Statistical Properties of Level Widths and Conductance Peaks in a Quantum Dot

TL;DR

This paper analyzes the statistical distribution of level widths and conductance peaks in quantum dots with extended contacts, revealing power-law behaviors and temperature-dependent fluctuations.

Contribution

It provides exact and numerical analysis of level width distributions for multi-point contacts, highlighting their divergence and impact on conductance peak statistics.

Findings

Level width distribution resembles independent wavefunction fluctuations.

Power-law behavior at small level widths depends on the number of contact points.

Conductance peak fluctuations decrease with larger lead size.

Abstract

We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wavefunction averaged over the contact area. The distribution function of level widths for a two-point contact is evaluated exactly. The distribution resembles closely the result obtained when the wavefunction fluctuates independently at each point, but differs from the one-point case. Analytical calculations and numerical simulations show that the distribution for many-point contacts has a power-law behavior at small level widths. The exponent is given by the number of points in the lead and diverges in the continuous limit. The distribution of level widths is used to determine the distribution of conductance peaks in the resonance regime. At intermediate temperatures, we find that the distribution tends to normal and fluctuations in the height of the peaks are suppressed as the lead size is increased.