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arXiv:cond-mat/0504665 · Physical Review Letters

Topological Structure of a Vortex in the Fulde-Ferrell-Larkin-Ovchinnikov State

Takeshi Mizushima, K. Machida, Masanori Ichioka

Published Sep 6, 2005• 58 citations
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Abstract

We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core for a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving a microscopic Bogoliubov-de Gennes equation to clarify its physical origin.

DOI
10.1103/physrevlett.95.117003

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We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core for a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving a microscopic Bogoliubov-de Gennes equation to clarify its physical origin.
We theoretically investigate the microscopic structure of neutral Fermionic systems with unequal atomic populations. By using fully microscopic Bogoliubov‐de Gennes framework, we study on the vortex structure in a single‐vortex state with and without the Fulde‐Ferrell‐Larkin‐Ovchinnikov (FFLO) modulation of the pairing field. It is found that the novel local density of states structure appears at intersection point of the FFLO nodal plane and the vortex line, which reflects the topological structure of the pairing field.
The possibility of a Fulde-Ferrell-Larkin-Ovchinnikov-like (FFLO-like) state in a population-imbalanced Fermi gas with a vortex is proposed. Employing the Bogoliubov-de Gennes formalism, we determine self-consistently the superfluid order parameter and the particle number density in the presence of a vortex. We find that, upon increasing the population imbalance, the superfluid order parameter spatially oscillates around the vortex core in the radial direction, indicating that the FFLO-like state becomes stable. We find that the radial FFLO-like states cover a wide region of the phase diagram in the weak-coupling regime at T=0T=0T=0, in contrast with the conventional case without a vortex. We show that this inhomogeneous superfluidity can be detected as peak structures of the local polarization rate associated with the node structure of the superfluid order parameter. Since the vortex in the three-dimensional Fermi gas with population imbalance has been already realized in experiments, our proposal is a promising candidate of a FFLO-like state in cold atom physics.
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two-component Fermi superfluid gases in a toroidal trap. We investigate the stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov--de Gennes equation. We find that two FFLO phases, i.e., the half-quantum-vortex state and the intermediate state of the Fulde-Ferrell (FF) state and the Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half-quantum-vortex state is shown in both the TTT-PPP plane and the TTT-hhh plane. We demonstrate characteristic features of these states, such as the order parameter, flux quantization, and local polarization. Several related works are discussed, and the advantages of cold Fermi gases are indicated.
We study an effect of rotation on the two component Fermi superfluid gases with population imbalance in a toroidal trap. We investigate how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is changed by the rotation using the Bogoliubov-de Gennes equation in the quasi-one-dimensional regime. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in T -Φ plane. We show the order parameter of these states.
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases near the BCS-BEC crossover. We investigate the superfluid gases at low temperatures on the basis of the Bogoliubov--de Gennes equation and examine the stability against thermal fluctuations using the TTT-matrix approach beyond the local-density approximation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap but not in the harmonic trap. The angular FFLO state is stable near the BCS-BEC crossover owing to the formation of pseudogap. Spatial dependences of number density and local population imbalance are shown for an experimental test.