Cotunneling renormalization in carbon nanotube quantum dots

We determine the level shifts induced by cotunneling in a Coulomb blockaded carbon nanotube quantum dot using leading-order quasidegenerate perturbation theory within a single nanotube “shell.” 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 K-K ′ mixing and spin-orbit coupling.