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arXiv:1307.2242 · Physical Review A

dxy -density wave in fermion-fermion cold-atom mixtures

Chen-Yen Lai, Wen-Min Huang, David K Campbell, Shan-Wen Tsai

Published Jul 14, 2014• 1 citation
arXivHTMLPDF

Abstract

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 ($s$ 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 ${d}_{xy}$-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 ${d}_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for ${d}_{xy}$-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 ${d}_{xy}$-density-wave instability.

DOI
10.1103/physreva.90.013610

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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 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.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
Ultra-cold atom system provides novel technology to simulate traditional solid state physics, including boson and fermion particles. Due to the flexibility of tuning pa- rameters, people can further understand basic physics behind strongly correlated effects, especially mechanism of unconventional density wave and superfluidity. Using weak cou- pling renormalization group method, we propose and study several models which can be realized in experiments. Ranging from most well-known extended Hubbard model, to spin- polarized Fermi Hubbard model and multi-flavor Fermi-Fermi mixture, we establish solid theories to explain the origin of new states of matter, and the experimental techniques to exploit them. The effects of lattice structure and particle density in fermionic system play important roles for determining phase diagram in low energy scale. Due to the presence of lattice, these systems have insulator phase at half-filled. The density imbalance, however, prevents formation of conventional density wave state, and the screening interaction dra- matically affects other species's behavior. The interplay between screening interaction and square lattice is key ingredient of unconventional density wave and superfluidity. Our studyvishows that the unconventional density wave and superfluidity can be realized and detected in ultra-cold atom experiments.
We show that unconventional spin order arises naturally in two-component dipolar Fermi gases of atoms or molecules, which recently became accessible experimentally, in optical lattices. Using an unbiased functional renormalization-group analysis, we find that dipolar interactions lead to an instability of the gas toward an $\ensuremath{\ell}=1$ spin-density wave state. This phase is the particle-hole analog of spin-triplet, ppp-wave Cooper pairs. The order parameter for such spin-density waves of ppp-wave orbital symmetry is a vector in spin space and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half filling on the square lattice as a function of the dipolar orientation and discuss how these exotic spin-density waves emerge amidst competition with superfluid and charge-density wave phases.
We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 two flavors remain half filled by cannibalizing the third flavor. For U<0 and odd N a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.