Prediction of Ideal Topological Semimetals with Triply Degenerate Points in theNaCu3Te2Family

Abstract

Triply degenerate points (TDPs) in band structure of a crystal can generate novel TDP fermions without high-energy counterparts. Although identifying ideal TDP semimetals, which host clean TDP fermions around the Fermi level (E_{F}) without coexisting with other quasiparticles, is critical to explore the intrinsic properties of this new fermion, it is still a big challenge and has not been achieved up to now. Here, we disclose an effective approach to search for ideal TDP semimetals via selective band crossing between antibonding s and bonding p orbitals along a line in the momentum space with C_{3v} symmetry. Applying this approach, we have successfully identified the NaCu_{3}Te_{2} family of compounds to be ideal TDP semimetals, where two, and only two, pairs of TDPs are located around the E_{F}. Moreover, we demonstrate a fundamental mechanism to modulate energy splitting between a pair of TDPs, and we illustrate the intrinsic features of TDP Fermi arcs in these ideal TDP semimetals.

From triple-point materials to multiband nodal links

“…Currently, nodal lines (NLs) [18][19][20][21] exhibiting a quantized Zak-Berry phase [22,23] are arguably the most investigated type of band degeneracy and were found to form intricate structures, including chains, links, and knots [24][25][26][27]. More recently, threefold-degenerate nodal points [28][29][30][31][32][33], also called triple points (TPs), received attention as peculiar intermediates between Weyl and Dirac points [34][35][36][37][38][39][40][41][42]. For spin-orbit-coupled (SOC) systems, TPs were classified into type A vs type B according to the absence or presence of attached nodal-line arcs [28], but they were also reported to occur in certain materials with negligible SOC [43][44][45][46][47], including Bernal graphite [48].…”

Observation of bulk states and spin-polarized topological surface states in transition metal dichalcogenide Dirac semimetal candidate NiTe2

“…These arise as emergent quasi-particles in crystals with linearly dispersing bands in vicinity of a degenerate band crossing point (either accidental or symmetry-enforced) and are protected by crystalline symmetries [5]. Double, triple and quadruple degeneracy of the band crossing leads to topologically protected Weyl [6][7][8][9][10][11][12][13][14], triple point [15][16][17][18][19][20][21] and Dirac fermions [22][23][24][25][26][27][28][29][30], respectively. In contrast to their high energy counter-parts, these emergent quasi-particles are not protected by Lorentz symmetry, and can also occur in a tilted form, giving rise to type-I and type-II Dirac fermions.…”

MgTa2N3 : A reference Dirac semimetal

“…The two-dimensional representation E 3/2 splits into two one-dimensional representations 1 E 3/2 and 2 E 3/2 , while E 5/2 changes into the twodimensional representation E 1/2 . Eventually, the DPs splits into two triple nodal points (TNPs) [31][32][33][34][35][36][37] . Type-B symmetry breaking preserves the C 3 symmetry while breaking all mirror symmetries σ v and σ d , thus resulting in the C 6 group or the C 3 group upon further breaking the C 2 symmetry.…”