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Keskeiskenttätutkimuksia pariutumisesta sekoitetussa geometriassa

Lehikoinen, Joel

Published Jan 1, 2012• 0 citations

Abstract

We study the pairing in an attractively interacting two-component Fermi gas in an optical lattice with a mixed geometry, where up-spin component is loaded on a honeycomb lattice while the down-spin component can occupy only the triangular sub-lattice of the honeycomb lattice. This system realizes a new type of the Fermi- Hubbard model, and we draw the phase diagram of the system within mean field theory. Our system differs from typical systems described by the usual BCS theory: First, it has three quasi particle energy bands. Second, the interaction is spatially inhomogeneous. Third, our system has natural mass-imbalance. We find that the ratio of the gap at zero temperature and the critical temperature does not agree with the value obtained from the BCS theory. We construct the phase diagram of the system by minimizing the grand potential to solve the superfluid order parameter. We find two qualitatively very different phase diagrams, one near the half-filling of the honeycomb lattice and the other at lower densities. In the near-half-filled systems, we find an exotic superfluid phase which resembles the breached pair phase. In this new phase, however, the minority component is not completely depleted in the momentum space breach. The state has two pairing channels. We find polarization even at zero temperature in this phase. We find out that the order of the superfluid phase transition depends also on the density. At low densities, we find tricritical points, at which the order of the transition changes. Near half-filling, we find no tricritical points and that the transition is always of second order. Our system has a nonuniform coupling, arising from the spatially inhomogeneous interaction. We find that this results in a chirally p-wave symmetric pairing, which is different from the usual isotropic (s-wave) pairing.

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We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.

We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.

Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to a new phase called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. For the strong SOC strength, the intraband BCS pairing always dominates in the whole parameter regime, including the half filling. We figure out the whole phase diagrams as functions of filling factor, SOC strength, and Zeeman field. Our results are qualitatively different from recent mean-field predictions. Finally, we address that our predictions could be observed in a weaker trapped potential.

We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the magnetically ordered and superfluid states are not realized, but the metal-insulator transition occurs. This transition is characterized by the Mott and pairing transitions discussed in the conventional repulsive and attractive Hubbard models. In the doped system, commensurability emerges owing to the repulsive interactions and the metal-insulator transition occurs down to quarter-filling.

In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here we take both contributions into account and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction, and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-field theory for the stationary Cooper pairs and the universal Berezinskii-Kosterlitz-Thouless (BKT) relation for the phase fluctuations.

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.