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Journal of Physics Conference Series

Current and spin correlations in Fulde–Ferrell–Larkin–Ovchinnikov state of a s-wave superconductor

Poulumi Dey, Saurabh Basu, Rishabh Kishore

Published Jan 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/273/1/012072

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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.
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.
We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarization. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wave vector $Q=\ensuremath{\mid}{k}_{F,\ensuremath{\uparrow}}\ensuremath{-}{k}_{F,\ensuremath{\downarrow}}\ensuremath{\mid}$ is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled one-dimensional (1D) systems and determine the region of stability of the 1D FFLO phase. This picture is corroborated by density-matrix-renormalization-group simulations of the spatial noise correlations in uniform and trapped systems, unambiguously revealing the presence of fermion pairs with nonzero momentum QQQ. This opens up an interesting possibility for experimental studies of FFLO states.
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.
We investigate different physical properties of a spin imbalanced fermionic superfluid described by an attractive Hubbard model in presence of a harmonic trap. To characterize the ground state of such a system, we compute various correlation functions, such as pairing, density and current correlations To underscore the effect of the trap, we compute these quantities as a function of strength of the trapping potential. A distinguishing feature of a superfluid state with population imbalance, is the appearance of a phase with spatially modulating gap function, called the Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) phase which is present for both with and without trap. Trapping effects induce lowering of particle density and yields an empty system in the limit of large trapping depths.
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity, Cooper pairing at finite-momentum driven by spin imbalance, remains difficult to study numerically in two dimensions. The fermion sign problem in the spin-imbalanced attractive Hubbard model severely limits quantum Monte Carlo access to the low temperatures where pairing correlations are most pronounced. We show that the Holstein model, in which the effective attraction is retarded by phonon dynamics, strongly suppresses sign fluctuations under spin imbalance, enabling unbiased determinant quantum Monte Carlo simulations deep in this regime. With increasing magnetization, zero-momentum pairing evolves into finite-momentum FFLO pairing, evidenced by oscillating real-space pair correlations and a shift of the pairing susceptibility peak to finite Q⃗\vec{Q}Q​. The finite-momentum susceptibility substantially exceeds its zero-momentum value. At high density n∼0.875n \sim 0.875n∼0.875, near magnetization m≈1−nm \approx 1-nm≈1−n where the majority-spin density approaches half filling, FFLO pairing coexists with checkerboard charge-density-wave order at short range, while staggered longitudinal spin correlations emerge as a magnetic halo at larger distances. These spatial textures provide experimentally accessible signatures of finite-momentum pairing and motivate cold-atom realizations of FFLO physics.
We study sss-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov--de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous ``breached pair'' superfluid phase. It reveals that Tc{T}_{c}Tc​ scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low Tc{T}_{c}Tc​ itself, while the spin-resolved density of states changes from the ``pseudogapped'' FFLO character to gapless and pseudogapped again with increasing temperature.