Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves

Abstract

We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU($N$)-symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the energy spectrum, the particle density and the current flowing through the impurity at varying interaction strengths, barrier heights, and number of components. We find that the physics of the system is governed by the competition between effective single-particle process and the formation of a high-stiffness spin-correlated state associated to the phenomenon of fractionalization of the flux quantum characterizing the $N$-component fermionic system. Our findings provide a route to probe the response of SU($N$) fermions to effective magnetic fields; at the same time, they hold significance for fundamental understanding of localized impurity problems.

Figures (2)

• Figure 1: Profiles of the energy $E(\phi)$ (top) and corresponding density at the impurity site $n_{\mathrm{imp}}$ (bottom) against the effective magnetic flux $\phi$ in the regime of strong interactions $U/t = 1024$ for various barrier strengths $\lambda/t$ in a ring of $N_{s}$ sites. Dotted lines highlight the connection between the energy peaks and density minima, whilst circles indicate the opening of the gaps in $E(\phi)$ and designated changes in $n_{\mathrm{imp}}$. The quadratic Casimir values $s$ for each energy parabola are $\{6,3,3,0,3,3,6\}$. Results obtained with exact diagonalization of the SU($N$) Hubbard model using the parameter set indicated in the figure.
• Figure 2: (a) Current $I(\phi)$ versus flux $\phi$ showcasing the interplay between the characteristic fractionalized sawtooth and a smoothened profile given by the presence of the impurity. (b) Maximum persistent current amplitude $I_{\mathrm{max}}$ as a function of interactions $U/t$ in the presence of a barrier with strength $\lambda/t=1$ for different number of particles $N_{p}$ and components $N$. In the main panel he current is normalized by the maximum current computed at $\lambda=0$ at all values of interactions, while inset shows the bare value of $I_\text{max}$ versus $U$. The competition between screening of the barrier and fractionalization results in $I_\text{max}U^{\nu}$, with $\nu\approx 0.7$ for $U/t\ll1$ and $\nu\approx -0.8$ for $U/t\gg1$). Results obtained with exact diagonalization of the SU($N$) Hubbard model.