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research article

Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples

Frank, Rupert L.
•
Lemm, Marius  
September 1, 2016
Annales Henri Poincaré

This paper consists of three parts. In part I, we microscopically derive Ginzburg–Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator KTc+V to be n-fold degenerate and the resulting GL theory then couples n order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure d-wave order parameters and (b) mixed (s + d)-wave order parameters, in two and three-dimensions. In part III, we present explicit choices of spherically symmetric interactions V which produce the examples in part II. In fact, we find interactions V which produce ground state sectors of KTc+V of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schrödinger operators −∇2+V, for which the ground state is always non-degenerate. Along the way, we prove the following fact about Bessel functions: At its first maximum, a half-integer Bessel function is strictly larger than all other half-integer Bessel functions.

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Type
research article
DOI
10.1007/s00023-016-0473-x
Author(s)
Frank, Rupert L.
Lemm, Marius  
Date Issued

2016-09-01

Published in
Annales Henri Poincaré
Volume

17

Issue

9

Start page

2285

End page

2340

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
CAMP  
Available on Infoscience
October 1, 2020
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/172098
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