Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

Abstract

Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops. These materials host a single hourglass Weyl loop circling around a high-symmetry point. Interestingly, there is also a spin-orbit Dirac point enabled by an additional screw axis. We show that the hourglass Weyl loop and the Dirac point are robust under a variety of applied strains. By breaking the screw axis, the Dirac point can be transformed into a second Weyl loop. Furthermore, by breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac point can both be transformed into a pair of spin-orbit Weyl points. Our work offers guidance and realistic material candidates for exploring fascinating physics of several novel 2D emergent fermions. arXiv:1902.09283v2 [cond-mat.mtrl-sci]

Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal

“…LG 80. Tight binding model on Si, Ge and Se elemental lattices [34] and DFT band structure of As 2 X 2 (X = Cl, F, I, Br) monolayers [35] [43]) splits linearly away from it, as justified numerically [43] (dispersion near X point was not discussed more closely). DFT band structure of monolayer Ta3SiTe6…”

“…1) For oblique and rectangular-p groups with all non-symmorphic elements having fractional translations parallel to one direction (for group 45), b 1 is perpendicular to that direction (to the symmorphic reflection plane). For group 34 (32,33,43) b 1 is along axis (screw axis) of order two.…”

Anisotropic correlation between the piezoelectricity and anion-polarizability difference in 2D phosphorene-type ternary GaXY (X = Se, Te; Y = F, Cl, Br, I) monolayers

“…As far, only two monolayer systems GaTeCl and GaTeI in the aforementioned GaXY family have been investigated systematically [23,24]. The possibility of exfoliation of GaTeCl and GaTeI monolayers from their bulk samples had been confirmed by calculating the corresponding exfoliation energy, and the dynamical stabilities were examined by phonon spectrum.…”

“…Very recently, Wu et al have realized the hourglass Weyl loops in the monolayer GaTeI-family based on first-principles calculations [23]. The 2D materials of this family possess black-phosphorene-type structure and have been predicted to be ferroelectric.…”

Al$_2$B$_2$ and AlB$_4$ monolayers: emergence of multiple two-dimensional Dirac nodal line semimetals with novel properties

“…Besides the important properties of these systems including non-dispersive Landau energy levels [35], high-temperature surface superconductivity [36], and specific long-range Coulomb interactions [37], one of the most notable characteristics of 2D NLSMs is that their topological features can be revealed by the angle-resolved photoemission spectroscopy (ARPES) measurements [38]. In spite of the large number of discovered 3D TSMs, there are a limited number of 2D materials exhibiting NLSMs [38][39][40][41][42]. Some examples include 2D Lieb lattice [43,44], monolayer borophene [45], honeycomb-Kagome lattice [46], transition metal chalcogenide monolayers [39], Cu 2 Si [47], and CuSe [48] monolayers, where the two last cases are experimentally realized.…”