Probing the topological phase transition via density oscillations in silicene and germanene

Abstract

We theoretically investigated two kinds of density oscillations, the Friedel oscillation and collective excitation in the silicene and germanene within the random phase approximation, and found that the tunable spin-valley coupled band structure could lead to some exotic properties in these two phenomena. Based on an exact analytical and numerical analysis, we demonstrated that the beating of the screened potential as well as the undamped plasmon mode can be taken as fingerprints of a topological phase transition in doped silicene and doped germanene. Thus our proposal here establishes the connection between the topological phase transition and the density oscillations that can be accessed by a variety of experimental techniques.The quantum spin Hall effect (QSHE) [1, 2] has been studied extensively in both theoretical and experimental aspects. It is well known that topologically protected helical edge states are a distinct feature which characterizes the QSHE [3]. The transport measurement of edge states requires that the bulk state must be insulating. In practice, the system is usually metallic resulting from defects, self-doping and charge transfer from metallic substrates, and thus the detection of the topological phase transition (TPT) when the bulk is metallic becomes urgent and important in two-dimensional systems. In this Rapid Communication, we connect the TPT with two kinds of density oscillations: Friedel oscillation [4] and collective excitation in silicene and germanene.Silicene [5,6], a single layer of silicon atoms forming a two-dimensional (2D) buckled honeycomb lattice, can be regarded as the silicon-based counterpart of graphene [7]. The buckled honeycomb structure gives rise to a tunable spin-valley coupled band structure, which accounts for many exotic transport and superconducting phenomena [8][9][10][11][12][13][14] and makes silicene a promising candidate for the QSHE [15]. So far silicene or its superstructure has only been synthesized on metallic surfaces [16][17][18][19], hence the transport measurement of the helical edge states is prevented due to the metallic bulk state. On the other hand, it has been claimed that a Dirac-like spectrum does exist in silicene from experimental observations [16,17]. Although there is some debate about the origin of the linear dispersion [20], it is still highly worthwhile to examine whether or not silicene hosts the QSH state.In this Rapid Communication, we propose a detection method of TPT by employing both the Friedel oscillation and collective excitation in silicene, and show how to extract the information about the TPT from these two * Electronic address: jhzhou@andrew.cmu.edu effects. First, the screened potential of charged impurities has a beating structure of Friedel oscillations (the interference pattern of two branches of density waves of electrons). As one band gap decreases (for example, the spin-up gap in Fig. 1), the beating of the screened potential gradually becomes faint and eventually vanishes at the TPT point. Second, the undamped pl...

Tunable Intrinsic Plasmons due to Band Inversion in Topological Materials

“…2. It is useful to point out that for the intrinsic gapped graphene [39,40], silicene and other buckled honeycomb lattices [42,43], the polarization function within the random phase approximation satisfies the relation Re[Π(q, ω)] ≤ 0 or Re[ε(q, ω)] ≥ 1 [39]. As a result, when the Fermi level lies in the band gap and has a vanishing DOS, these systems hardly develop a plasmon excitation at zero temperature.…”

Spin and valley polarization of plasmons in silicene due to external fields

“…In graphene they have been studied extensively both theoretically 20 and experimentally 21 . So far though in silicene the relevant studies are limited 22,23 and do not take into account the effect of an exchange field M which can be induced by ferromagnetic adatoms 24 or a ferromagentic substrate 25,26 . This is important as this field leads to spin-and valley-polarized currents 27 and, as will be shown, brings a spin and valley texture to the particlehole excitation spectrum (PHES).…”

Relaxation times and charge conductivity of silicene

“…Density-density response function at the zero Rashba limit. As we have already pointed out, the intrinsic Rashba spin-orbit coupling is very small, and it is often reasonable to neglect it for simplicity [33,34]. Taking λ R = 0, the Hamiltonian (1) becomes diagonal in the spin space,…”