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arXiv:1508.05321 · Physical Review A

Superfluid phases of fermions with hybridized s and p orbitals

Shaoyu Yin, J. E. Baarsma, Miikka O. J. Heikkinen, J.-P. Martikainen, Päivi Törmä

Published Nov 17, 2015• 15 citations
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Abstract

We explore the superfluid phases of a two-component Fermi mixture with hybridized orbitals in optical lattices. We show that there exists a general mapping of this system to the Lieb lattice. By using simple multiband models with hopping between $s$- and $p$-orbital states, we show that superfluid order parameters can have a $\ensuremath{\pi}$-phase difference between lattice sites, which is distinct from the case with hopping between $s$ orbitals. If the population imbalance between the two spin species is tuned, the superfluid phase may evolve through various phases due to the interplay between hopping, interactions, and imbalance. We show that the rich behavior is observable in experimentally realizable systems.

DOI
10.1103/physreva.92.053616

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We explore the superfluid phases of a two-component Fermi mixture with hybridized orbitals in optical lattices. We show that there exists a general mapping of this system to the Lieb lattice. By using simple multiband models with hopping between sss- and ppp-orbital states, we show that superfluid order parameters can have a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase difference between lattice sites, which is distinct from the case with hopping between sss orbitals. If the population imbalance between the two spin species is tuned, the superfluid phase may evolve through various phases due to the interplay between hopping, interactions, and imbalance. We show that the rich behavior is observable in experimentally realizable systems.
We obtain a phase diagram of the spin-imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types of FFLO phases, i.e., superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the center-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behavior of these phases.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.
We study a balanced two-component system of ultracold fermions in one dimension with attractive interactions and subject to a spin-dependent optical lattice potential of opposite sign for the two components. We find states with different types of modulated pairing order parameters which are conceptually similar to π phases discussed for superconductor-ferromagnet heterostructures. Increasing the lattice depth induces sharp transitions between states of different parity. While the origin of the order parameter oscillations is similar to the Fulde-Ferrel-Larkin-Ovchinnikov phase for paired states with spin imbalance, the current system is intrinsically stable to phase separation. We discuss experimental requirements for creating and probing these novel phases.
The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a kkk-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find a remarkable behavior of its superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show this enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.