (2013),

Chinese Phys. Lett. 29 037402 (2012) Iron Based Heterostructures

Feng, et.

al, Nat. Commun. 5:5044 (2014)

Slide13

Bulk

FeSe8K!Slide14

STO is key!Slide15

Nano-grainsSlide16

Abeles, Cohen, Cullen, Phys. Rev.

Lett., 17, 632 (1966) A.M. Goldman, Dynes, Tinkham…Single grains?Crow, Parks, Douglass, Jensen,

Giaver, Zeller.... Slide17

Odd-even effects

 ~ Superconductivity? Isolated grain?Yes, superconductivity

1959

Ralph, Black,Tinkham, Superconductivity in Single

Metal Particles PRL 74, 3241-3244 (1995).

Rediscovery of

Richardson’s equationsNo yet quantitative Slide18

0 nm

7 nmSlide19

BCS superconductivity

Finite size effects

V





Δ

~



D

e-1/



V finite Δ=?

Shell Effects

Parmenter

, Phys. Rev. 166, 392 (1967)L ~ 5nm

Level Degeneracy

20T

c

!Slide20

 >> 

Heiselberg (2002): harmonic potentials, cold atomKresin, Ovchinnikov, Boyaci (2007) : Spherical, too high T

c

Peeters, et al, (2005-): BCS, BdG

in a wire, cylinder..

Olofsson

(2008): Estimation of fluctuations in BCS Devreese

(2006): Richardson equations in a boxGrainsSlide21

 >> 

Expansion in 1/kFL, /∆0

L ~ 10nm

AGG,

Altshuler, PRL 100, 187001 (2008) AGG,

Altshuler, PRB 83, 014510

(2011) Slide22

R ~ 4-30nm

Single, Isolated Sn and Pb grainsA gap is still observedTunneling conductance

Almost hemispherical

Kern

Bose

STM

0 nm

7 nmSlide23

+

Bose, AGG, Nature Materials 2010Slide24

Richardson’s equations

Static Path ApproachBrihuega, AGG, Ribeiro, Bose, Kern PRB 84,104525 (2011)Editor‘s SuggestionQuantum Fluctuations

Thermal Fluctuations

and

Beyond mean field

 ~ Slide25

Quantum + Thermal?Ribeiro and AGG, Phys.

Rev. Lett. 108, 097004 (2012)T, / Δ0 << 1 Divergences at intermediate T

Rossignoli and

CanosaAnn. of Phys. 275, 1, (1999)

Harmful Zero Modes

Polar coordinates

Quantum fluctuations ~ Charging effectsSlide26

Mason, et al, Nature Physics 8 59 (2012)

Josephson array? True phase coherence in single nanograins?

No

M

aybeSlide27

Engineering inhomogeneous materials

Nano-granularity Mayoh, AGG. PRB 90, 134513 (2014

)

James

Mayoh

Disorder,

Mayoh, AGG, 1412.0029 PRX (?)

Global

Tc > Bulk

T

c?

Topology, Matthews,

Ribeiro, and AGG, PRL 112, 247001(2014)

Inhomogeneous JJ arrays

Experimentally feasible

Charging effects

3D nano-spheres

 Slide28

3D Array

H

O

M

O

G

E

NE

OUS

I

N

HO

MOGE

NEOU

SPercolation ?

T

#SCG

Schoen,

Zaikin

, Fazio

Charging

Hopping

Quasiparticles

1

N

ano-Grain

Tunnelling

+Slide29

Percolation?Tc

?T

#

SCgrains

Phase fluctuations?

R=5nm

=1nm =0.3Slide30

 Packing = FCC, BCC, Cubic

Enhancement!

Patent

Mark

Blamire

CambridgeSlide31

SURPRISE!Slide32

Xue

Tsinghua

Lara BenfattoRome

Nano-granularity

Interface design

Xue

et.al PRB B91 060509(R) (2015)Engineering

FeSe/STOSlide33

Inhomogeneities by disorderCan disorder enhance superconductivity?

