A full gap above the Fermi level: the charge density wave of monolayer VS2

Camiel Van Efferen,Katharina Ollefs,Thomas Michely,Joshua Hall,Felix Huttmann,Eline Plaar,Stefan Kraus,Erik Van Loon,Tim Wehling,Nick Brookes,Arne Schobert,Jan Berges,Nico Rothenbach,Tobias Wekking,Heiko Wende,Lucas Machado Arruda,Kurt Kummer,Gunnar Schönhoff

doi:10.1038/s41467-021-27094-x

Abstract

In the standard model of charge density wave (CDW) transitions, the displacement along a single phonon mode lowers the total electronic energy by creating a gap at the Fermi level, making the CDW a metal–insulator transition. Here, using scanning tunneling microscopy and spectroscopy and ab initio calculations, we show that VS2 realizes a CDW which stands out of this standard model. There is a full CDW gap residing in the unoccupied states of monolayer VS2. At the Fermi level, the CDW induces a topological metal-metal (Lifshitz) transition. Non-linear coupling of transverse and longitudinal phonons is essential for the formation of the CDW and the full gap above the Fermi level. Additionally, x-ray magnetic circular dichroism reveals the absence of net magnetization in this phase, pointing to coexisting charge and spin density waves in the ground state.

Highlights

In the standard model of charge density wave (CDW) transitions, the displacement along a single phonon mode lowers the total electronic energy by creating a gap at the Fermi level, making the charge density waves (CDWs) a metal–insulator transition
From density functional theory (DFT) and density functional perturbation theory (DFPT), we find that, a transverse phonon mode initially becomes unstable in the harmonic approximation, the final CDW has a substantial admixture of longitudinal modes
Prompted by the prediction of ferromagnetism for monolayer 1T-VS2 in its q 1⁄4 2=3 ΓK CDW phase[21], we examined the magnetic properties of VS2, by means of X-ray magnetic circular dichroism (XMCD)

Summary

Introduction

In the standard model of charge density wave (CDW) transitions, the displacement along a single phonon mode lowers the total electronic energy by creating a gap at the Fermi level, making the CDW a metal–insulator transition. Of particular interest are the coexistence or competition between charge density waves (CDWs), as found in many 2D transition metal dichalcogenides (TMDCs), with superconducting and magnetic phases[1,2]. Peierls’ explanation for the CDW in a one-dimensional chain of atoms states that periodic lattice distortions open an electronic gap at the nesting wavevector This gap at the Fermi level lowers the energy of the occupied states and the total energy, while increasing the energy of the unoccupied states that do not contribute to the total energy. At the Fermi energy, the undistorted phase and the CDW can have different

Methods

Results

Conclusion