We study the Higgs amplitude mode in the s-wave superfluid state on the honeycomb lattice inspired by recent cold atom experiments. We consider the attractive Hubbard model and focus on the vicinity of a quantum phase transition between semi-metal an
d superfluid phases. On either side of the transition, we find collective mode excitations that are stable against decay into quasiparticle-pairs. In the semi-metal phase, the collective modes have Cooperon and exciton character. These modes smoothly evolve across the quantum phase transition, and become the Anderson-Bogoliubov mode and the Higgs mode of the superfluid phase. The collective modes are accommodated within a window in the quasiparticle-pair continuum, which arises as a consequence of the linear Dirac dispersion on the honeycomb lattice, and allows for sharp collective excitations. Bragg scattering can be used to measure these excitations in cold atom experiments, providing a rare example wherein collective modes can be tracked across a quantum phase transition.
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 pairin
g 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 stripe-like 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 non-trivial 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.
We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined $T$-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of s
tates (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature $T_{rm c}$, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures $T^*$ and $T^{**}$ at which the pseudogap structures in these quantities completely disappear. Determining $T^*$ and $T^{**}$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensate) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures, are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal state properties of this strongly interacting Fermi system.
We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [J. T. Stewart {it et al}., Nature textbf{454}, 744 (2008)]. This quantity gives us very useful information about single-particle properties
in the BCS-BEC crossover. In this letter, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential is an important key to understand the observed spectrum. In the crossover region, while strong pairing fluctuations lead to the so-called pseudogap phenomenon in the trap center, such strong-coupling effects are found to be weak around the edge of the gas. Our results including this effect are shown to agree well with the recent photoemission data by JILA group.
We investigate strong-coupling effects on normal state properties of an ultracold Fermi gas. Within the framework of $T$-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the s
pectral weight, over the entire BCS-BEC crossover region above the superfluid phase transition temperature $T_{rm c}$. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above $T_{rm c}$, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature $T^*$ where the dip structure in DOS vanishes. The value of $T^*$ is shown to be very different from another characteristic temperature $T^{**}$ where a BCS-type double peak structure disappears in the spectral weight. While one finds $T^*>T^{**}$ in the BCS regime, $T^{**}$ becomes higher than $T^*$ in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold $^6$Li and $^{40}$K Fermi gases.
