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

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.

arXiv comment14 pages, 11 figures

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• Direct observation of a magnetic field-induced Wigner crystal
• Dielectric permittivity, conductivity and breakdown field of hexagonal boron nitride
• Edge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Isospin Pomeranchuk effect and the entropy of collective excitations in twisted bilayer graphene
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• Strong-Magnetic-Field Magnon Transport in Monolayer Graphene
• The Floquet Fermi Liquid
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• Spin-valley entangled quantum Hall states in graphene
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• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Optical readout of the chemical potential of two-dimensional electrons
• Built-in Bernal gap in large-angle-twisted monolayer-bilayer graphene
• Residual bulk viscosity of a disordered 2D electron gas
• Chiral transport of hot carriers in graphene in the quantum Hall regime
• Competing Laughlin state and Wigner crystal in bilayer graphene
• Spin and valley ordering of fractional quantum Hall states in monolayer graphene
• Quantum Monte Carlo at the Graphene Quantum Hall Edge
• Density Dependence of the Phases of the $\nu =1$ Integer Quantum Hall Plateau in Low Disorder Electron Gases
• Spontaneous localization at a potential saddle point from edge state reconstruction in a quantum Hall point contact
• Electrostatic Control of Magneto-Optic Excitonic Resonances in the van der Waals Ferromagnetic Semiconductor Cr${}_2$Ge${}_2$Te${}_6$