Correlation effects on resonant tunneling in one-dimensional quantum wires

We study resonant tunneling in a Luttinger liquid with a double barrier enclosing a dot region. Within a microscopic model calculation the conductance $G$ as a function of temperature $T$ is determined over several decades. We identify parameter regimes in which the peak value $G_p\left(T\right)$ shows distinctive power-law behavior. For intermediate dot parameters, $G_p$ behaves in a nonuniversal way.

Figure 1

The conductance as a function of gate voltage for $N_D=6$, $U=0.5$, $V_{l∕r}=10$, $N={10}^4$, and different $T$.

Figure 2

Upper panel: $G_p\left(T\right)$ for $U=0.5$, $N={10}^4$, $V_{l∕r}=10$, and $N_D=2$ (circles), 6 (squares), and 100 (diamonds). The arrows indicate ${\Delta }_D$. The solid curve shows $G\left(T\right)∕2$ for a single barrier with $V=10$, $U=0.5$, and $N={10}^4$. Lower panel: The logarithmic derivative of $G_p\left(T\right)$. Solid line: $2{\alpha }_B^{\mathrm{RG}}$; dashed line: ${\alpha }_B^{\mathrm{RG}}-1$; dashed-dotted line: $2{\alpha }_B^{\mathrm{RG}}-1$.

Figure 3

Upper panel: $G_p\left(T\right)$ for $U=1.5$, $N={10}^4$, $N_D=10$ with $V_{l∕r}=0.8$ (circles), $N_D=30$ with $V_{l∕r}=1.5$ (squares), and $N_D=50$ with $V_{l∕r}=0.8$ (diamonds). The arrows indicate ${\Delta }_D$. Lower panel: The logarithmic derivative of $G_p\left(T\right)$. Solid line: $2{\alpha }_B^{\mathrm{RG}}$; dashed line: ${\alpha }_B^{\mathrm{RG}}-1$.