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arXiv:1206.6797 · Physical Review B

Correlated phases of population imbalanced Fermi-Fermi mixtures on an optical lattice

Chen-Yen Lai, Chuntai Shi, Shan-Wen Tsai

Published Feb 21, 2013• 8 citations
arXivHTMLPDF

Abstract

We study a two-species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with onsite interspecies repulsive interaction. Such a model can be realized in a cold-atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable interspecies interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various $p$-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.

DOI
10.1103/physrevb.87.075134

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We study a two-species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with onsite interspecies repulsive interaction. Such a model can be realized in a cold-atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable interspecies interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various ppp-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.
We present a detailed study of the population imbalanced three-component Hubbard chain with attractive interactions. Such a system can be realized experimentally with three different hyperfine states of ultra cold 6^66Li atoms in an optical lattice. We find that there are different phases that compete with each other in this system: A molecular superfluid phase in which the three fermion species pair up to form molecules (trions), a usual pairing phase involving two species with exactly opposite momenta, and a more exotic generalized Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase consisting of three competing pairing tendencies with different non-zero center-of-mass momenta. At large attractive interactions the system exhibits strong tendencies towards collapse and phase separation. Employing the density-matrix-renormalization-group-method (DMRG) to determine the decay exponents of the various correlators we establish the phase diagram of this model for different fillings and interactions. We also discuss the experimentally relevant situation in a trap and report the existence of an additional region where two species are dynamically balanced.
We study density wave instabilities in a doubly degenerate Fermi-Fermi mixture with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional (sss wave) number density waves are formed with a $\ensuremath{\pi}$-phase difference between them to minimize the interspecies repulsion. Upon moving one species away from half-filling, an unconventional density wave with dxy{d}_{xy}dxy​-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the dxy{d}_{xy}dxy​-density wave phase based on a four-patch model. We find a robust and general mechanism for dxy{d}_{xy}dxy​-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to a phase-space discrepancy for different interspecies umklapp couplings. Using a phase-space argument for leading corrections in the one-loop renormalization-group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intraspecies umklapp couplings and that this triggers the dxy{d}_{xy}dxy​-density-wave instability.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (UUU) and nearest-neighbor (VVV) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when 4V>U4V>U4V>U gives way to a dxy{d}_{xy}dxy​-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive VVV and a range of on-site repulsive interaction UUU. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while dxy{d}_{xy}dxy​ pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
We explore ordering tendencies in weakly coupled Hubbard and t-J models on the two-dimensional square lattice for fermions with N flavors. Such systems may be realized using ultracold atoms with several hyperfine states in optical lattices. The analysis is based on a functional renormalization group approach. In the repulsive Hubbard model for N > 6 and half band filling staggered flux order is found as the dominant instability, in agreement with the large-N limit. In the t-J model without occupancy constraint this type of ground state is suggested already for N > 2. In the attractive case and odd N a full Fermi surface coexists with a superfluid in the ground state. We describe how these unconventional paired states can be identified in the density response of the fermions.
We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.
With a recently developed time-evolving block decimation algorithm, we numerically study the ground-state quantum phase diagram of Fermi mixtures with attractive interspecies interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.