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arXiv:1701.05002 · Physical Review A

Finite-temperature phases of two-dimensional spin-orbit-coupled bosons

Eiji Kawasaki, Markus Holzmann

Published May 10, 2017• 14 citations
arXivHTMLPDF

Abstract

We determine the finite-temperature phase diagram of two-dimensional bosons with two hyperfine (pseudospin) states coupled via a Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berezinskii-Kosterlitz-Thouless superfluid phase with quasi-long-range order. We show that the spin order of the quasicondensate is driven by the anisotropy of the interparticle interaction, favoring either a homogeneous plane-wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin-density correlation function. For a fully isotropic interparticle interaction, our calculations indicate a fractionalized quasicondensate where the mean-field degeneracy of the plane-wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single-particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a crossover remains for finite-size systems.

DOI
10.1103/physreva.95.051601

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We determine the finite-temperature phase diagram of two-dimensional bosons with two hyperfine (pseudospin) states coupled via a Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berezinskii-Kosterlitz-Thouless superfluid phase with quasi-long-range order. We show that the spin order of the quasicondensate is driven by the anisotropy of the interparticle interaction, favoring either a homogeneous plane-wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin-density correlation function. For a fully isotropic interparticle interaction, our calculations indicate a fractionalized quasicondensate where the mean-field degeneracy of the plane-wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single-particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a crossover remains for finite-size systems.
In this Rapid Communication we study finite-temperature properties of spin-1/21/21/2 interacting bosons with spin-orbit coupling in two dimensions. When the ground state has stripe order, we show that thermal fluctuations will first melt the stripe order and lead to a superfluid of boson pairs if the spin-orbit coupling is isotropic or nearly isotropic. Such a phase supports fractionalized quantum vortices. The Kosterlitz-Thouless transition from superfluid to normal state is driven by proliferation of half vortices. When the ground state is a plane-wave state, the transition to normal state is driven by conventional Kosterlitz-Thouless transition. However, the critical temperature will drop to zero for isotropic spin-orbit coupling.
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We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson ttt matrix at zero energy. Then, with the ttt matrix as the effective interaction, we find the ground-state phase diagrams of bosons in mean field as a function of the spin-orbit coupling, the anisotropy, and the scattering lengths between particles in the same and in different pseudospin states. The resulting phase diagrams have much richer structures than those obtained using mean-field couplings, exhibiting three different phases: a plane-wave condensate, a striped condensate, and an unstable phase. The differences between the present approach using the ttt matrix compared to using mean-field couplings is significant for large scattering lengths, large spin-orbit-coupling strength, or small anisotropy.
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