The tremendous development of cold atom physics has opened up a whole new opportunity to study novel states of matter which are not easily accessible in solid-state systems. Here we propose to realize the $f$ -wave pairing superfluidity of spinless fermions in ${p}_{x,y}$ -orbital bands of two-dimensional honeycomb optical lattices. The nontrivial orbital band structure, rather than strong correlation effects, gives rise to the unconventional pairing with the nodal lines of the $f$ -wave symmetry. With a confining harmonic trap, zero-energy Andreev bound states appear around the circular boundary with a sixfold symmetry. The experimental realization and detection of this novel pairing state are feasible.The tremendous development of cold atom physics has opened up a whole new opportunity to study novel states of matter which are not easily accessible in solid-state systems. Here we propose to realize the $f$-wave pairing superfluidity of spinless fermions in ${p}_{x,y}$-orbital bands of two-dimensional honeycomb optical lattices. The nontrivial orbital band structure, rather than strong correlation effects, gives rise to the unconventional pairing with the nodal lines of the $f$-wave symmetry. With a confining harmonic trap, zero-energy Andreev bound states appear around the circular boundary with a sixfold symmetry. The experimental realization and detection of this novel pairing state are feasible.

arXiv:0905.1146Physical Review ANov 10, 201030 citations

Orbital Order in Mott Insulators of Spinless p -Band Fermions

Erhai Zhao, W. Vincent Liu

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.

arXiv:0801.0589Physical Review LettersApr 22, 200893 citations

From Berry's Phase to Wilson Lines in a Honeycomb Optical Lattice

Monika Schleier-Smith

Bulletin of the American Physical SocietyMar 15, 20160 citations

Quantum phase transition of cold atoms trapped in optical lattices

Yao-hua Chen, Wéi Wú, Guo-cai Liu +2 more

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.

Frontiers of PhysicsMar 16, 20128 citations

Inter-orbital interactions in state-dependent optical lattices

Luis Riegger, Nelson Darkwah Oppong, Moritz Hoefer +2 more

Bulletin of the American Physical SocietyJun 7, 20170 citations

f

-wave pairing superfluidity of spinless fermions in

{p}_{x,y}

-orbital bands of two-dimensional honeycomb optical lattices. The nontrivial orbital band structure, rather than strong correlation effects, gives rise to the unconventional pairing with the nodal lines of the

f

-wave symmetry. With a confining harmonic trap, zero-energy Andreev bound states appear around the circular boundary with a sixfold symmetry. The experimental realization and detection of this novel pairing state are feasible.