Universal Impurity-Induced Bound State in Topological Superfluids (original) (raw)
Related papers
Topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases
Physical Review A, 2012
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases under Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well-known that the system is either a Bardeen-Cooper-Schrieffer (BCS) superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zeroenergy Majorana modes. However, in the weakly interacting regime the spin-orbit coupling does not favor the spatially oscillating FFLO order parameter. As a result, it seems difficult to create an inhomogeneous topological superfluid in current cold-atom experiments.
Three-component topological superfluid in one-dimensional Fermi gases with spin-orbit coupling
Physical Review A, 2014
We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of the Zeeman field. By solving the Bogoliubov-de Gennes equations, we obtain the phase diagram at a given chemical potential and order parameter. We show that, with increasing the intensity of the Zeeman field, in addition to undergoing a phase transition from Bardeen-Cooper-Schrieffer (BCS) superfluid to topological superfluid, similar to the two-component system, the three-component system may exhibit some other interesting topological phase transitions. For example, by appropriately adjusting the chemical potential μ, the system can be in a nontrivial topological superfluid in the whole region of the Zeeman field h. It also may initially be a topological superfluid and then translate to a topologically trivial BCS superfluid with increasing the field h. Even more exotically, the system may exhibit a re-entrance behavior, being a topological superfluid at small and large fields but a topologically trivial BCS superfluid in between at a mediate Zeeman field. It can therefore have two regions with zero-energy Majorana fermions. As a consequence of these interesting topological phase transitions, the system of the three-component spin-orbit-coupled Fermi gases in a certain parameter range is more optimizing for the experimental realization of the topological phase due to the smaller magnetic field needed. Thus, a promising candidate for the realization of the topological phase is proposed.
Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases
Physical Review a, 2013
We theoretically predict a new topological matter -topological inhomogeneous Fulde-Ferrell superfluid -in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near s-wave Feshbach resonances. The realization of such a spin-orbit coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a non-trivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel onedimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin orbit coupling (SOC), and an s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T = 0) Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes, and show that the T = 0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with non-zero center of mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center of mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the 3D and the 1D system and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one-dimensional. We also find evidence of the existence of a Zeeman tuned topological quantum phase transition (TQPT) within the FFLO phase itself and for large values of the Zeeman field and small SOC the TQPT gives rise to a topologically distinct FFLO phase.
Fulde–Ferrell–Larkin–Ovchinnikov states in a superfluid Fermi gas
Journal of Physics and Chemistry of Solids, 2005
Recently, both the experimental and theoretical studies to realize superfluid states in atomic gases have been performed by using a 50-50 mixture of atoms in two hyperfine spin states. We discuss favorable superfluid states in an unequal mixture. Such situation is analogous to a superconducting state in the presence of a magnetic field acting on the electron spins and then the natural candidate for the ground state is known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state which is a spatially inhomogeneous superfluid state. We examine the possibility of the FFLO state in two species gas of fermions confined in a realistic three-dimensional harmonic trap. We propose an clear experimental way to create and directly detect the spatially modulated FFLO state from the macroscopic signature.
Quantized Superfluid Vortex Rings in the Unitary Fermi Gas
Physical Review Letters, 2014
In a recent article, Yefsah et al., Nature 499, 426 (2013) [1] report the observation of an unusual excitation in an elongated harmonically trapped unitary Fermi gas. After phase imprinting a domain wall, they observe oscillations almost an order of magnitude slower than predicted by any theory of domain walls which they interpret as a "heavy soliton" of inertial mass some 200 times larger than the free fermion mass or 50 times larger than expected for a domain wall. We present compelling evidence that this "soliton" is instead a quantized vortex ring by showing that the main aspects of the experiment can be naturally explained within the framework of time-dependent superfluid density functional theories (DFTs). We demonstrate how the imprinted domain wall decays into a stable quantized vortex ring which executes nearly harmonic oscillations in agreement with the experiment, including the dependence of the period on interaction strength and aspect ratio, and of anti-damping on temperature. Finally we explain why a rather intricate imaging protocol is required to resolve these objects: the vortex rings, which have a scale of roughly the interparticle spacing and a 50% core depletion, expand asymmetrically by an order of magnitude to produce a resolvable density oscillation that resembles a thick, "heavy soliton" with only a 10% depletion.
Magnetic impurities in a two-dimensional superfluid Fermi gas with spin-orbit coupling
The European Physical Journal B, 2012
We consider magnetic impurities in a two dimensional superfluid Fermi gas in the presence of spin-orbit coupling. By using the methods of t-matrix and Green's function, we find spin-orbit coupling has some dramatic impacts on the effects of magnetic impurities. For the single impurity problem, the number of bound states localized around the magnetic impurity is doubled. For the finite concentration n of impurities, the energy gap is reduced and the density of states in the gapless region is greatly modified.
Physical Review A, 2013
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel onedimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin orbit coupling (SOC), and an s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T = 0) Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes, and show that the T = 0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with non-zero center of mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center of mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the 3D and the 1D system and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one-dimensional. We also find evidence of the existence of a Zeeman tuned topological quantum phase transition (TQPT) within the FFLO phase itself and for large values of the Zeeman field and small SOC the TQPT gives rise to a topologically distinct FFLO phase.
Physical Review Letters, 2007
We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period aL, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V = Vc. We compute the universal ratio Vcma 2 L / 2 at N = ∞ in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.
Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas
Physical Review A, 2010
We study a 1D Fermi gas with attractive short range-interactions in a disordered potential by the density matrix renormalization group (DMRG) technique. This setting can be implemented experimentally by using cold atom techniques. We identify a region of parameters for which disorder enhances the superfluid state. As disorder is further increased, global superfluidity eventually breaks down. However this transition occurs before the transition to the insulator state takes place. This suggests the existence of an intermediate metallic `pseudogap' phase characterized by strong pairing but no quasi long-range order.