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Journal of Shanxi University

Pairing Imbalance of Two-component Ultracold Fermi Gas in Two-dimensional with Spin Orbit Coupling

Zhao Lon

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

We study the ground-state properties of a two-component ultracold superfluid Fermi gas with Rashba spin-orbit coupling at zero temperature in two-dimensional.The gap-order parameter and number densities are found analytically throught the thermodynamic potential at saddle point by using the functional and integral method.We obtain the phase diagram by solve the self-consistent equations.Under the influence of spin orbit couping,and we construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states.The balance of pairing will be broken due to the unequal chemical potentials in the two-component ultracold Fermi gas in two-dimensional with spin orbit coupling.

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We study the ground-state properties of a two-component ultracold superfluid Fermi gas with Rashba spin-orbit coupling at zero temperature in two-dimensional.The gap-order parameter and number densities are found analytically throught the thermodynamic potential at saddle point by using the functional and integral method.We obtain the phase diagram by solve the self-consistent equations.Under the influence of spin orbit couping,and we construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states.The balance of pairing will be broken due to the unequal chemical potentials in the two-component ultracold Fermi gas in two-dimensional with spin orbit coupling.
We investigate the ground state of a uniform two-dimensional polarized Fermi gas with Rashba spin-orbit coupling at zero temperature. We construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states in detail. Due to the competition between polarization and spin-orbit coupling, we find that phase-separated states in the phase diagram can be topologically trivial and nontrivial. These two topologically distinct phase-separated states can not be connected without topological phase transition. The spin-orbit coupling reduces the effect of the population imbalance. Therefore, the phase-separated states are unstable to the superfluid phases for a large spin-orbit coupling.
Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin–orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin–orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin–orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin–orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.
We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is ${\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2$, but it becomes 3 in the three-component case.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.
We investigate the ground state of the two-dimensional polarized Fermi gas with spin-orbit coupling and construct the phase diagram at zero temperature. We find there exist phase separation when the binding energy is low. As the binding energy increasing, the topological nontrivial superfluid phase coexist with topologically trivial superfluid phase which is topological phase separation. The spin-orbit coupling interaction enhance the triplet pairing and destabilize the phase separation against superfluid phase.
Abstract The equal Rashba-Dresselhaus (ERD) spin-orbit coupling, as the first type to be implemented in cold atom experiments, provides a unique platform for exploring topological quantum phases. This work investigates the ground state of a two-dimensional Fermi gas featuring both ERD coupling and a Zeeman field, mapping out its topological phase diagram throughout the BCS-BEC crossover. We classify the homogeneous superfluid phases into topologically trivial gapped or nontrivial gapless phase based on the nodal structure of the quasiparticle excitation spectrum. We reveal the evolution of topological superfluid states under various conditions by systematically characterizing the phase distribution across key parameters including the spin-orbit coupling strength, two-body binding energy, Zeeman field, and chemical potential. Our findings indicate that spin-orbit coupling enhances triplet pairing and stabilizes the gapless superfluid phase. Moreover, small binding energy, and strong Zeeman field are found to promote the emergence of the gapless phase, particularly the US-II phase identified in this work. These results elucidate the phase transition mechanisms in low-dimensional quantum systems.