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arXiv:1604.01225 · Physical review. B./Physical review. B

Triplet superfluidity on a triangular ladder with dipolar fermions

Bradraj Pandey, Swapan Kumar Pati

Published Feb 3, 2017• 3 citations
arXivHTMLPDF

Abstract

Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions on a triangular ladder at half filling. Using density matrix renormalization group method, in the presence of onsite repulsion and intersite attractive interaction, we find an exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of the spin-triplet superfluid phase by varying hopping along the rungs of the triangle. The possibility of fermionic supersolidity has also been discussed, by considering three-body interaction in the Hamiltonian. We also study the effect of spin-dependent hopping on the stability of the spin-triplet superfluid phase.

DOI
10.1103/physrevb.95.085105

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Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions on a triangular ladder at half filling. Using density matrix renormalization group method, in the presence of onsite repulsion and intersite attractive interaction, we find an exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of the spin-triplet superfluid phase by varying hopping along the rungs of the triangle. The possibility of fermionic supersolidity has also been discussed, by considering three-body interaction in the Hamiltonian. We also study the effect of spin-dependent hopping on the stability of the spin-triplet superfluid phase.
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 study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.
The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole-dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole-dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.
The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.
Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.
Abstract We investigate the topological supersolid states of dipolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the stripe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dipolar interaction. We demonstrate that it can be maintained when the dipolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dipolar interaction strength U , the system will undergo a phase transition among p x + i p y superfluid state, p y -wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.