Half-Heusler topological insulators

Abstract

We predict the existence of triple point fermions in the band structure of several half-Heusler topological insulators by ab initio calculations and the Kane model. We find that many half-Heusler compounds exhibit multiple triple points along four independent C3 axes, through which the doubly degenerate conduction bands and the nondegenerate valence band cross each other linearly nearby the Fermi energy. When projected from the bulk to the (111) surface, most of these triple points are located far away from the surface ¯ Γ point, as distinct from previously reported triple point fermion candidates. These isolated triple points give rise to Fermi arcs on the surface, that can be readily detected by photoemission spectroscopy or scanning tunneling spectroscopy. The discovery of topological insulators (TIs) [1, 2] has generated much interest in the search for other novel topological states in condensed matter physics and materials science. As quasiparticle analogues of elementary particles of the standard model, Dirac fermions [3-6] and Weyl fermions [7-14] have recently been found in several materials (see reviews Refs. 15 and 16). Both Dirac and Weyl fermions exhibit Fermi arcs, unclosed Fermi surfaces, on the boundary, as a hallmark for the experimental detection. More recently, several exotic types of fermions, which do not have elementary particle counterparts, have been theoretically predicted as quasiparticle excitations near certain band crossing points that are protected by specific space-group symmetries [17, 18]. In particular, triple point (TP) fermions have been predicted in many materials with triply degenerate band crossing points [19-25]. These predictions have stimulated intensive experimental studies to search for their signatures, for example, using angle-resolved photoemission spectroscopy (ARPES) [26] and transport properties [27]. TPs can be viewed as an intermediate phase between fourfold degenerate Dirac points and twofold degenerate Weyl points. They also give rise to Fermi arcs when projected onto certain specific crystal facets. However, the detection of TP-induced Fermi arcs remains challenging from the material point of view. A pair of TPs are protected by the C 3v symmetry group (generated by a C 3 rotation and a σ v mirror operation) in certain compounds [19-24], for example, tensile-strained HgTe [19], MoP [20], and antiferromagnetic (AFM) half-Heusler compounds (e.g. GdPtBi) [24]. Even presuming that samples can be grown, the natural cleavable surface is usually the facet that is perpendicular to the C 3 axis. Consequently, two TPs at the unique C 3 axis are projected to the same ¯ Γ point of the surface Brillouin zone (BZ), resulting in the disappearance of Fermi arcs, as shown in a recent ARPES measurement on MoP [26]. Therefore, TP materials with easily measurable Fermi arcs are still required for the final experimental verification of TP fermions. In this work, we predict the existence of multiple TPs in several half-Heusler compounds in which the detection of Fermi arcs by ARPE...

Heusler, Weyl and Berry

“…In Heusler compounds, the variety of accessible electronic and magnetic properties together with the existence of a topological band order generates highly tunable and versatile multifunctional properties such as topological superconductivity or spin-structured topological surface states etc [33][34][35][36][37] . For application in modern devices, it is therefore essential to understand the origin and stability of the various exotic properties of these novel topological states.…”

“…By increasing spin-orbital interaction (such as replacing Sb by Bi), a topological phase transition occurs along with s-p band inversion. A large family of tunable materials, there are more than 50 Heusler compounds predicted to have non-trivial band order36,53,67 , and some of them have been experimentally verified via magneto transport measurements or angle resolved photoemission spectroscopy (ARPES)25,35,68,69 .The inverted band structure in Heusler compounds can be used to obtain a variety of other topological states; a typical example is the WSM. The half-Heusler compound GdPtBi (with Néel temperature TN = 9.2 K) has an electronic structure with inverted band order and a quadratic band touching at the Γ point25,70,71 .…”

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments

“…Majorana zero modes with their non-Abelian statistics offer a unique platform for future topological quantum computation devices10. Prominent candidates for 3D topological superconductivity are the Cu intercalated TI Bi 2 Se 3 1112, the doped topological crystalline insulator Sn 1− x In x Te13 and selected topological half-Heusler compounds141516.…”

Model Hamiltonian and time reversal breaking topological phases of antiferromagnetic half-Heusler materials

“…Around 50 half-Heusler compounds are theoretically predicted to possess inverted band structure and can be driven into the topological insulating phase by applying strains [38][39][40][41][42] . Unusual surface states were recently observed experimentally in LnPtBi(Ln=Lu, Y) 43 and LuPtSb 44 , and serve as an evidence of non-trivial bulk topology.…”