Finite size effects on the statistical angle of an electron induced dyon in proximity to a topological insulator

TL;DR

This paper investigates how the statistical angle of an electron-induced dyon near a topological insulator depends on distance and sample size, revealing conditions for experimental measurement of non-trivial statistics.

Contribution

It demonstrates that the statistical angle can be isolated in a two-electron system within specific size limits, clarifying the 2+1D nature of the effect.

Findings

Total angular momentum is zero for a single electron outside finite TI samples.

A non-trivial statistical angle can be observed in a two-electron system within intermediate size loops.

The results specify conditions for experimental detection of the statistical angle.

Abstract

A pointlike electric charge close to the surface of a three dimensional topological insulator induces a magnetic monopole mirror charge. We study the distance dependence of the statistical angle describing this induced dyon system. We find that the total angular momentum, which sometimes is used as signature of the statistical angle, for an electron outside a finite size spherical or tube shaped topological insulator is zero for any finite distance between the electron and the surface. However, we show that in the 2-electron system one can indeed isolate a non-trivial statistical angle for intermediate size loops, that is loops much larger than the distance of the charge to the sample but much smaller than the size of the sample. The necessity for this limit confirms the 2+1 dimensional nature of the non-trivial statistical angle found in previous work. Our results clarify the conditions under which the statistical angle of this system could be measured in real experiments.