Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimetals. Such ideal Weyl semimetals could further provide a unique platform to study emergent phenomena such as the interplay between ideal Weyl fermions and superconductivity in the half-Heusler compound LaPtBi.
Recently, topological quantum states of non-Hermitian systems, exhibiting rich new exotic states, have attracted great attention in condensed-matter physics. As for the demonstration, most of non-Hermitian topological phenomena previously focused on are in one-and two-dimensional systems. Here, we investigate three-dimensional non-Hermitian nodal-line semimetals in the presence of a particle gain-and-loss perturbation. It is found that this perturbation will split the original nodal ring into two exceptional rings (ERs). The topological nature of the bulk electronic structure is characterized by two different topological invariants, namely, the vorticity and the winding number defined for a one-dimensional loop in momentum space, both of which are shown to take half-integer (integer) values when an odd (even) number of ERs thread through the loop. The conventional bulksurface correspondence in non-Hermitian nodal-line semimetals is found to break down, where the surface zero-energy flat bands are no longer bounded by projections of bulk ERs. Alternatively, a macroscopic fraction of the bulk eigenstates can be localized near the surface, thus leading to the so-called non-Hermitian skin effect.
Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2 are ideal Weyl semimetals, having largely separated Weyl points (∼ 0.05Å −1 ) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-power and high-speed electronics.Weyl fermions, originally introduced as massless chiral fermions, are described by the Weyl equation [1]. Even though a number of elementary particles were considered as candidates of Weyl fermions, conclusive evidences of Weyl fermions as elementary particles are still lacking. Weyl fermions were also proposed as emergent low-energy quasiparticles in condensed matter systems breaking either time-reversal or spatial-inversion symmetry [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. One hallmark of Weyl semimetals is the existence of Fermi arcs in surface states [3]. So far the only experimentally known Weyl semimetals are the TaAs-class compounds, in which two sets of inequivalent Weyl points away from the Fermi level and complex Fermi surfaces were found by ARPES experiments [17][18][19]. Experimental evidences of negative magnetoresistance [2,20] induced by the chiral anomaly were also reported [21][22][23][24][25][26]. However, definite signatures of the chiral anomaly in the quantum limit, such as the linear-B negative magnetoresistance [2,20,27] and the emergent supersymmetry [28], and others [29][30][31][32] haven't been experimentally observed in known Weyl semimetals, which is partly due to the facts that the Weyl points are not all at the Fermi level and that there are coexisting trivial Fermi pockets. Therefore, it is urgent to discover ideal Weyl semimetals with only symmetry-related Weyl points at the Fermi level.In this work, we focus on a large family of ternary chalcopyrites ABC 2 at stoichiometry, which were of great interest because of potential applications including the thermoelectric effect, non-linear optics and solar cells [33,34]. Recently, some ternary chalcopyrites were predicted to be topological insulators [35]. Here, our first-principles calculations find that the chalcopyrite compounds CuTlSe 2 , AgTlTe 2 , AuTlTe 2 and ZnPbAs 2 are a class of ideal Weyl semimetals having eight symmetry-related Weyl points exactly at the Fermi level, but without any fine tuning. CuTlTe 2 and ZnPbSb 2 are also Weyl semimetals having eight symmetry-related Weyl points in energy gaps but have a few coexisting trivial bands around the X point; consequently they are not ideal Weyl semimetals at stoichiometry but can be tuned to be ideal Weyl semimetals by gating or doping. The ideal Weyl semimetals predicted in the chalcopyrites are analogous to those in compressively strained Hg...
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