Low-Temperature Properties of the Fermionic Mixtures with Mass Imbalance in Optical Lattice

Abstract

We study the attractive Hubbard model with mass imbalance to clarify the low-temperature properties of fermionic mixtures in an optical lattice. By combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulation, we discuss the competition between the superfluid and density wave states at half filling. By calculating the energy and order parameter for each state, we clarify that the coexisting (supersolid) state, where the density wave and superfluid states are degenerate, is realized in the system. We then determine the phase diagram at finite temperatures.KEYWORDS: superfluid, density wave, mass-imbalanced system, continuous-time Monte Carlo simulationThe superfluid state in ultracold fermionic systems has attracted considerable interest since the successful realization of the Bose-Einstein condensation in 6 Li 2 molecules. 1,2) Owing to the high controllability of the system, remarkable phenomena have been observed such as the BCS-BEC crossover 3,4) and the superfluid state in a spin-imbalanced system, 5,6) where Cooper pairs are composed of ions with distinct hyperfine states. Recently, fermionic mixtures with distinct ions, e.g., 6 Li and 40 K, have experimentally been realized, 7,8) which stimulates further theoretical investigations on superfluid states in a mass-imbalanced system. [9][10][11][12][13][14][15][16][17] One of the interesting questions in such a massimbalanced system is how the superfluid state is realized when the lattice potential is loaded, so called an optical lattice. 18) In the lattice system, 19) the density wave (DW) state is naively expected, in addition to the SF state, since less mobile fermions tend to crystallize in the lattice, particularly, at half filling. It is desired to systematically discuss how the SF state competes or coexists with the DW state in an optical lattice system. This topic is closely related to an important issue in condensed matter physics, so called the supersolid state, [20][21][22][23][24] since the DW state can be regarded as a type of solid state. Therefore, an optical lattice system with mass imbalance should provide an ideal stage for studies of supersolid state in fermionic systems.Motivated by this, we study the low-temperature properties of a fermionic mixture in an optical lattice, combining dynamical mean-field theory (DMFT) 25) with continuoustime quantum Monte Carlo (CTQMC) simulation. 26,27) By calculating the order parameters for the DW and SF states, we determine the phase diagram at finite temperatures and clarify how the coexisting state is stabilized against the mass imbalance.In this paper, we consider the following attractive Hubbard model with different masses 19) aswhere hi; ji denotes the nearest neighbor site, c y i ðc i Þ is the creation (annihilation) operator of a fermion at the ith site with spin ð¼ "; #Þ and n i ¼ c y i c i . U ð> 0Þ is the attractive interaction and t is the hopping amplitude for the fermion with spin , where the effect of the mass imbalance is taken into account.We examine the low-t...

Superconductivity in the two-band Hubbard model

“…The DMFT treatment allows us to discuss the stability of the s-wave SC state more quantitatively than the static BCS mean-field theory [26]. In fact, the DMFT method has been successfully applied to various strongly correlated fermion systems with SC and superfluid states [27][28][29][30][31][32][33][34].…”

Stability of the superfluid state in three-component fermionic optical lattice systems

“…This allows us to discuss the stability of the s-wave SF state more quantitatively beyond the static BCS mean-field theory [36]. In fact, the DMFT method has successfully been applied to various strongly correlated fermion systems with SF or superconducting states [32,[37][38][39][40][41][42][43].…”

Excitation properties and effects of mass imbalance in the BCS-BEC crossover regime of an ultracold Fermi gas

“…Since the achievement of the superfluid phase transition in 40 K [1] and 6 Li [2][3][4] Fermi gases, various possibilities beyond this simplest s-wave pairing state have been discussed in this field, such as a p-wave superfluid [5][6][7][8][9][10][11][12][13], the Sarma phase [14][15][16][17], a dipolar Fermi condensate [18][19][20][21][22], and a mass-imbalanced Fermi superfluid [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Although none of these states has been observed yet, the high tunability of cold Fermi gases makes us expect that some of them may be realized in the near future.…”

“…Among various possibilities discussed in ultracold Fermi gases, in this paper, we pick up a hetero-pairing state in the presence of mass imbalance [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. In this state, Cooper pairs are formed between different species with different masses, which is quite different from the ordinary homo-Cooper pairs in metallic superconductivity.…”