An excursion into modern superconductivity: from nanoscience to cold atoms and holography

kitefleaΠολεοδομικά Έργα

15 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

68 εμφανίσεις

An excursion into modern
superconductivity: from

nanoscience

to cold atoms and holography

Yuzbashyan
Rutgers

Altshuler
Columbia

Urbina
Regensburg

Richter
Regensburg

Sangita

Bose, Tata,
Max Planck Stuttgart

Kern
Stuttgart

Diego Rodriguez
Queen Mary

Sebastian Franco
Santa Barbara

Masaki
Tezuka

Kyoto

Jiao Wang
NUS

Antonio M.
Garc
í
a
-
Garc
í
a

Superconductivity in
nanograins

New forms of
superconductivity

New tools
String Theory

Increasing the
superconductor
T
c


Superconductivity


Practical


Technical


Theoretical

Enhancement and control of
superconductivity in nanograins

Phys. Rev. Lett. 100,
187001 (2008)

Yuzbashyan
Rutgers

Altshuler
Columbia

Urbina
Regensburg

Richter
Regensburg

Sangita Bose, Tata,
Max Planck Stuttgart

Kern
Ugeda, Brihuega


arXiv:0911.1559

Nature Materials

L

1. Analytical description
of
a
clean, finite
-
size
BCS superconductor?

2.
Are
these results
applicable to realistic
grains?

Main goals

3
. Is it possible to
increase the critical
temperature?

The
problem

Semiclassical
1/k
F

L <<1

Berry, Gutzwiller, Balian

Can I combine
this?

Is it already
done?

BCS gap equation

?

V
finite
Δ
=
?


V bulk

Δ
~

D
e
-
1/



Relevant Scales



Mean level spacing

Δ
0

Superconducting gap


F

Fermi Energy


L typical length

l coherence length


ξ

Superconducting
coherence length

Conditions

BCS

/
Δ
0

<< 1

Semiclassical
1/k
F
L << 1

Quantum coherence
l >> L
ξ

>> L

For Al
the optimal region is L ~ 10nm

Go ahead!

This has not been
done before

Maybe it is possible

It is possible but,
is it relevant?

If so, in what range of
parameters?

Corrections
to BCS
smaller or
larger?

Let’s think about this

A little history

Parmenter
,
Blatt
, Thompson (60’s) : BCS in a
rectangular
grain

Heiselberg (2002): BCS in harmonic potentials, cold atom appl.

Shanenko, Croitoru (2006): BCS in a wire

Devreese (2006): Richardson equations in a box

Kresin, Boyaci, Ovchinnikov (2007) Spherical grain, high T
c

Olofsson (2008): Estimation of fluctuations in BCS, no correlations

Superconductivity in
particular geometries

Nature of superconductivity (?)
in ultrasmall systems

Breaking of superconductivity for


Δ
0

> 1?


Anderson (1959)

Experiments

Tinkham

et al. (1995)
.
Guo

et al., Science
306, 1915, Superconductivity Modulated by
quantum Size

Effects.

Even for

/
Δ
0

~ 1 there is

supercondutivity



T
= 0 and


Δ
0

>
1
(1995
-
)
Richardson, von Delft, Braun, Larkin,
Sierra,
Dukelsky
,
Yuzbashyan

Thermodynamic properties

Muhlschlegel
,
Scalapino

(1972
)

Description beyond
BCS

Estimation.
No rigorous!

1.Richardson’s
equations:
Good but
Coulomb,
phonon
spectrum
?

2.BCS fine until

/
Δ
0

~ 2


/
Δ
0

>> 1

We are in business!

No
systematic

BCS
treatment of the dependence
of size and shape

Hitting a bump

Fine, but the
matrix
elements?

I ~1/V?

I
n,n

should admit a
semiclassical expansion
but how to proceed?

For the cube
yes but for a
chaotic grain
I am not sure


λ

/V ?

Yes, with help,
we
can

From desperation to hope

)
,
,
'
(
)
'
,
(
2
2
L
f
L
k
B
L
k
A
I
V
F
F
F










?

Regensburg, we have got a problem!!!

