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 insights into important questions about the SIT in solid state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.
Highlights
Understanding superconductor (SC)-insulator transitions (SIT) has long been an important challenge in condensed matter physics
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
Summary
Understanding superconductor (SC)-insulator transitions (SIT) has long been an important challenge in condensed matter physics. Before describing our work in detail, we comment on its relationship with the classic paper by Nozières and Pistolesi on “pairing across a semiconducting gap” [13] They used MFT and estimates of phase fluctuations to analyze superconductivity in a system with a band gap that separates two bands, each with a constant density of states. The SIT has been studied [14] in an attractive Hubbard model on a square lattice with near- and nextnear-neighbor hopping and a staggered (“ionic”) potential to double the unit cell This model differs from ours in that it has one additional parameter and exhibits CDW order in a limiting case. The singleparticle energy gap Eg remains finite across the SIT: Eg 1⁄4 E0g in the insulator, Eg 1⁄4 1⁄2ðE0gÞ2 þ Δ21=2 in the BEC regime near the SIT, and Eg 1⁄4 Δ in the BCS regime
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