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arXiv:1007.0782 · Europhysics Letters (EPL)

Spin-charge-density wave in a rounded-square Fermi surface for ultracold atoms

D. Makogon, I. B. Spielman, C. Morais Smith

Published Jan 20, 2012• 10 citations
arXivHTMLPDF

Abstract

We derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, spin-flip term. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously at the random-field-approximation level, and show that the system can develop a coupled spin-charge-density wave order. Our generic approach can be used to study spin and charge instabilities in many materials, such as high- T c superconductors, organic compounds, graphene, and iron pnictides.

DOI
10.1209/0295-5075/97/33002

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We derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, spin-flip term. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously at the random-field-approximation level, and show that the system can develop a coupled spin-charge-density wave order. Our generic approach can be used to study spin and charge instabilities in many materials, such as high- T c superconductors, organic compounds, graphene, and iron pnictides.
We study instabilities of single-species fermionic atoms in the ppp-orbital bands in two-dimensional optical lattices at noninteger filling against interactions. Charge density wave and orbital density wave orders with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superfluid phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible phase transitions from orbital stripe order to liquid-crystal phases and obtain the phase diagram. The condition of nearly-perfect Fermi-surface nesting, which is key to the above results, is shown robustly independent of fermion fillings in such ppp-orbital systems, and the $(2{k}_{F},\ifmmode\pm\else\textpm\fi{}2{k}_{F})$ momentum of density wave oscillation is highly tunable. Such remarkable features show the promise of making those exotic orbital phases, which are of broad interest in condensed-matter physics, experimentally realizable with optical lattice gases.
We propose an experimental setup using ultracold atoms to implement a bilayer honeycomb lattice with Bernal stacking. In the presence of a potential bias between the layers and at low densities, fermions placed in this lattice form an annular Fermi sea. The presence of two Fermi surfaces leads to interesting patterns in Friedel oscillations and RKKY interactions in the presence of impurities. Furthermore, a repulsive fermion-fermion interaction leads to a Stoner instability towards an incommensurate spin density wave order with a wave vector equal to the thickness of the Fermi sea. The instability occurs at a critical interaction strength which goes down with the density of the fermions. We find that the instability survives interaction renormalization due to vertex corrections and discuss how this can be seen in experiments. We also track the renormalization group flows of the different couplings between the fermionic degrees of freedom, and find that there are no perturbative instabilities, and that Stoner instability is the strongest instability which occurs at a critical threshold value of the interaction. The critical interaction goes to zero as the chemical potential is tuned towards the band bottom.
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We present an ab initio, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling. The ground state of this system is a supersolid, with coexisting charge and superfluid order. The superfluid is composed of both singlet and triplet pairs induced by spin-orbit coupling. We perform large-scale calculations using the auxiliary-field quantum Monte Carlo method to provide the first full, quantitative description of the charge, spin, and pairing properties of the system. In addition to characterizing the exotic physics, our results will serve as essential high-accuracy benchmarks for the intense theoretical and especially experimental efforts in ultracold atoms to realize and understand an expanding variety of quantum Hall and topological superconductor systems.
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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.