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arXiv:cond-mat/0604604 · Physical Review Letters

Novel Route to a Finite Center-of-Mass Momentum Pairing State for Superconductors: A Current-Driven Fulde-Ferrell-Larkin-Ovchinnikov State

Hyeonjin Doh, Matthew Song, Hae‐Young Kee

Published Dec 18, 2006• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.97.257001

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Fulde-Ferrell-Larkin-Ovchinnikov Superfluids with PPP-wave Symmetry in Spinless Fermionic Optical Lattices
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose Cooper pairing hosts a non-zero center-of-mass momentum, is predicted and well studied in spin-singlet superfluids in past decades. Different from previous works that engineer FFLO superfluids in spinful cold atoms, we show that the FFLO superfluids, with ppp-wave symmetry, can emerge in a spinless environment associated with nearest-neighbor-site interactions. The novel mechanism of the FFLO superfluids lies on the split Fermi surfaces at low filling factor, which naturally gives rise to Cooper pairings with finite momentum. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. The exotic topological transition can be explained by the spontaneously-broken translational invariance of order parameters. Finally, we investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of the FFLO state, and show its possibility to be observed at finite temperature.
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.
In a magnetic field superconductors (SC) with small orbital effect exhibit the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase above the Pauli limiting field. It is characterized by Cooper pairs with finite center of mass momentum and is stabilized by the gain in Zeeman energy of depaired electrons in the imbalanced Fermi gas. The ground state is a coherent superposition of paired and depaired states. This concept, although central to the FFLO state lacks a direct experimental confirmation. We propose that STM quasiparticle interference (QPI) can give a direct momentum space image of the depaired states in the FFLO wave function. For a proof of principle we investigate a 2D single orbital tight binding model with a SC s-wave order parameter. Using the equilibrium values of pair momentum and SC gap we calculate the spectral function of quasiparticles and associated QPI spectrum as function of magnetic field. We show that the characteristic depaired Fermi surface parts appear as a fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its evolution with field strength. Its observation in STM experiments would constitute a direct proof for FFLO ground state wave function.
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 show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around [ π , π ] evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.