Chapter

Theoretical Studies of Superconductor–Insulator Transitions

Yen Loh Lee and Nandini Trivedi

in Conductor-Insulator Quantum Phase Transitions

Published in print June 2012 | ISBN: 9780199592593
Published online September 2012 | e-ISBN: 9780191741050 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199592593.003.0017
Theoretical Studies of Superconductor–Insulator Transitions

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This chapter presents a theoretical treatment of two types of superconductor-insulator transitions — the disorder-tuned transition and the parallel-magnetic-field-tuned transition. This is performed within the framework of the attractive Hubbard model, which is a ‘minimal’ lattice model that nevertheless captures much of the essential physics. The effects of hopping, attraction, disorder, and parallel magnetic field are taken into account one by one in proressively more refined approximations, from pairing-of-exact-eigenstates to Bogoliubov-de Gennes to determinant quantum Monte Carlo. By examining the successes and failures of each approach, the chapter elucidates the role of amplitude and phase fluctuations. This pedagogical approach provides considerable details of the calculation of thermodynamic, transport, and spectral properties, such that a suitably inclined reader should be able to reproduce many of the results.

Keywords: superconductivity; unconventional insulators; quantum phase transitions/critical phenomena; strongly correlated fermions; transport properties; spectral functions; disorder; localization; Bardeen-Cooper-Schrieffer; Bogoliubov-de Gennes; quantum Monte Carlo

Chapter.  22831 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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