Do not worry. It is not
an easy job but you are
in good hands

Nice closed
results that do
not depend on
the chaotic
cavity

f(L
,

-


’,

F
) is a
simple function


For l>>L ergodic
theorems assures
universality


Semiclassical (1/k
F
L >> 1) expression
of the matrix elements valid for l >> L!!

ω

=

-



A few
months
later

Relevant in
any mean field approach with
chaotic one body dynamics

Now it is easy

3d chaotic

Sum is
cut
-
off

ξ

Universal function

Boundary
conditions

Enhancement of SC!

3d chaotic

Al grain

k
F

= 17.5 nm
-
1



㴠㜲㜹⽎/浖


0

= 0.24mV


L = 6nm, Dirichlet,

/
Δ
0
=0.67


L= 6nm, Neumann,

/
Δ
0,
=0.67


L = 8nm, Dirichlet,

/
Δ
0
=0.32



L = 10nm, Dirichlet,

/
Δ
0
,= 0.08

For L< 9nm leading
correction
comes
from
I(

,

’)


3d integrable

Numerical & analytical

Cube & rectangle

From theory to
experiments

Real (small) Grains

Coulomb interactions

Surface Phonons

Deviations from mean field

Decoherence

Fluctuations


No, but no strong
effect expected

No, but screening
should be effective

Yes

Yes

No

Is it taken into
account?

L ~ 10 nm Sn, Al…

Mesoscopic corrections versus
corrections to mean field

Finite size
corrections to BCS


Matveev
-
Larkin

Pair breaking
Janko,1994

The leading mesoscopic corrections
contained in

⠰(⁡牥慲来爠

周攠
捯牲散瑩潮c
瑯t

⠰(灲潰p牴楯湡氠瑯t


桡h⁤楦晥牥湴f獩杮

Experimentalists are coming

arXiv:0904.0354v1

Sorry but in
Pb only
small
fluctuations

Are you
300% sure?

Pb and Sn are very different because their
coherence lengths are very different
.

!!!!!!!!!!!!!
!!!!!!!!!!!!!
!!!

However
in Sn is
very
different

BN
STM
tip
Pb/Sn
nano
-
particle
Rh(111)
V
I
BN
STM
tip
Pb/Sn
nano
-
particle
Rh(111)
V
I
5
.
33
Å
0
.
00
Å
5
.
33
Å
0
.
00
Å
0 nm

7 nm

dI
/
dV

)
(
T

+

Theory

Direct observation of thermal fluctuations
and the gradual breaking of
superconductivity in single, isolated
Pb

nanoparticles

?

Pb

Theoretical
description of
dI
/
dV


Thermal fluctuations + BCS Finite size
effects + Deviations from mean field

dI
/
dV

)
(
T

?

Solution

Dynes
formula

Dynes fitting

Problem:


>


Thermal fluctuations

Static Path approach

BCS finite size effects

Part I

Deviations from BCS

Richardson formalism

No quantum fluctuations!

Finite T

How?

T=0

BCS finite size effects

Part I

Deviations from BCS

Richardson formalism

No quantum fluctuations!

Not important h ~ 6nm

Altshuler
,
Yuzbashyan
, 2004

Cold atom physics and novel
forms of superconductivity

Cold atoms
settings

Temperatures can be lowered
up to the nano Kelvin scale

Interactions can be controlled
by
Feshbach

resonances

Ideal
laboratory to
test quantum
phenomena

Until
2005

2005
-

now

1. Disorder &
magnetic fields

2. Non
-
equilibrium
effects

3. Efimov physics

Test
ergodicity

hypothesis

Bound states of three
quantum particles do exist
even if interactions are
repulsive

Test of Anderson
localization, Hall Effect

Stability of the
superfluid

state in a disordered 1D
ultracold

fermionic

gas

Masaki
Tezuka

(U. Tokyo),

Antonio M. Garcia
-
Garcia

What is the effect of disorder
in 1d Fermi gases?

arXiv:0912.2263

Why?

