Size Effect of Local Current-Voltage Characteristics of MX$_2$ Nanoflakes: Local Density of States Reconstruction from Scanning Tunneling Microscopy Experiments

TL;DR

This paper introduces a flexible method based on Tersoff formulae to reconstruct the local density of states in MX$_2$ nanoflakes from STM measurements, revealing size-dependent electronic properties.

Contribution

It develops a novel variational approach to reconstruct LDOS from STM data, applicable to complex-shaped LD-TMD nanoflakes, improving upon existing models.

Findings

Reconstructed LDOS for MoS$_2$ nanoflakes across different layers.

Identified size effects related to nanoflake thickness and shape.

Provided insights into local band structure and electronic properties.

Abstract

Local current-voltage characteristics for low-dimensional transition metal dichalcogenides (LD-TMD), as well as the reconstruction of their local density of states (LDOS) from scanning tunneling microscopy (STM) experiments is of fundamental interest and can be useful for advanced applications. Most of existing models are either hardly applicable for the LD-TMD of complex shape (e.g., those based on Simmons approach), or necessary for solving an ill-defined integral equation to deconvolute the unknown LDOS (e.g., those based on Tersoff approach). Using a serial expansion of Tersoff formulae, we propose a flexible method how to reconstruct the LDOS from local current-voltage characteristics measured in STM experiments. We established a set of key physical parameters, which characterize the tunneling current of a STM probe - sample contact and the sample LDOS expanded in Gaussian functions. Using a direct variational method coupled with a probabilistic analysis, we determine these parameters from the STM experiments for MoS2 nanoflakes with different number of layers. The main result is the reconstruction of the LDOS in a relatively wide energy range around a Fermi level, which allows insight in the local band structure of LD-TMDs. The reconstructed LDOS reveals pronounced size effects for the single-layer, bi-layer and three-layer MoS$_2$ nanoflakes, which we relate with low dimensionality and strong bending/corrugation of the nanoflakes. We hope that the proposed elaboration of the Tersoff approach allowing LDOS reconstruction will be of urgent interest for quantitative description of STM experiments, as well as useful for the microscopic physical understanding of the surface, strain and bending contribution to LD-TMDs electronic properties.