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arXiv:1902.02758 · Physical review. B./Physical review. B

Fate of a strongly correlated d -wave superconductor in a Zeeman field: The Fulde-Ferrel-Larkin-Ovchinnikov perspective

Anushree Datta, Kun Yang, Amit Ghosal

Published Jul 16, 2019• 6 citations
arXivHTMLPDF

Abstract

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of a strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in $d$-wave superconductors. We investigate the FFLO state in a strongly correlated $d$-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and the Gutzwiller approximation. We find that the crucial effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp midgap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational-symmetry-breaking competing order in the ground state. This is demonstrated by considering a broken-symmetry ground state with a simultaneous presence of the $d$-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.

DOI
10.1103/physrevb.100.035114

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The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of a strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in ddd-wave superconductors. We investigate the FFLO state in a strongly correlated ddd-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and the Gutzwiller approximation. We find that the crucial effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp midgap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational-symmetry-breaking competing order in the ground state. This is demonstrated by considering a broken-symmetry ground state with a simultaneous presence of the ddd-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.
ddd-wave FFLO state and charge-2e supersolidity in the ttt-t′t't′-JJJ model under Zeeman fields
Unconventional superconductivity under strong Zeeman fields--particularly beyond the Pauli paramagnetic limit--remains a central challenge in condensed matter physics. The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in particular, remains in need of definitive study within fundamental electronic models. Here we employ state-of-the-art finite-temperature and ground-state tensor network approaches to systematically explore the superconducting (SC) phase diagram of the ttt-t′t't′-JJJ model subjected to Zeeman fields. We find that zero-momentum ddd-wave superconductivity persists until the spin gap closes, coexisting with charge density waves. A novel ddd-wave FFLO phase emerges under a higher Zeeman field even above the Pauli limit, concomitant with a field-enhanced spin density waves. We identify these phases, characterized by the simultaneous presence of pairing condensate and density wave orders, as charge-2e supersolids. Analysis of Matsubara Green's function reveals that the FFLO pairing momentum is locked to the underlying Fermi surface. Our results provide microscopic insights into field-induced unconventional pairing mechanisms and reveal the long-sought FFLO state in a fundamental correlated electron model, offering a promising route for its realization in ultracold atom optical lattice.
In an attempt to characterize the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase in a two dimensional s-wave superconductor, we investigate current-current and spin-spin correlations and compare them with those in the BCS phase. The existence of the FFLO phase is demonstrated using a weakly attractive fermionic Hubbard model in presence of a harmonic trap and a population imbalance, caused by a magnetic field. The lower and upper values of the magnetic field, between which the order parameter shows spatial modulations (owing to a finite center of mass momentum pairing), mark the extent of the FFLO phase. In this regime, the current-current correlations show spatial modulation similar to the behaviour of the order parameter, while the longitudinal spin-spin correlations show modulations with a period half of that of the order parameter in the absence of trap and a bimodal distribution in the presence of the harmonic confinement, thereby underlining a dissimilarity in behaviour between the spin and charge sectors.
We numerically study the ground-state properties of a one-dimensional lattice model in the presence of a quasiperiodic Zeeman field, by means of the density matrix renormalization group algorithm. We map out a global phase diagram, which encloses a Bardeen-Cooper-Schrieffer (BCS) phase, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase where the Cooper pairs obtain a finite center-of-mass momentum, and a localized phase. The FFLO phase is promoted by the quasiperiodic Zeeman field, which demonstrates a power-law pairing correlation with a critical exponent ${\ensuremath{\eta}}_{\mathrm{FFLO}}<1$ decaying much slower than the charge density and spin density correlations. By tuning the interaction and the filling factor, we find the FFLO phase is suppressed in the strong interaction and low filling regions. A large Zeeman field destroys the FFLO state and drives a superconductor-insulator transition. Furthermore, we propose this FFLO phase and the superconductor-insulator transition could be observed in the optical lattice experiment.
We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting ddd-wave altermagnetic spin splitting under sss-wave pairing. Within the Bogoliubov-de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper-type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and sss-wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.
The previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is stabilized by a magnetic field via the Zeeman coupling in spin-singlet superconductors. Here we suggest a novel route to achieve nonzero center-of-mass momentum pairing states in superconductors with Fermi surface nesting. We investigate two-dimensional superconductors under a uniform external current, proportional to a finite pair momentum of q(e). We find that an FFLO state with a spontaneous pair momentum of q(s) is stabilized above a certain critical current that depends on the direction of the external current. A finite q(s) arises in order to make the total pair-momentum of q(t)(=q(s) + q(e)) perpendicular to the nesting vector, which is independent of spin states of Cooper pairs. We also discuss experimental signatures of the FFLO state.