• Open Access

Superconductor-Insulator Transition and Fermi-Bose Crossovers

Yen Lee Loh, Mohit Randeria, Nandini Trivedi, Chia-Chen Chang, and Richard Scalettar
Phys. Rev. X 6, 021029 – Published 31 May 2016

Abstract

The direct transition from an insulator to a superconductor (SC) in Fermi systems is a problem of long-standing interest, which necessarily goes beyond the standard BCS paradigm of superconductivity as a Fermi surface instability. We introduce here a simple, translationally invariant lattice fermion model that undergoes a SC-insulator transition (SIT) and elucidate its properties using analytical methods and quantum Monte Carlo simulations. We show that there is a fermionic band insulator to bosonic insulator crossover in the insulating phase and a BCS-to-BEC crossover in the SC. The SIT is always found to be from a bosonic insulator to a BEC-like SC, with an energy gap for fermions that remains finite across the SIT. The energy scales that go critical at the SIT are the gap to pair excitations in the insulator and the superfluid stiffness in the SC. In addition to giving insight into important questions about the SIT in solid-state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.

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  • Received 21 July 2015

DOI:https://doi.org/10.1103/PhysRevX.6.021029

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yen Lee Loh1, Mohit Randeria2, Nandini Trivedi2, Chia-Chen Chang3, and Richard Scalettar3

  • 1Department of Physics and Astrophysics, University of North Dakota, Grand Forks, North Dakota 58202, USA
  • 2Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
  • 3Department of Physics, University of California, Davis, California 95616, USA

Popular Summary

One of the outstanding questions in condensed matter physics is whether and how superconductivity arises in an insulator (in particular, in a Fermi band insulator when attractive interactions are turned on). In the standard paradigm of superconductivity, it arises as an instability of the Fermi surface in a metallic state in the presence of an attractive interaction between electrons. On the other hand, there are many examples in nature where an insulating state undergoes a direct quantum phase transition to a superconductor. Understanding this insulator-to-superconductor transition necessarily requires going beyond the standard paradigm of superconductivity since gapped insulators do not have a Fermi surface of gapless excitations.

Using a two-dimensional lattice fermion model—specifically, a triangular lattice bilayer—and a variety of analytical approaches together with quantum Monte Carlo simulations, we show that there are Fermi-to-Bose crossovers in both the insulator and in the superconductor. We provide clear, experimentally measurable criteria for distinguishing between the fermionic and bosonic regimes in both phases. The Bose insulator has a gap to pair excitations that is smaller than the gap to single-particle excitations. Furthermore, the insulator-to-superconductor transition is from a bosonic insulator to a superconductor in the Bose-Einstein condensate regime in which the minimum superconducting gap opens at zero momentum. This situation is in contrast with the gap in the standard paradigm of superconductivity that opens at the Fermi surface. Our predictions for this specific model can be quantitatively tested in experiments involving cold-atom optical lattices that are realizable using current fabrication technologies.

We expect that our findings will be generalizable to a variety of quantum materials, including disordered thin films and superconductivity in compensated semimetals such as FeSe and FeSeTe.

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Vol. 6, Iss. 2 — April - June 2016

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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