Magnetic-Field Dependence of Tunnel Couplings in Carbon Nanotube Quantum Dots
K. Grove-Rasmussen, S. Grap, J. Paaske, K. Flensberg, S. Andergassen,, V. Meden, H. I. J{\o}rgensen, K. Muraki, and T. Fujisawa

TL;DR
This study investigates how magnetic fields influence tunnel couplings in carbon nanotube quantum dots, revealing disorder effects and valley mixing that can be controlled via magnetic field adjustments.
Contribution
It demonstrates the impact of magnetic fields on tunnel couplings and valley mixing in carbon nanotube quantum dots, supported by experimental spectroscopy and modeling.
Findings
Magnetic field reduces valley mixing effects.
Tunnel couplings vary with gate voltage and magnetic field.
Disorder-induced valley mixing causes level renormalization.
Abstract
By means of sequential and cotunneling spectroscopy, we study the tunnel couplings between metallic leads and individual levels in a carbon nanotube quantum dot. The levels are ordered in shells consisting of two doublets with strong- and weak-tunnel couplings, leading to gate-dependent level renormalization. By comparison to a one- and two-shell model, this is shown to be a consequence of disorder-induced valley mixing in the nanotube. Moreover, a parallel magnetic field is shown to reduce this mixing and thus suppress the effects of tunnel renormalization.
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