Phase diagram and dynamics of Rydberg-dressed fermions in two dimensions

We investigate the ground-state properties and the collective modes of a two-dimensional two-component Rydberg-dressed Fermi liquid in the dipole-blockade regime. We find instability of the homogeneous system toward phase-separated and density ordered phases, using the Hartree-Fock and random-phase approximations, respectively. The spectral weight of collective density oscillations in the homogenous phase also signals the emergence of density-wave instability. We examine the effect of exchange hole on the density-wave instability and on the collective-mode dispersion using the Hubbard local-field factor.

Figure 1

Effective Rydberg-dressed potential in momentum space $v_{\mathrm{R}}\left(q\right)$ (in units of $2\pi D/r_c^4$) vs $q{r}_c$. The inset shows the real-space potential $v_{\mathrm{R}}\left(r\right)$ (in units of $D/r_c^6$) vs $r/r_c$.

Figure 2

(a) Ground-state energy of a single-component 2D Rydberg-dressed liquid within the HF approximation (in units of the noninteracting ground-state energy ${\varepsilon }_0=E_0{\lambda }^2/4$ of a single-component system) vs the coupling strength $\lambda$ for several values of $r_c/r_0$. (b) Comparison of the HF energies of mixed and phase-separated states (in units of $E_0{\lambda }^2/4$) vs $\lambda$ for $r_s=0.7r_0$. The phase-separated state becomes lower in energy for $\lambda \lesssim 2.5$.

Figure 3

Competition between mixed and phase-separated states of a two-dimensional two-component Rydberg-dressed system in the $\lambda -\tilde{r}$ parameter space, obtained within the Hartree-Fock approximation.

Figure 4

Regions of stable homogeneous liquid (HL) and the density-wave instability (DWI) of a single-component two-dimensional Rydberg-dressed liquid in the $\lambda -\tilde{r}$ plane. Black solid lines show the phase boundary within the random-phase approximation, and red dotted lines refer to the phase boundary obtained using the Hubbard approximation for local-field factor. Within both approximations, only the unstable regions with $q_I\le 2k_{\mathrm{F}}$ for the instability wave vector have been retained.

Figure 5

(a) Dispersion of the zero-sound mode of a single-component 2D Rydberg-dressed liquid within the RPA (in units of $\hslash k_{\mathrm{F}}^2/m$) vs $q/k_{\mathrm{F}}$ for several values of $r_c/r_0$. (b) Effects of the Hubbard LFF on the dispersion of zero-sound for $\lambda =2$ and $r_c=0.5r_0$. Filled areas in gray color indicate the particle-hole continuum.

Figure 6

Imaginary part of the density response function within the RPA vs $\omega$ (in units of $\hslash k_{\mathrm{F}}^2/m$) and $q$ (in units of $k_{\mathrm{F}}$) at a fixed density parameter $\lambda =10$, and for $\tilde{r}=0.45$ (a) and $\tilde{r}=0.3$ (b). These two parameter values for $\tilde{r}$ respectively correspond to the homogenous liquid and density-wave unstable regions of the phase diagram (see Fig. 4). Note that the Dirac delta peak of the spectral weight outside the PHC has been broadened by $\sim 0.01$ for a better visibility.