Numerical study of the Coulomb blockade in an open quantum dot

The Coulomb blockade in an open quantum dot connected to a bulk lead by a single mode point contact is studied numerically using the path-integral Monte Carlo method. The Coulomb oscillation of the average charge and capacitance of the dot is investigated and is compared with the analytic expression for strong tunneling. At the degeneracy point, we observe logarithmic divergence of the capacitance for strong backscattering at the point contact. This observation supports the conjecture that the nature of the present system at the degeneracy point is described by the two-channel Kondo problem for an arbitrary strength of tunneling.

Figure 1

Schematic figure of an open quantum dot connected to a bulk lead by a single mode point contact. The dot is formed by applying negative voltage to the gates (gray regions). The solid line shows the boundary of the two-dimensional electron gas. The dimensionless gate voltage $N$ controls the charge in the dot. The width of the constriction is adjusted by the parameter $V$ so that only a single transverse mode is allowed to tunnel through the point contact.

Figure 2

(Color online) Coulomb oscillation of the average charge of the quantum dot for different temperatures $L=10$, 20, 50, 100, 200, and 400. A bundle of curves with smaller amplitude corresponds to $V=4$, and the other to $V=8$. (Inset) Comparison of the average charge for $V=4$ and 8 between our PIMC data at $L=400$ (crosses) and the analytic result for small $V$ at zero temperature (solid line).

Figure 3

(Color online) Coulomb oscillation of the capacitance of the dot for different temperatures $L=10$, 20, 50, 100, 200, and 400. A bundle of curves with smaller amplitude corresponds to $V=4$, and the other to $V=8$.

Figure 4

(Color online) Temperature dependence of the capacitance of the dot for $V=8$. The gate voltage $N$ is varied from 0.15 to 0.50 (from bottom to top) at intervals of 0.005. The curve for $N=0.475$ is also shown.

Figure 5

(Color online) Logarithmic divergence of the capacitance of the dot for $N=1/2$. The capacitance is plotted as a function of the inverse temperature $L$. The backscattering strength $V$ is varied from 1 to 8 at intervals of 1 (from bottom to top). The logarithmic fit of the data points for each value of $V$ is also shown by a dotted line. (Inset) $V$ dependence of the coefficient of the logarithmic divergence. The solid line shows the analytic result.