Possible quantum phase-manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. Different effective interactions and novel correlated quantum many-body phases may be engineered in these systems, with the different phases being tunable via external parameters. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak inter-species interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by to the on-site inter-species interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge density wave instability in the two-leg ladder after the renormalization group transformation. Parameterizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system.Comment: 4 pages and 3 figure

Fermion pairing in mixed-dimensional atomic mixtures

We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s$-wave, $p$-wave, $d_{x^2-y^2}$-wave, and $g_{xy(x^2-y^2)}$-wave pairing symmetries. Other instabilities such as a charge-density wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d$-wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d$-wave pairing), an even higher critical temperature may be achieved.Comment: 10 pages, 10 figure

Unconventional superconducting phases on a two-dimensional extended Hubbard model

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} 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 (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-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

Renormalization-group exponents for superconducting phases in two-leg ladders

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length $l_d$ and a set of renormalization-group exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, non-trivial constraints among the exponents are derived and explained.Comment: 4 pages, 3 figures; minor revisions with references adde