Local Measurements of Shubnikov-de Haas Oscillations in Graphene Systems

TL;DR

This paper demonstrates that Shubnikov-de Haas oscillations, typically measured via transport, can be directly observed in graphene using scanning tunneling spectroscopy, enabling Fermi-surface and Berry phase analysis without gating.

Contribution

It introduces a novel method to measure SdH oscillations in graphene through STS, eliminating the need for transport measurements or gate electrodes.

Findings

SdH oscillations observed in STS spectra of graphene.

Fermi-surface properties and Berry phases extracted from STS data.

Method applicable to various 2D materials without gating.

Abstract

Shubnikov-de Haas (SdH) oscillations, the most well-known magneto-oscillations caused by the quantization of electron energy levels in the presence of magnetic fields in two-dimensional (2D) electron systems, can be used to determine Fermi-surface properties and directly measure the Berry phase of the 2D systems. It is usually thought that transport measurements are required to measure the SdH oscillations. Contradicting this belief, we demonstrate that the SdH oscillations can be measured in graphene systems by carrying out scanning tunneling spectroscopy (STS) measurements. The energy-momentum dispersions and Berry phases of monolayer, Bernal-stacked bilayer, and ABC-stacked trilayer graphene are obtained according to the measured SdH oscillations in the STS spectra. It is possible to obtain the SdH oscillations when the size of the 2D systems is larger than the magnetic length and, importantly, no gate electrode is required in the STS measurement, therefore, the reported method in this work is applicable to a wide range of materials.