# Solitonic self-sustained charge and energy transport on the superconducting cylinder

## TL;DR

This paper presents an exact solution for a charged scalar field on a superconducting cylinder, demonstrating self-sustained charge and energy transport driven by topological charge, relevant for nanotube superconductivity.

## Contribution

It introduces a novel exact time-dependent solution modeling self-sustained charge transport in a superconducting cylindrical geometry with topological features.

## Key findings

- Self-sustained electric current without external fields
- Topological charge characterized by winding number
- Relevance to superconducting nanotubes

## Abstract

We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a $s$-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.