Experimental determination of the energy per particle in partially filled Landau levels

TL;DR

This paper introduces an experimental method to measure the chemical potential in atomically thin materials, enabling the determination of energy per particle in Landau levels and validating theoretical models with high precision.

Contribution

The study presents a novel high-sensitivity technique for measuring chemical potential in layered materials, allowing direct comparison of experimental data with numerical calculations of Landau level energies.

Findings

Excellent agreement between experiment and theory in N=0 Landau level.

Revealed the significance of valley anisotropic interactions in N=1 Landau level.

Detected valley-textured electron solids near odd filling factors.

Abstract

We describe an experimental technique to measure the chemical potential, $\mu$, in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of $\mu$ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating $\mu$ over filling factor, $\nu$, we obtain the ground state energy per particle, which can be directly compared with numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters, as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, comparison between experimental and numerical data reveals the importance of valley anisotropic interactions and the presence of valley-textured electron solids near odd filling.