Bilayer honeycomb lattice with ultracold atoms: Multiple Fermi surfaces and incommensurate spin density wave instability

TL;DR

This paper proposes an ultracold atom setup to realize a bilayer honeycomb lattice with multiple Fermi surfaces, revealing potential for observing incommensurate spin density wave instabilities and related phenomena.

Contribution

It introduces a novel experimental configuration for bilayer honeycomb lattices with Bernal stacking using ultracold atoms, analyzing Fermi surface effects and magnetic instabilities.

Findings

Multiple Fermi surfaces lead to unique Friedel oscillations and RKKY interactions.

A critical interaction strength induces incommensurate spin-density-wave order.

The instability persists under interaction renormalization and is the dominant instability.

Abstract

We propose an experimental setup using ultracold atoms to implement a bilayer honeycomb lattice with Bernal stacking. In 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 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.