Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe

Abstract

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While a detailed accessible conception exists from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Due to the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.The discovery of topological insulators has inspired a remarkably broad interest in materials whose band structures exhibit relativistic properties. The effects of a linear dispersion in one-dimensional edge channels of quantum spin Hall insulators [1], as well as in twodimensional surface states of three-dimensional topological insulators [2,3], have already been extensively studied. The implications of a linear band dispersion in threedimensional conductors, however, have only recently begun to be explored. Such materials, dubbed Dirac or Weyl semimetals, represent a condensed matter realization of the Weyl/Dirac equations, and may provide an environment for studying the properties of quasiparticles which have been postulated, but not yet unambiguously demonstrated, to exist in nature.In many of these materials [4], the Weyl or Dirac band crossing is caused by a band inversion, and is intimately connected to the point group symmetry of the crystal lattice. This lends similarities to the prototypical setup of topological insulators. In fact, both in the alkali pnictide (AB 3 , where A=(Na,K,Rb), B=(As,Sb,Bi)) and Cd 2 As 3 families that boast a number of important Weyl/Dirac compounds, the inversion occurs between metallic s-like and chalcogenic p-like orbitals, a situation very similar to that found in HgTe. The correspondence in terms of band structure between these compounds and HgTe has indeed been known since the 1970's [5]. The common motif is that, for the alkali pnictides and Cd 2 As 3 , the p-like j = 3/2 bands (Γ 8 in the T d point group) cross and yield Dirac (or Weyl) points, while in HgTe the Γ 8 bands just touch, derives from the higher (zincblende) point group symmetry of the HgTe crystal. Small crystal distortions from the zincblende symmetry, as present in Weyl/Dirac semimetals, are sufficient to crucially modify the electronic structure at low energies.In the 19...

Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs

“…Until today, angle-resolved photoelectron spectroscopy (ARPES) experiments have confirmed a number of materials as Weyl semimetals (WSM), based on a comparison of the measured bulk band structure to band calculations and the observation of surface Fermi arcs 1 , 9 , 10 , 14 , 15 . Manifestations of the nontrivial topology have also been found, accordingly, in magnetotransport experiments 16 , by scanning tunneling microscopy 17 , and via optically induced photocurrents 18 . The winding of the electronic wave functions in momentum space, however, which characterizes the immediate effect of a Berry flux monopole and thus the topology of the WSM, has so far remained elusive.…”

Volkov-Pankratov states in topological graphene nanoribbons

“…Such massive edge states were first described by Volkov and Pankratov [26][27][28], and are therefore refered to as Volkov-Pankratov (VP) states. Recently, VP states have attracted attention again in the context of topological insulators (TIs) [29][30][31][32][33] and topological superconductors [34]. Although VP states in TIs are not topologically protected, they are of topological origin, because they result from the band inversion between a topological and a trivial material [30].…”

Terahertz Magnetospectroscopy of Cyclotron Resonances from Topological Surface States in Thick Films of CdxHg1−xTe

“…The calculations below show that instead of a single topologically protected state, the interface now can host multiple VPS. [ 16,19,56,57 ] Similar to the case of the sharp interface, the energies of VPS lie in between the energies of the strain‐split light and heavy holes. Figure 13 schematically shows a sharp interface (as in sample #C, Figure 13a) and a smooth interface (as in sample #A or #B, Figure 13b).…”

“…These results indicate that smooth interfaces lead to the emergence of multiple surface states, known as Volkov–Pankratov states (VPS). [ 16,19,56,57 ] As the number N of these states is not fixed by topology (apart from the requirement ), their number and properties should be sensitive to a particular choice of materials, growth conditions, form of interfaces, strain profile, and so on. The dynamics of carriers occupying multiple VPS can be effectively 3D, similar to conventional quasi‐2D electrons occupying multiple sub‐bands in a wide quantum well, which would immediately explain our observations.…”

“…[ 7,8 ] Due to their specific energy dispersion, HgTe quantum wells and strained bulk films have revealed fascinating effects in magnetotransport [ 2,9 ] (for recent achievements, see refs. [10–19]), as well as in magneto‐ and terahertz‐spectroscopy. [ 20–30 ]…”