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arXiv:1702.02193 · Physical Review A

Critical behavior in one dimension: Unconventional pairing, phase separation, BEC-BCS crossover, and magnetic Lifshitz transition

Andrzej Ptok, Agnieszka Cichy, Karen Rodríguez, Konrad Jerzy Kapcia

Published Mar 13, 2017• 19 citations
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Abstract

We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground-state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the $\ensuremath{\eta}$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows us to determine optimal regimes for the FFLO phase as well as $\ensuremath{\eta}$-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at $T=0$. Finally, the obtained results show that in spite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.

DOI
10.1103/physreva.95.033613

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The paper is devoted to a study of superconducting properties of population-imbalanced fermionic mixtures in quasi -one-dimensional optical lattices. The system can be effectively described by the attractive Hubbard model with the Zeeman magnetic field term. We investigated the ground-state phase diagram of the model as a function of the chemical potential and the magnetic field. The ground state of the system exhibits the conventional BCS-type superconductivity as well as the unconventional so-called Fulde-Ferrell-Larkin-Ovchinnikov state, in which the total momentum of Cooper pairs is non-zero. We determine the orders of transitions as well as the behavior of order parameters with a change of the model parameters.
We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground-state phase diagrams including the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by atypical behavior of the Cooper-pair total momentum. We show that the momentum changes its value as well as direction with a change of the system parameters. We discuss the influence of Van Hove singularities on the possibility of the reentrant FFLO phase occurrence, without a BCS precursor.
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We investigate the superconductivity of two-dimensional spin-1/2 Fermi systems with ddd-wave altermagnetism under external magnetic field near zero temperature. At large altermagnetic coupling, without magnetic field, we show that altermagnetism drives a second-order phase transition from the standard Bardeen-Cooper-Schrieffer (BCS) state to an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The inclusion of a magnetic field turns the BCS state into a long-sought polarized BCS superconductor with spin-population imbalance. It also shrinks the parameter window of the FFLO state and eventually leads to a nontrivial quantum tricritical Lifshitz point, where two second-order phase transition lines between the polarized BCS, FFLO, and normal states intersect. At small altermagnetic coupling, we find the usual route to the FFLO state driven by magnetic field. The presence of altermagnetic coupling narrows the phase window of the FFLO state and creates another quantum Lifshitz point, where a first-order transition curve meets a second-order transition line. Between the two Lifshitz points, the transition from the polarized BCS state to the normal state is smooth. Our predicted rich phase diagram is relevant to some recently discovered unconventional magnets, including RuO2{\mathrm{RuO}}_{2}RuO2​ that exhibits a relatively high superconducting temperature in the thin film limit under applied strain. Our results of unconventional superfluidity are also testable in ultracold atom laboratories, where a spin-1/2 altermagnetic Fermi gas might be realizable upon loading into two-dimensional Hubbard lattices.
Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to a new phase called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. For the strong SOC strength, the intraband BCS pairing always dominates in the whole parameter regime, including the half filling. We figure out the whole phase diagrams as functions of filling factor, SOC strength, and Zeeman field. Our results are qualitatively different from recent mean-field predictions. Finally, we address that our predictions could be observed in a weaker trapped potential.
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