In this article we describe a multi-layered honeycomb lattice model of interacting fermions which supports a new kind of parity-preserving skyrmion superfluidity. We derive the low-energy field theory describing a non-BCS fermionic superfluid phase by means of functional fermionization. Such effective theory is a new kind of non-linear sigma model, which we call double skyrmion model. In the bi-layer case, the quasiparticles of the system (skyrmions) have bosonic statistics and replace the Cooper-pairs role. Moreover, we show that the model is also equivalent to a Maxwell-BF theory, which naturally establishes an effective Meissner effect without requiring a breaking of the gauge symmetry. Finally, we map effective superfluidity effects to identities among fermionic observables for the lattice model. This provides a signature of our theoretical skyrmion superfluidy that can be detected in a possible implementation of the lattice model in a real quantum system.
In this article we describe a multi-layered honeycomb lattice model of interacting fermions which supports a new kind of parity-preserving skyrmion superfluidity. We derive the low-energy field theory describing a non-BCS fermionic superfluid phase by means of functional fermionization. Such effective theory is a new kind of non-linear sigma model, which we call double skyrmion model. In the bi-layer case, the quasiparticles of the system (skyrmions) have bosonic statistics and replace the Cooper-pairs role. Moreover, we show that the model is also equivalent to a Maxwell-BF theory, which naturally establishes an effective Meissner effect without requiring a breaking of the gauge symmetry. Finally, we map effective superfluidity effects to identities among fermionic observables for the lattice model. This provides a signature of our theoretical skyrmion superfluidy that can be detected in a possible implementation of the lattice model in a real quantum system.
I consider a gas of ``free'' anyons with statistical parameter \ensuremath{\delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling \ensuremath{\theta}=1/2\ensuremath{\delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field \ensuremath{\rho}/\ensuremath{\theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If \ensuremath{\delta}=\ensuremath{\pi}/m and the density \ensuremath{\rho}=r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If q is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of \ensuremath{\rho} and \ensuremath{\delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.
The two-body loss associated with inelastic interactions between fermions plays a significant role in realistic many-body systems. Here we study a two-component non-Hermitian Bardeen-Cooper-Schrieffer superfluidity with spin imbalance and two-body loss characterized by a complex-valued s-wave interaction in a square lattice. At the mean-field level, we map out the zero-temperature phase diagram and observe a dissipation-induced transition from superfluid to normal phase as well as a distinctive revival of the superfluid state in the weakly interacting regime applicable to both spin-balanced and spin-imbalanced systems. In the spin-imbalanced case, we find that the effective density of states involving weight functions reduces the regions in k space contributing to pairing, hence leading to a pronounced expansion of the normal phase on the phase diagram. Additionally, we analyze the order parameter, condensate energy, quasiparticle spectra, momentum distribution, and compressibility to characterize the presenting phases and phase transitions.
Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak coupling, we find that the maximum mean-field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean-field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripelike density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry-breaking charge-ordered state on the honeycomb lattice. The latter provides a nontrivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.
This thesis concerns ultracold two-dimensional atomic gases and the associated novel superfluid phases in an optical lattice subjected to staggered rotations. In the first part, we study the Berezinskii-Kosterlitz-Thouless (BKT) transition in a two-dimensional Bose gas. Motivated by recent experiments on the cold gas in the BKT regime, we employ a modified Popov theory and a renormalization group theory to describe the system. The two-dimensional renormalization group flow equations display unique features, which we interpret as precursors of the BKT physics. We further calculate higher correlation functions close to the BKT transition, which can serve as observables for detecting effects beyond mean-field. Finally, we obtain the density profile under the conditions of the experiment performed in the group of Dalibard in Paris, France. In the second part of the thesis, we study a recent experimental proposal of a time-dependent optical lattice with staggered rotations. We show that in the tight-binding regime, the system can be effectively described by a (Bose-)Hubbard model subjected to an artificial staggered magnetic field. The staggered magnetic field (flux) in the lattice leads to conical points in the band structure which possesses distinct minima for different strength, and can give rise to Dirac-like dispersions. For bosons, we show that besides the homogenous superfluid phase, a staggered-vortex superfluid phase is stabilized for large flux values. We show that the staggered flux renormalizes the phase boundary and find a multi-critical point separating the two superfluid phases and the Mott insulating phase. Finally, the full phase diagram of the generalized Bose-Hubbard model at zero temperature is determined. We then generalize the model for a mixture of ultracold bosons and spin-1/2 fermions. By using the Bogoliubov theory for the bosonic sector, we show that the bosonic superfluid mediates attractive interactions between fermions up to the nearest-neighbor site. The resulting model is an extended Hubbard model in the presence of a staggered magnetic field, where the on-site and the nearest-neighbor attractive interactions can be tuned independently. We then employ the Bardeen-Cooper-Schrieffer theory for superconductivity, by considering an on-site pairing order parameter competing with a nearest-neighbor resonating-valence-bond order parameter. Due to conical points in the energy band, the system possesses quantum critical property and the resulting phase diagram displays features which are strikingly similar to that of high-critical-temperature superconductors or heavy-fermion superconductors.
Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.
We develop a general description of the superconductivity of lattice fermions based on the BCS theory. We propose a modeling of the density of states (DOS) of lattice fermions, where divergent and semi-metallic structures are described by asymptotic expansions around the Fermi energy. This modeling leads to a unified representation of the transition temperature Tc at half filling, which reproduces asymptotic forms of Tc derived in several lattices, such as the square, honeycomb, and Lieb lattices, for the weakly interacting limit. The derived asymptotic forms of Tc are categorized into four types, which is attributed to the different responses of the degenerate fermions depending on the DOS structures. The DOS with a delta-functional singularity induces the highest Tc in the weakly interacting region, where Tc is linearly proportional to the pairing interaction U. Three kinds of universal ratios defined in the BCS theory no longer reduce to constants independent of the system parameters but can be parameterized with a certain variable that characterizes the singular structures of the DOS. We find universal relationship among thermodynamic quantities that holds for all parameter regions. Further, we numerically demonstrate that in multi-band systems the correlation effects can induce an effective delta-functional singularity. This phenomenon generally appears in multi-energy (or multi-gap) systems and may provide a plausible guideline for material designs of high-Tc superconductor.