Birman-Schwinger and the number of Andreev states in Bardeen-Cooper-Schrieffer superconductors

Journal Article · Sun May 01 00:00:00 EDT 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.83.184505· OSTI ID:21544762

Klich, Israel ^[1]

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1. Department of Physics, University of Virginia, Charlottesville, Virginia 22904 (United States)

The number of bound states resulting from inhomogeneities in a BCS superconductor is usually established either by variational means or via exact solutions of particularly simple, symmetric perturbations. Here, we propose estimating subgap states using the Birman-Schwinger principle. We derive upper bounds on the number of subgap states for small normal regions and find a suitable Cwikel-Lieb-Rozenblum inequality. We also estimate the number of such states for large normal regions using high dimensional generalizations of the Szego theorem. The method works equally well for local inhomogeneities of the order parameter and for external potentials.

• OSTI ID: 21544762
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 83, Issue 18; Other Information: DOI: 10.1103/PhysRevB.83.184505; (c) 2011 American Institute of Physics; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BCS THEORY
BOUND STATE
DISTURBANCES
EXACT SOLUTIONS
ORDER PARAMETERS
PERTURBATION THEORY
SIMULATION
SUPERCONDUCTORS
SYMMETRY
DIMENSIONLESS NUMBERS
MATHEMATICAL SOLUTIONS