A. V. Lopatin

Collaborators: Nayana Shah, Valerii Vinokur

1. Quantum critical point in thin superconducting films and wires in parallel magnetic field

Argonne National Laboratory

Fluctuation conductivity of thin films and nanowires near a parallel-field-tuned superconducting quantum phase transition

5. Comparison with experimental data

2. Fluctuation conductivity: review of different contributions

4. Magneto-resistance at low temperatures.

3. Fluctuation conductivity of homogeneously disordered films and wires in the vicinity of the quantum critical point.

6. Related theoretical works on magneto-resistance

Quantum critical point in superconductors with magnetic impurities.

Superconductivity in the presence of the magnetic impurities is described in terms of the pairbreakin parameter α ~ magnetic impurity concentration

Tc

α

QCP

Classical thermal fluctuations

Quantum fluctuations

Critical temperature:

Disadvantage – concentration of impurities cannot be tuned.

Classical region was studied by Ramazashvili and Coleman ( PRL 97 ) and Mineev Sigrist ( PRB 2001 ) based on

Abrikosov Gorkov

TDGL:

Example:

QCP in thin superconducting wires and films in parallel magnetic filed.

Thin wire or film in parallel magnetic field.

H H

Thickness (diameter) is less then the coherence length

Critical temperature ?

Depairing parameter α d – diameter of the wire t – thickness of the film

Depairing parameter is a function of the magnetic filed !

Usadel equation close to the critical temperature:

D – diffusion coefficientf – Green- function

Critical temperature:

Fluctuation conductivity around the QCP.

Quantum fluctuations

Tc

QCP

Classical thermal fluctuations

Depairing parameter can be tuned by magnetic filed

Fluctuation conductivity ?

Zeeman effect?

diameter ( thickness )

mean free time

Zeeman effect can be neglected as long as

Review of different contributions to fluctuation conductivity.

Aslamazov-Larkin:

Pair propagators

Gives a positive contribution since it represents an additional channel for conductivity.

In case of dirty superconducting films

Contribution due to local superconducting regions that appear due to thermal fluctuations

Superconducting regions that appear due to thermal fluctuations

I

Diagram:

Current vertices

In case of QPT, at zero temperature one expects less singular contribution.

Maki – Thompson contribution.

Physical meaning: Scattering of an electron by a Cooper pair

Pair propagator Cooperon

MT contribution does not have a prescribed sign a) b)In dirty 2D films:

- Dephasing parameter

a) small dephasing parameter

- stronger than AL correction

b) large dephasing parameter

- weaker than AL correction

Density of states contribution

impurity

Physical meaning: Density of states on the Fermi level is reduced due to proximity to the superconducting state

=

In homogeneously disordered films at temperatures close to the critical DOS contributionis always small.

Negative sign

Exception – granular metals where the DOS contribution may be the dominant one

Fluctuation conductivity at zero temperature.

Analogues diagrammatic approach

Pair propagator:

All diagrams are of the same order !

AL MT

DOS

Low temperatures:

Fluctuation conductivity at zero temperature.

Final answer at T=0:

D – diffusion coefficient

Negative magnetoresistance !

Time dependent Ginzburg-Landau approach would not give the correct result

Plot of dimensionless correction

Numerical coefficient b : b=0.386 for d=1 b=0.070 for d=2

Critical exponent 1

Comparison with other corrections at T=0

1. Localization correction - sensitive to the magnetic filed:

Results in:

due to WL correction: due to proximity to superconducting QCP :

Magnetoresistance:

2. Altshuler-Aronov correction

Not sensitive to the magnetic filed !

Finite temperatures:

Largest contribution comes from the AL correction

Total correction:

Zero temperature correction Finite temperature correction

Classical regime:

Intermediate regime:

In the quantum regime the fluctuation correction is essentially temperature independent

Quantum regime:

Quantum regime

Resistivity behavior as a function of magnetic field ( temperature ).

Tc

α

Classical thermal fluctuations

a.

b.

T

RR

b. Dependence on α for fixed temperature Ta. Dependence on temperature T for fixed α

Experiments.

Amorphous InO films in parallel field:

Gantmakher, Golubkov, Dolgopolov, Shashkin, Tsydynzhapov (2000) Expected to be microscopically granular

Parallel filedPerpendicular filed

Qualitative agreement

Experiment with hollow cylinder

Depairing parameter:

When

Tc

Monotonic dependence on temperature ! – not consistent with the theory.

Lowest temperature 20mk

Liu at. al. Science 294,2332 (2001)

H

Other related theoretical studies

1. Fluctuation conductivity in granular metals:

At T=0 DOS diagram has the largest contribution.

Negative magnetoresistance at T=0.

2. Fluctuation conductivity in thin films in perpendicular magnetic field.

Al three examples give negative fluctuation correction to the conductivity

I. S. Beloborodov and K. B. Efetov, PRL 82, 3332 (1999)  

V. M. Galitski, A.I. Larkin, PRB 63, 174506 (2001)

All three corrections were found to be of the same order at T=0

The total correction is negative.

Conclusions

1. Fluctuation conductivity in the vicinity of parallel field induced superconducting QCP was found

2. Three regimes are identified

3. Zero temperature corrections negative

2d – agreement with theory

1d - ?

5. Effective functional approach ( time dependent Ginzburg- Landau) would fail at T=0.

6. Negative zero temperature fluctuation corrections in all other known cases.