The Coulomb Blockade in Quantum Boxes

TL;DR

This paper uses a numerical renormalization group approach to analyze Coulomb blockade phenomena in quantum boxes across various regimes, revealing new behaviors and confirming theoretical scenarios.

Contribution

It introduces a comprehensive numerical method to study Coulomb blockade in quantum boxes, capturing all regimes and uncovering reentrant behaviors and Kondo effects.

Findings

Reentrant Coulomb blockade staircase at large tunneling amplitudes.

Confirmation of Matveev's scenario near perfect transmission.

Observation of two-channel Kondo behavior at degeneracy points.

Abstract

The charging of a quantum box connected to a lead by a single-mode point contact is solved for arbitrary temperatures, tunneling amplitudes, and gate voltages, using a variant of Wilson's numerical renormalization group. The charge inside the box and the capacitance of the junction are calculated on equal footing for all physical regimes, including weak tunneling, near perfect transmission, and the crossover regime in between. At the charge plateaus, perturbation theory is found to break down at fairly small tunneling amplitudes. Near perfect transmission, we confirm Matveev's scenario for the smearing of the Coulomb-blockade staircase. A surprising reentrance of the Coulomb-blockade staircase is found for large tunneling amplitudes. At the degeneracy points, we obtain two-channel Kondo behavior directly from the Coulomb-blockade Hamiltonian, without the restriction to two charge configurations or the introduction of an effective cutoff.