Coupled Ferromagnetic and Nematic Ordering of Fermions in an Optical Flux Lattice

Ultracold atoms in Raman-dressed optical lattices allow for effective momentum-dependent interactions among single-species fermions originating from short-range $s$-wave interactions. These dressed-state interactions combined with the very flat bands encountered in the recently introduced optical flux lattices push the Stoner instability towards weaker repulsive interactions, making it accessible with current experiments. As a consequence of the coupling between spin and orbital degrees of freedom, the magnetic phase features Ising nematic order.

Figure 1

Bandwidth $W$ of the lowest band as a function of lattice depth of the optical flux lattice discussed in the main text (with $\theta =0.3$ and $ϵ=0.4$). The inset shows the dispersion of the lowest two bands for $V_0/E_R=2.25$. As the lattice is ramped up, the dispersion of the lowest band develops a minimum at the center of the Brillouin zone causing reconstruction of the Fermi surface for noninteracting particles. The locations where these reconstructions occur for filling $\nu =1/4$ are marked by the dashed lines. For vanishing lattice depth $V_0=0$, the Fermi circles of the spin $\uparrow$ (red) and spin $\downarrow$ (blue) are displaced from each other to the corners of the Brillouin zone.

Figure 2

Magnetization of the ground state of interacting fermions in the lowest band of the optical flux lattice at uniform filling factor $\nu =1/4$ as a function of lattice depth $V_0/E_R$ and dimensionless coupling strength $\tilde{g}$. The gray shaded areas on the insets illustrate occupied states in the first Brillouin zone. White lines mark transitions between unmagnetized states of different Fermi surface topology.

Figure 3

Left: Magnetization for $V_0/E_R=2$, $\theta =0.3$, $ϵ=0.4$, and $\tilde{g}=1.9$ as a function of temperature and chemical potential (scale same for $m_z$ as in Fig. 2). $W$ is the bandwidth, and $\mu -{ϵ}_{\min }$ is the chemical potential measured from the bottom of the lowest band. The red dots lie on the spinodal where the symmetric state becomes unstable (the line is a guide to the eye). Right: Occupation numbers $n_{\mathbf{k}}$ within the first Brillouin zone for $(\mu -{ϵ}_{\min })/W=0.89$, 1.69, 2.19 correspond to (a), (b), (c).

Figure 4

Experimental signatures of adiabatic band mapping. (a) Contour plot of the dispersion ${ϵ}_{\mathbf{k}}$ for $V_0/E_R=1.8$, indicating a rhombus-shaped reciprocal lattice unit cell. The Bloch states inside the upper red (lower blue) triangle in (a) map to spin-$\uparrow$ ($\downarrow$) states with free-space momentum $\mathbf{q}$ illustrated in (b). For a completely filled lowest band, one would observe a fully occupied hexagram (b). When the atoms pass subsequently through a Stern-Gerlach filter, the two spin states can be separately resolved. This would allow clear signatures of the transition from the (c) unmagnetized to the (d) magnetized phase.