Cotunneling renormalization in carbon nanotube quantum dots

TL;DR

This paper investigates how cotunneling affects energy levels and $g$-factor renormalization in Coulomb blockaded carbon nanotube quantum dots, revealing mixing of degenerate states and magnetic field effects.

Contribution

It provides a theoretical analysis of cotunneling-induced level shifts and $g$-factor renormalization in carbon nanotube quantum dots using perturbation theory.

Findings

Degenerate $K$ and $K'$ states are mixed by cotunneling, leading to energy splitting.

Cotunneling causes a gate-dependent renormalization of the $g$-factor.

Different experimental scenarios depend on intrinsic $KK'$ splitting and spin-orbit coupling.

Abstract

We determine the level-shifts induced by cotunneling in a Coulomb blockaded carbon nanotube quantum dot using leading order quasi-degenerate perturbation theory within a single nanotube quartet. It is demonstrated that otherwise degenerate and equally tunnel-coupled $K$ and $K'$ states are mixed by cotunneling and therefore split up in energy except at the particle/hole-symmetric midpoints of the Coulomb diamonds. In the presence of an external magnetic field, we show that cotunneling induces a gate-dependent $g$-factor renormalization, and we outline different scenarios which might be observed experimentally, depending on the values of both intrinsic $KK'$ splitting and spin-orbit coupling.