Transport and scattering in inhomogeneous quantum wires

We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if perfect ballistic transport is possible in the low-temperature limit. We demonstrate that a conducting fixed point surprisingly exists even for large abrupt changes, which in the considered model corresponds to a velocity-matching condition. The general position-dependent Green's function is calculated in the presence of a sudden change, and is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources, offering a route to design experiments where the effects of the contacts are minimized.

Figure 1

The local response in the density $\chi$ for a jump in interaction from $U_{\ell }=0$ to $U_r=1.8t_r$ at $T=0.1t_r$. Circles (blue): No discontinuity in hopping, $t_{\ell }=t_r$. Squares (red): The hopping on the left is adjusted to $t_{\ell }\approx 1.518t_r$ in order to match the velocities on both sides. Solid lines (black) are fits to the predicted behavior in Eq. (14) for even and odd sites separately.

Figure 2

Effective backscattering amplitude $R\left(T\right)$ on a logarithmic scale extracted from the amplitude of the density oscillations in Eq. (14) for a jump from (a) $U_{\ell }=0$ to $U_r=1.8t$ ($T_K=3.4\times {10}^{-4}t$), and (b) $U_{\ell }=1t$ to $U_r=1.4t$ with $t=t_{\ell }=t_r$ ($T_K=6\times {10}^{-6}t$). The amplitudes are extracted from fitting the local response for $x<0$ (“left side”) and $x>0$ (“right side”) separately.

Figure 3

The alternating part of the density oscillations at $T=0.1t_r$ on the interacting side $U=1.8t_r$, where the hopping on the noninteracting side is adjusted so that $u_{\ell }=0.98u_r$, $u_{\ell }=u_r$, and $u_{\ell }=1.02u_r$, respectively.