Global TcEnergy gapOrder parameter

 Slide34

Some bad news

BdG too difficultBCS doable

b

ut valid only if

 Slide35

Anderson TheoremMa & Lee 80’s

Localization and SC can coexist Trivedi et al., Meir 90’s Numerical BdG

Emergent granularity

Disorder and superconductivity

Gorkov, Anderson 50’s

(Do not worry about disorder)

Weak localization weakens SC

Maekawa, Finkelstein 80’s

Pseudogap, Goldstone, Higgs modes, gap distribution function

Sacepe

,

Benfatto,

RaychaudhuriMultifractal

disorderKravtsov

, MirlinSlide36

Enhancement of Tc by disorder

Bianconi, et al., Nature 466, 841 (2010)Fractal distributions of dopants

enhance Tc

in

cuprates

Inhomogeneities

Higher

T

c

PRL 108, 017002 (2012)

PRL, 98

, 027001 (2007)Slide37

Strong

multifractality

and superconductivity

~ 0.4

Feigelman

,

Ioffe

,

Kravtsov

,

Yuzbashyan

, Phys. Rev. Lett. 98, 027001 (2007)

I. S. Burmistrov, I. V.

Gornyi,

A. D. Mirlin, Phys. Rev. Lett. 108, 017002 (2012)

3d MITSlide38

Weak

multifractality and superconductivity

(Ultra) Thin films

2D + Spin orbit

1D + Long Range

energy dependence

J.

Mayoh

and AGG, PRB 92 174526 (2015)

Where?

What?

spatial distribution

Global

T

c

!

Can disorder enhance SC?

How?

Percolation

energy gap

 Slide39

Still unrealistic

Why?

Inhomogenous

SC

Not true Tc

 Slide40

Sacepe

et al., Nat. Phys. 7 239 (2011)

Global Tc?

Lemarie

,

Benfatto

, et al., PRB 87,

184509 (2013)

Tracy-

Widom?

Log-Normal distributionSlide41

Global Tc?

Enhancement?YesBut

Al is fine!

FeSe

/STO?

 Slide42

Out of equilibrium superconductivitySlide43

Unbroken Phase

Broken phase Tc

T(t)

The out of equilibrium birth of a superfluid

Phys. Rev. X 5,

021015 (2015)

Hong Liu

MIT

Paul

Chesler

Harvard

 Slide44

Kibble

J. Phys. A: Math. Gen. 9: 1387. (1976)Vortices in the sky

Causality

Generation of Structure

Cosmic strings

Weyler

, Nature 2008

Krusius

, 2006Slide45

t

Adiabatic

Adiabatic

Frozen

Kibble-

Zurek

mechanism

Zurek

Nature 317

(1985

) 505

T

cSlide46

KZ scaling with the quench speed

Too few defectsSlide47

Adiabatic at tfreeze?

Defects without a condensate?

is relevant

Chesler

, AGG, Liu

Issues with KZ

Too many defects

Phys. Rev. X 5,

021015 (2015)Slide48

ScalingLinear response

Slow Quenches

Frozen

Coarsening

Adiabatic

Frozen

Adiabatic

KZ

US

 Slide49

t

eq is the relevant scaleNumericsU(1) theory with a gravity dualSlide50

Adiabatic

Non adiabatic

Slow quenchesSlide51

~

25 times less defects than KZ prediction!!Relevant for 4He, materials ?SlowFast

Slow

Fast

 Slide52

Out of equilibriumQuantum InformationEmergent quantum matter

Thermalization, steady non-thermal, dynamical transitions Many-body Efimov in condensed matter, topology

Bounds on transport “Universal quantum constraints on the butterfly effect” D.

Berenstein, AGG, 1510.08870

Materials nano

-design

Interfaces

HeterostructuresSlide53

THANKS!

感谢您的关注Slide54

Can disorder enhance superconductivity? Anderson theorem is all but a theorem

Be careful with BCS+PerturbationAnderson theoremAnderson, J. Phys. Chem. Solids 11, 26 (1959

)

Gor'kov and

Abrikosov

Weak localization

Maekawa S, Fukuyama H, 1982

Finkelstein A M, 1987

Numerics

Trivedi

, Meir…..

S

trong coupling and disorder

Experiments

Pratap

, Sacepe…..

Strong disorder and no weak coupling

Abeles,… 60’s

AGG,Tezuka, 2011Slide55

Many body

Efimov Physics

Efimov

70’s

Bound states

Scaling Slide56

RGM

Born-OppenheimerSlide57

Strongly coupled field theory in d

N=4 Super-Yang MillsCFTAnti de Sitter spaceAdSWeakly coupled gravity in d+1

AdS

/CFT

Maldacena1997

Easy to compute in the gravity dual

Detailed dictionary

&

QCD Quark gluon plasma

Holographic superconductivity

2003

2008

2012

Quantum criticality, non-equilibrium.. Slide58
Slide59
Slide60
Slide61
Slide62

Multifractal eigenstates

Anderson Metal-Insulator Transitions

Wegner, Aoki,

Castellani

,

EfetovSlide63

Experimental testsSTM in thin films log2

distribution Transport to test higher global TcL ~ 5-10nm?DisorderNano engineering

Enhancement?

Only in boring materials?

MgB2?

FeSe

? Sure

Conclusion