Statics and dynamics of multivalley charge density waves in Sb(111)

Anton Tamtögl,Michael Mayrhofer-Reinhartshuber,Patrick Kraus,Giorgio Benedek,Davide Campi,Daniele Dragoni,Marco Bernasconi,Wolfgang E Ernst

doi:10.1038/s41535-019-0168-x

Abstract

Charge density waves (CDWs), periodic modulations of the charge density, are among the most abundant and non-trivial ordered phases in condensed matter. Here we demonstrate the occurrence of multi-valley charge density waves (MV-CDW) on the semimetal Sb(111), a phenomenon previously observed at semiconductor surface inversion layers. The topological nature of the pocket surface states in Sb(111) ensures perfect nesting conditions giving rise to sharp peaks in helium atom scattering (HAS) diffraction spectra. The peculiar temperature dependence permits to distinctly associate the diffraction peaks with surface electron and hole-pocket states due to the non-trivial surface electronic band structure known from recent experimental data and present ab-initio calculations. Inelastic HAS spectra, besides providing the surface phonon dispersion curves in agreement with density functional perturbation theory calculations, reveal two additional dispersion curves of elementary excitations in the gap well below Rayleigh waves. They are attributed to collective excitations of the quasi-commensurate MV-CDWs associated with the surface electron M-pocket states at the Fermi level. These findings suggest that HAS can be regarded as a choice spectroscopy for the investigation of surface electronic excitations in the THz domain, opening up a new window for the search of collective phases at surfaces.

Highlights

Fermi level multivalley states occurring around distinct wavevectors of some semimetal surfaces provide a basis for the occurrence of charge density waves (CDWs).[1,2,3] The mechanism of multivalley CDWs at semiconductor surfaces, first described by Kelly and Falicov in the 70 s is conceptually similar to that of 1D Peierls CDWs.[4]
We show that the spin-selected nesting between the states of narrow pockets at the Fermi level, peculiar of topological semimetals, yields sharp features in the helium atom scattering (HAS) diffraction spectra corresponding to multivalley CDWs, and clear signatures of collective phase and amplitude CDW excitations in the THz spectral region
Energy resolution is optionally added by chopping the He beam with a chopper and measuring the time-of-flight. b The crystal structure of Sb(111) showing the first bilayer and the first atomic plane of the second bilayer, with the surface unitpffiffi cell p(ffifffiull line; lattice constant a = 4.308 Å) and the ð2= 3 ́ 2= 3ÞR30° surface unit cell of the electron pocket pmffiffiultivalley CDW. c Diffraction scans for Sb(111) along the ΓK azimuth for different surface temperatures and beam energies

Summary

Introduction

Fermi level multivalley states occurring around distinct wavevectors of some semimetal surfaces provide a basis for the occurrence of charge density waves (CDWs).[1,2,3] The mechanism of multivalley CDWs at semiconductor surfaces, first described by Kelly and Falicov in the 70 s is conceptually similar to that of 1D Peierls CDWs.[4] Both mechanisms are based on an almost perfect nesting between states with wavevectors k concentrated around welldefined values at the Fermi level. In the ordinary two (three)dimensional case, where nesting is defined by stationary diameters across the Fermi contour (surface), fluctuations admix states with any Δk connecting the continuum of states at the Fermi level. In multivalley systems with narrow pockets, fluctuations can only mix states with Δk either very small or close to the intervalley nesting vectors, making intervalley CDWs more robust against fluctuations. Multivalley CDWs are generally, albeit not necessarily, stabilised by electron–phonon (e–ph) interaction.[3,5,6,7]

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Results

Conclusion