DMRG analysis of

Speckel potential

pure random with correlations

localization for any


Our model!!

quasiperiodic

localization transition at finite
 
2

speckle

incommensurate lattice

Modugno

Only two types of disorder can be
implemented experimentally

Results I

Attractive interactions
enhance localization

U = 1


c

= 1<2

Results II

Weak disorder
enhances
superfluidity

Results III

A pseudo gap
phase
exists.
Metallic
fluctuations
break long
range order

Results IV

Spectroscopic
observables are
not
related
to long
range order

Strongly coupled
field theory

Applications in high
Tc

superconductivity

Why?

Powerful tool to deal with
strong interactions

What

is
next?

Transition from qualitative
to
quantitative


Why
now?

New field.
Potential for high impact

N=4 Super
-
Yang Mills

CFT

Anti de Sitter space

AdS

String theory meets
condensed matter

Phys. Rev.
D 81
, 041901 (2010)

JHEP
1004:092
(2010)

Collaboration with string theorists

Weakly
coupled
gravity dual

Problems


1.
Estimation of the validity of the
AdS
-
CFT approach


2. Large
N
limit

For what condensed matter systems
these problems are minimized?

Phase Transitions triggered by thermal
fluctuations

1. Microscopic Hamiltonian is not
important

2. Large N approximation
OK

Why?

1.
d=2
and AdS
4
geometry

2. For c
3

= c
4

= 0
mean field results

3. Gauge field A is U(1) and


is a scalar

4.
A realization in string theory and M theory is
known
for certain choices of ƒ

5.
By tuning ƒ we can reproduce many
types of phase transitions

Holographic approach to phase transitions

Phys. Rev.
D 81
, 041901 (2010)

For c
4

> 1 or c
3

> 0 the transition becomes first order

A
jump in the condensate at the
critical temperature is clearly
observed for c
4

>
1

The
discontinuity for c
4

> 1 is
a signature of a first order
phase transition.

Results I

Second order phase transitions with non mean field
critical exponents different are also accessible

1. For c
3
<
-
1

2
/
1
1
2





c
T
T
O

2. For


2
/
1
1
2






Condensate for c


=
-
1
and c
4

= ½.
β

= 1, 0.80,
0.65, 0.5 for


=
3, 3.25,
3.5, 4,
respectively

2
1




Results II

The spectroscopic gap
becomes
larger and
the coherence peak narrower as c
4

increases
.

Results III

Future

1. Extend results to
β

<1/2

2. Adapt holographic techniques to spin discrete

3. Effect of phase fluctuations.
Mermin
-
Wegner
theorem?

4. Relevance in high temperature superconductors

THANKS!

Unitarity regime

and Efimov states

3 identical bosons with a
large

scattering length
a

1
/
a

Energy

trimer

trimer

trimer

3 particles

Ratio

= 514

Efimov trimers

Naidon,
Tokyo

Bound states exist even
for repulsive interactions!

Predicted by V.
Efimov in 1970

Form an infinite series
(scale invariance)

Bond is purely
quantum
-

mechanical

What would I bring to
Seoul

National

University
?

Expertise in interesting problems in condensed
matter theory

Cross disciplinary profile and interests with the
common thread of superconductivity

Collaborators

Teaching and leadership experience from a top US
university

Decoherence and
geometrical deformations

Decoherence

effects and small geometrical
deformations

weaken
mesoscopic

effects

How much?

To what extent is
our formalism
applicable?

Both effects can be
accounted analytically by
using an effective cutoff in
the trace formula for the
spectral density

Our approach
provides
an effective
description of
decoherence


Non oscillating
deviations present
even for L ~ l

What
next?

Quantum Fermi gases

From few
-
body to many
-
body

Discovery of new forms
of quantum matter

Relation to high Tc
superconductivity

1. A condensate that is non zero at low T and that
vanishes at a certain T =
T
c


2. It is possible to study different
phase transitions

3. A string theory embedding is
known

Holographic approach to phase transitions

Phys. Rev.
D 81
, 041901 (2010)

A U(1) field

, p scalars
F Maxwell tensor

E. Yuzbashyan,
Rutgers

B. Altshuler

Columbia

JD Urbina


Regensburg

S. Bose


Stuttgart

M. Tezuka


Kyoto


S. Franco,


Santa Barbara

K. Kern,

Stuttgart

J. Wang

Singapore

D. Rodriguez

Queen Mary

K. Richter


Regensburg


Let’s do
it!!



P. Naidon

Tokyo