Nonconventional Quantized Hall Resistances Obtained with $\nu = 2$ Equilibration in Epitaxial Graphene $p-n$ Junctions

TL;DR

This paper reports the fabrication of epitaxial graphene p-n junctions with simplified processing that exhibit nonconventional fractional quantized Hall resistances at 9=2, supported by circuit modeling for future device exploration.

Contribution

It introduces a rapid fabrication method for graphene p-n junctions and demonstrates fractional quantum Hall resistance measurements with a theoretical framework for future device design.

Findings

Observed fractional quantized Hall resistances at 9=2 with various coefficients

Fabrication process significantly faster than traditional electron beam lithography

Provided circuit simulation framework for exploring fractional quantum Hall effects

Abstract

We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene $p-n$ junction devices using simple ultraviolet photolithography, thereby significantly reducing device processing time compared to that of electron beam lithography typically used for obtaining sharp junctions. This work presents measurements yielding nonconventional, fractional multiples of the typical quantized Hall resistance at $\nu=2$ ($R_H\approx 12906 {\Omega}$) that take the form: $\frac{a}{b}R_H$. Here, $a$ and $b$ have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of $R_H$. Additionally, we provide a framework for exploring future device configurations using the LTspice circuit simulator as a guide to understand the abundance of available fractions one may be able to measure. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.