We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in two dimensions. We argue that at low density, its ground state is a composite fermion state with a Chern-Simons gauge field and filling factor of one. The chemical potential of such a state scales with the density as $\ensuremath{\mu}\ensuremath{\propto}{n}^{3/2}$. This is a lower energy per particle than $\ensuremath{\mu}\ensuremath{\propto}n$ for the earlier suggested ground-state candidates: a condensate with broken time-reversal symmetry and a spin-density wave state.
We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in two dimensions. We argue that at low density, its ground state is a composite fermion state with a Chern-Simons gauge field and filling factor of one. The chemical potential of such a state scales with the density as \ensuremathμ\ensuremath∝n3/2. This is a lower energy per particle than \ensuremathμ\ensuremath∝n for the earlier suggested ground-state candidates: a condensate with broken time-reversal symmetry and a spin-density wave state.
We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the v = 1/2 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of π around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, C P. The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors n/(2n + 1) and (n + 1)/(2n + 1), which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, n and n + 1, is now mapped to the same half-integer filling factor n + 1/2 of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as d -wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while s -wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a C P -breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive theory.
Ground-state phase diagram of two-component Bose gases with Rashba spin-orbit coupling is determined via a variational approach. A phase in which the fully polarized condensate occupies zero momentum is identified. This zero-momentum phase competes with the spin density wave phase when interspecies interaction is stronger than intraspecies interaction, and the former one is always the ground state for weak spin-orbit coupling. When the energies of these two phases are close, there is a phase separation between them. At finite temperature, such a zero-momentum condensation can be induced by a ferromagnetic phase transition in normal state. The spontaneous spin polarization removes the degeneracy of quasiparticles' energy minima, and consequently the modified density of state accommodates a Bose condensation to appear below a critical temperature.
We develop a symmetry classification scheme to find ground states of pseudo-spin-21, spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin-21 condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin-21 system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.
We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature Tc. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below Tc the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.
Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well established microscopic theory of the fractional quantum Hall effect and the 1/2 state, which is based on {\em non-relativistic} composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor ν=1/2 corresponds to an effective time reversal transformation (i.e. {kj}→{−kj}) for composite fermions, and discuss how this connects to the absence of 2kF backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion Λ levels (analogs of electronic Landau levels) we determine the Λ level spacing and find it to be very nearly independent of the Λ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a normal form for the unprojected wave functions of the n/(2pn−1) states that correctly capture the topological properties even without lowest Landau level projection.
We investigate the properties of a condensed-matter system modeled as an ideal atomic Fermi gas with a synthetic spin-orbit coupling. The coupling has been taken to be isotropic and possessing an infinitely degenerate ground state manifold given by a sphere in momentum space is 3D analogue of the Rashba-type. It is found that the chemical potential of such a system exhibits an anomalous behavior typically akin to dimensional reduction. The study shows that some other properties also get affected by the SO coupling and the effects could be attributed to be thermodynamic signatures of Majorana fermions.