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arXiv:1209.1571 · Physical Review Letters

Topological Transitions of Gapless Paired States in Mixed-Geometry Lattices

DH Kim, Joel S. J. Lehikoinen, Päivi Törmä

Published Jan 28, 2013• 7 citations
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Abstract

We propose a mixed-geometry system of fermionic species selectively confined in lattices of different geometry. We investigate how such asymmetry can lead to exotic multiband fermion pairing in an example system of honeycomb and triangular lattices. A rich phase diagram of interband pairing with gapped and gapless excitations is found at zero temperature. We find that the two-band contribution of the honeycomb lattices to the paired state helps to stabilize the gapless phase with one or two Fermi surfaces. We also show that the Fermi surface topology further divides the gapless phase into subclasses between which the system undergoes density-driven Lifshitz transitions.

DOI
10.1103/physrevlett.110.055301

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We propose a mixed-geometry system of fermionic species selectively confined in lattices of different geometry. We investigate how such asymmetry can lead to exotic multiband fermion pairing in an example system of honeycomb and triangular lattices. A rich phase diagram of interband pairing with gapped and gapless excitations is found at zero temperature. We find that the two-band contribution of the honeycomb lattices to the paired state helps to stabilize the gapless phase with one or two Fermi surfaces. We also show that the Fermi surface topology further divides the gapless phase into subclasses between which the system undergoes density-driven Lifshitz transitions.
We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: (1) both spins in a triangular lattice and (2) a mixed geometry with up spins in honeycomb and down spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically nontrivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.
We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, the mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.
We propose a model for realizing exotic paired states in cold Fermi gases by using a spin-dependent optical lattice to engineer mismatched Fermi surfaces for each hyperfine species. The BCS phase diagram shows a stable paired superfluid state with coexisting pockets of momentum space with gapless unpaired carriers, similar to the Sarma state in polarized mixtures, but in our case the system is unpolarized. We propose the possible existence of an exotic "Cooper-pair Bose-metal" phase, which has a gap for single fermion excitations but gapless and uncondensed "Cooper-pair" excitations residing on a "Bose surface" in momentum space.
We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via sss-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of ppp-wave pairing.
Similar to what has recently been achieved with Bose-Bose mixtures [G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($\ensuremath{\sigma}\ensuremath{\equiv}{\ensuremath{\uparrow},\ensuremath{\downarrow}}$), in such a way that both species are confined to quasi--two-dimensional geometries determined by their hoppings along the lattice direction. We investigated the ground-state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and found normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we found a stable gapless superfluid phase where the unpaired $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.
We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces, which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero interband exchange interaction and a large asymmetry between the two bands.