Friedel oscillations at the surfaces of rhombohedral $N$-layer graphene

Abstract

The low-energy physics of rhombohedral $N$-layer graphene mainly arises on the external layers, where most of the π electrons are located. Their Bloch band structure defines a two-band semimetal; the dispersion relation scales as $\pm q^N$ with the momentum norm $q$ in the vicinity of two nonequivalent valleys. In this paper, we address the problem of elastic scattering through a localized impurity located either on the surface of the material or within the bulk, and focus on the quantum interferences it induces on the two external layers. It is apprehended in the framework of a $T$-matrix approach, both numerically and analytically, regardless of the impurity magnitude, which enables the description of realistic scatters. In rhombohedral multilayer graphene, the impurity induces Friedel oscillations that always decay as $1/r$. As a result, monolayer graphene is the only material of the rhombohedral class that exhibits $1/r^2$-decaying Friedel oscillations. The interference patterns are subsequently analyzed in momentum space. This analysis enables a clear distinction between monolayer graphene and multilayer graphene. It also shows that the interference pattern reveals the whole Bloch band structure, and highlights the number of layers stacked in the material, as well as the $\pi$-quantized Berry phases that characterize the existence of nodal points in the semimetallic spectrum. Experimentally, these features may be probed from scanning tunneling microscopy, when imaging the local density of states at the surfaces of suspended rhombohedral $N$-layer graphene.

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• Observation of Kekulé vortices induced in graphene by hydrogen adatoms
• Characterization and manipulation of intervalley scattering induced by an individual monovacancy in graphene
• Wavefront dislocations reveal the topology of quasi-1D photonic insulators
• Anisotropic Friedel oscillations in graphene-like materials: The Dirac point approximation in wave-number dependent quantities revisited
• Quasiparticle interference patterns in bilayer graphene with trigonal warping
• Defects in Graphene : A Topological Description
• Geometrical phase shift in Friedel oscillations
• Robust wavefront dislocations of Friedel oscillations in gapped graphene
• Recent advances of defect-induced spin and valley polarized states in graphene
• Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
• Intervalley quantum interference and measurement of Berry phase in bilayer graphene
• Real-space study of zero-field correlation in tetralayer rhombohedral graphene
• Experimental evidence of the topological obstruction in twisted bilayer graphene
• Wavefront dislocations in graphene systems revealed by transport measurement
• Detecting the topological winding of superconducting nodes via Local Density of States
• Analogue of atomic collapse for adatoms on rhombohedral multilayer graphene
• Pseudospin-mediated Atomic-scale Vortices and Their Quantum Interferences in Monolayer Graphene
• Surface states and quasiparticle interference in Bernal and rhombohedral graphite with and without trigonal warping
• High conductivity from cross-band electron pairing in flat-band systems
• Charge waves and dynamical signatures of topological phases in Su-Schrieffer-Heeger chains