Electronic structure of $2H$-NbSe$_2$ single-layers in the CDW state

TL;DR

This study uses density functional theory to analyze the electronic structure of NbSe₂ single-layers in the charge density wave state, revealing that the CDW is not driven by Fermi surface nesting and highlighting the role of atomic and electronic reorganization.

Contribution

It provides a detailed theoretical analysis of the CDW state in NbSe₂ single-layers, challenging the nesting mechanism hypothesis and exploring STM image variations.

Findings

CDW barely affects the Fermi surface, ruling out nesting as the cause.

CDW stabilizes levels around 1.5 eV below the Fermi level with Nb-Nb bonding character.

STM images vary with bias voltage, influenced mainly by atomic corrugation and electronic reorganization.

Abstract

A density functional theory study of NbSe$_2$ single-layers in the normal non-modulated and the $3\times3$ CDW states is reported. We show that, in the single layer, the CDW barely affects the Fermi surface of the system, thus ruling out a nesting mechanism as the driving force for the modulation. The CDW stabilizes levels lying around 1.5 eV below the Fermi level within the Se-based valence band but having a substantial Nb-Nb bonding character. The absence of interlayer interactions leads to the suppression of the pancake-like portion of the bulk Fermi surface in the single-layer. We perform scanning tunneling microscopy simulations and find that the images noticeably change with the sign and magnitude of the voltage bias. The atomic corrugation of the Se sublayer induced by the modulation plays a primary role in leading to these images, but the electronic reorganization also has an important contribution. The analysis of the variation of these images with the bias voltage does not support a Fermi surface nesting mechanism for the CDW. It is also shown that underlying graphene layers (present in some of the recent experimental work) do not modify the conduction band, but do affect the shape of the valence band of NbSe$_2$ single-layers. The relevance of these results in understanding recent physical measurements for NbSe$_2$ single-layers is discussed.