Mott transition of fermionic mixtures with mass imbalance in optical lattices

We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized when one of the species is localized. The evolution of the spectral functions testifies that a continuous loss of coherence and a destruction of the Fermi liquid occur as the imbalance grows. The two species display distinct properties and experimentally observable deviations from the behavior of a balanced Fermi mixture.

Figure 1

Phase diagram of the Mott-insulator–fluid transition.

Figure 2

Quasiparticle weight $Z_{\alpha }$ at the Fermi level as a function of the interaction strength $U/D$ for $\zeta =(t_{\ell }-t_h)/(t_{\ell }+t_h)=0.4$ (upper panel) and $0.8$ (lower panel).

Figure 3

Spectral functions of the heavy fermions for $U=0.5D$ and $\zeta =0.8,0.98,0.998,0.9998$. The $\omega$ axis is renormalized by $D_h$ and the spectral functions $A_h$ are multiplied by $1/2\pi D_h$. The inset shows the same quantities as a function of $\omega /D$.

Figure 4

Spectral functions of the light species for different values of the mass imbalance $\zeta =0.8,0.98,0.998,0.9998$. The energy $\omega$ is renormalized by $D_{\ell }$ and the spectral density $A_l\left(\omega \right)$ is multiplied by a factor $1/2\pi D_{\ell }$. The inset shows the very-low energy part rescaling the energy axis by $D_h$ instead of $D_{\ell }$ in order to show the effect of the heavy species on the light one.

Figure 5

Spectral functions of the light species for $U=2D$ and $\zeta =0.2,0.4,0.8,0.98,0.99$. All spectral functions are multiplied by $1/2\pi D_{\ell }$.

Figure 6

Spectral functions of the heavy species for $U=2D$ and $\zeta =0.2,0.4,0.8,0.98,0.99$. All spectral functions are multiplied by $1/2\pi D_h$. In the inset, the same quantities are plotted on a log-log scale.