Type-II Dirac semimetals in the YPd2Sn class

Abstract

The Lorentz-invariance-violating Weyl and Dirac fermions have recently attracted intensive interests as new types of particles beyond high-energy physics, and they demonstrate novel physical phenomena such as angle-dependent chiral anomaly and topological Lifshitz transition. Here we predict the existence of Lorentz-invariance-violating Dirac fermions in the YPd2Sn class of Heusler alloys that emerge at the boundary between the electron-like and hole-like pockets in the Brillouin zone, based on the first-principles electronic structure calculations. In combination with the fact that this class of materials was all reported to be superconductors, the YPd2Sn class provides an appropriate platform for studying exotic physical properties distinguished from conventional Dirac fermions, especially for realizing possible topological superconductivity.Conceptually by generalizing topological characterization from insulator to metal, it has been realized that the Dirac [1][2][3][4] and Weyl semimetals [5][6][7][8][9] are new classes of three dimensional (3D) topological materials, different from the well-studied 3D topological insulators (TI) [10][11][12][13]. For Dirac semimetals with both timereversal and space-inversion symmetries, a Dirac point is a linear crossing of two doubly-degenerate bands nearby the Fermi energy with its stability protected by additional symmetry such as a certain crystalline symmetry, while a Weyl point can be obtained by breaking either the time-reversal or the space-inversion symmetry in Dirac semimetals, being a linear crossing of two nondegenerate bands nearby the Fermi energy only available in 3D. A Weyl point acts as a magnetic monopole with either positive or negative charge (chirality) in 3D moment space, while a Dirac point represents a pair of magnetic monopoles with opposite charges. Thus, the Dirac and Weyl semimetals possess a large variety of novel phenomena, such as quantum magnetoresistance [14] and chiral anomaly [15]. In addition, the Dirac and Weyl fermions in condensed matter physics correspond to the relativistic Dirac and Weyl fermions in high-energy physics. Nevertheless, the Lorentz invariance is only strictly required in high-energy physics but not necessary in condensed matter physics [16]. This brings hope for condensed matter physicists to discover new types of fermions in real materials.Very recently, the Lorentz-invariance-violating, namely the type-II, Weyl and Dirac fermions were first conceptually proposed and further predicted in several compounds [16][17][18][19][20][21][22] [48,49]. Although the intensive attention has been paid on half Heusler alloys, the likely topological electronic states of full Heusler alloys are rarely studied [50,51].Here, we predict the existence of type-II Dirac fermions in the full Heusler alloys YPd 2 Sn, ScPd 2 Sn, ZrPd 2 Al, HfPd 2 Al, ZrNi 2 Al, and HfNi 2 Al , namely the YPd2Sn class, by using the first-principles electronic structure calculations. For this class, we find that there are three pairs of symmetry-protected type...

A general route to form topologically-protected surface and bulk Dirac fermions along high-symmetry lines

“…Furthermore, the presence of trigonal symmetry is not a pre-requisite. The 'Heusler' alloys (O h ) ({Y, Sc,}Pd 2 Sn), ({Zr, Hf,}Pd 2 Al) and ({Zr, Hf,}Ni 2 Al), have been recently verified to host type-II bulk Dirac cones at the Fermi level [36]. At higher energies (approximately 1 eV below the Fermi level in YPd 2 Sn), however, calculations ( Fig.…”

“…(a) Orbitally projected band structure calculation of β-CuI (D 3d ) adapted from[35]. (b) Band structure calculations of YPd2Sn (O h ) reprinted with permission from[36]. Copyright (2019) by the American Physical Society.…”

Ternary wurtzite CaAgBi materials family: A playground for essential and accidental, type-I and type-II Dirac fermions

“…In addition, since accidental Dirac points are located at k-points with lower symmetry (compared with essential ones), the dispersions around them are less constrained. It is possible to have the Dirac cone completely tipped over along certain direction [22,23], realizing a so-called type-II Dirac point [24], which has been identified in VAl 3 [24], PdTe 2 [25][26][27], PtSe 2 family [28][29][30] and others [31][32][33]. Fascinating yet distinct physics have been proposed for type-I and type-II points, and it has been theoretically argued in the context of Weyl points that when both types coexist in a single hybrid material, even more interesting effects could appear [34,35].…”

Emergence of Type-II Dirac Points in Graphynelike Photonic Lattices

“…While type-I Dirac cones (DCs) are common in honeycomb configurations and other two-(2D) and three-dimensional (3D) materials [3][4][5][6][7][8][9][10][11][12][13][14], this is not the case for type-II DCs. In recent studies, type-II Dirac semimetals [26][27][28][29] and 3D topological photonic crystal structures [30] have been demonstrated. Along these lines, of interest would be to identify 2D photonic systems with analogous dispersion characteristics, akin to those proposed in solid state physics [31,32].…”