an excursion into modern superconductivity: from nanoscience to cold atoms and holography
DESCRIPTION
An excursion into modern superconductivity: from nanoscience to cold atoms and holography. Antonio M. Garc í a- Garc í a. Sangita Bose, Tata, Max Planck Stuttgart. Diego Rodriguez Queen Mary. Masaki Tezuka Kyoto. Yuzbashyan Rutgers. Altshuler Columbia. Jiao Wang NUS. - PowerPoint PPT PresentationTRANSCRIPT
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. García-García
Superconductivity in nanograins
New forms of superconductivity
New tools String Theory
Increasing the superconductor
Tc
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/kF L <<1 Berry, Gutzwiller, Balian
Can I combine this?
Is it already done?
BCS gap equation
?V finite
Δ=?
V bulk Δ~
De-1/
Relevant Scales
Mean level spacing
Δ0 Superconducting gap
F Fermi Energy
L typical length
l coherence length
ξ Superconducting coherence length
Conditions
BCS / Δ0 << 1
Semiclassical1/kFL << 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 Tc
Olofsson (2008): Estimation of fluctuations in BCS, no correlations
Superconductivity in particular geometries
Nature of superconductivity (?) in ultrasmall systems
Breaking of superconductivity for / Δ0 > 1? Anderson (1959)
Experiments Tinkham et al. (1995) . Guo et al., Science 306, 1915, Superconductivity Modulated by quantum Size Effects.
Even for / Δ0 ~ 1 there is “supercondutivity
T = 0 and / Δ0 > 1 (1995-)
Richardson, von Delft, Braun, Larkin, Sierra, Dukelsky, Yuzbashyan
Thermodynamic propertiesMuhlschlegel, Scalapino (1972)
Description beyond BCS
Estimation. No rigorous!
1.Richardson’s equations: Good but Coulomb, phonon spectrum?
2.BCS fine until / Δ0 ~ 2
/ Δ0 >> 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?
In,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
),,'()',(22 LfLk
B
Lk
AIV F
FF
?
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/kFL >> 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
kF = 17.5 nm-1
= 7279/N mV
0 = 0.24mV
L = 6nm, Dirichlet, /Δ0=0.67
L= 6nm, Neumann, /Δ0,=0.67
L = 8nm, Dirichlet, /Δ0=0.32
L = 10nm, Dirichlet, /Δ0,= 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 (0) are larger
The correction to (0) proportional to has different sign
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)
VI
BN
STM tip
Pb/Sn nano-particle
Rh(111)
VI
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 THow?
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 gasMasaki 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 D
Our model!!
quasiperiodic
localization transition at finite = D 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
A solution looking for a problem
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 MillsCFT
Anti de Sitter spaceAdS
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 AdS4 geometry
2. For c3 = c4 = 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 transitionsPhys. Rev. D 81, 041901 (2010)
For c4 > 1 or c3 > 0 the transition becomes first order
A jump in the condensate at the critical temperature is clearly observed for c4 > 1
The discontinuity for c4 > 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 c3 < -1
2/112 cTTO
2. For 2/112
Condensate for c = -1 and c4 = 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 c4
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 = Tc
2. It is possible to study different phase transitions
3. A string theory embedding is known
Holographic approach to phase transitionsPhys. Rev. D 81, 041901 (2010)
A U(1) field , p scalars F Maxwell tensor
E. Yuzbashyan, Rutgers
B. AltshulerColumbia
JD Urbina Regensburg
S. Bose Stuttgart
M. Tezuka Kyoto
S. Franco, Santa Barbara
K. Kern, StuttgartJ. Wang
Singapore
D. RodriguezQueen Mary
K. Richter Regensburg
Let’s do it!!
P. NaidonTokyo