Numerical analysis of the Novikov problem of a normal metal in a strong magnetic field

TL;DR

This paper numerically investigates the fractal structures in magnetoresistance behavior of a normal metal with two Fermi surfaces under strong magnetic fields, focusing on a simplified case with genus 3 surfaces.

Contribution

It provides the first detailed numerical analysis of Novikov's fractal structures in a specific, simplified Fermi surface configuration.

Findings

Identified complex fractal patterns in magnetoresistance

Demonstrated the influence of Fermi surface topology on electron trajectories

Extended understanding of Novikov's problem in condensed matter physics

Abstract

We present the results of our numerical exploration of the fractal structure found by S.P. Novikov in the problem of the behviour of magnetoresistance in a normal metal under a strong magnetic field. The case we discuss in this paper is the simplest non-trivial one, namely the case of 2 Fermi Surfaces that cut the brillouin zone along of the coordinate axes (i.e. Fermi surfaces have genus 3).