Spin-orbit coupling and proximity effects in metallic carbon nanotubes

TL;DR

This paper investigates spin-orbit coupling effects in metallic carbon nanotubes using a Tomonaga-Luttinger liquid framework, revealing a new regime with inverted mini-gap hierarchy and analyzing proximity-induced superconductivity.

Contribution

It derives an effective low-energy theory for specific metallic CNTs near charge neutrality, identifying a novel spin-orbit induced phase with unique gap structure and characterizing the resulting superconducting order.

Findings

Identification of a new regime with inverted mini-gap hierarchy due to spin-orbit coupling

Derivation of an effective low-energy field theory for certain metallic CNTs

Proximity coupling results in a topologically trivial s-wave superconducting phase

Abstract

We study spin-orbit coupling in metallic carbon nanotubes (CNTs) within the many-body Tomonaga-Luttinger liquid (TLL) framework. For a well defined sub-class of metallic CNTs, that contains both achiral zig-zag as well as a sub-set of chiral tubes, an effective low energy field theory description is derived. We aim to describe system at finite dopings, but close to the charge neutrality point (commensurability). A new regime is identified where spin-orbit coupling leads to an inverted hierarchy of mini-gaps of bosonic modes. We then add a proximity coupling to a superconducting (SC) substrate and show that the only order parameter that is supported within the novel, spin-orbit induced phase is a topologically trivial s-SC.