Comment on: ``Zero temperature conductance of parallel T-shape double quantum dots'' [Physica E 39 (2007) 214, arXiv:0708.1842v1]

TL;DR

This paper critiques a recent study on quantum dot conductance, identifying errors in their derivation that lead to unphysical results, thereby clarifying the correct approach for such calculations.

Contribution

The authors identify and correct an error in the derivation of conductance formulas for double quantum dots in T-shape configurations.

Findings

The original derivation contains an unphysical result due to an error.

Corrected conductance expression aligns with established physics.

Highlights importance of accurate derivation in quantum transport calculations.

Abstract

In a recent paper [Physica E 39 (2007) 214, arXiv:0708.1842v1] Crisan, Grosu and Tifrea revisited the problem of the conductance through a double quantum dot molecule connected to electrodes in a T-shape configuration. The authors obtained an expression for the conductance that disagrees with previous results in the literature. We point out an error in their derivation of the conductance formula and show that it gives unphysical results even for non-interacting quantum dots.