Pressure engineering of the Dirac fermions in quasi-one-dimensional Tl₂Mo₆Se₆

Abstract

Topological band dispersions other than the standard Dirac or Weyl fermions have garnered the increasing interest in condensed matter physics. Among them, the cubic Dirac fermions were recently proposed in the family of quasi-one-dimensional conductors A 2 Mo 6 X 6 (A= Na, K, In, Tl; X= S, Se, Te), where the band crossing is characterized by a linear dispersion in one k-space direction but the cubic dispersion in the plane perpendicular to it. It is not yet clear, however, how the external perturbations can alter these nontrivial carriers and ultimately induce a new distinct quantum phase. Here we study the evolution of Dirac fermions, in particular the cubic Dirac crossing, under external pressure in the representative quasi-one-dimensional Tl 2 Mo 6 Se 6 via the first-principles calculations. Specifically, it is found that the topological properties, including the bulk Dirac crossings and the topological surface states, change progressively under pressure up to 50 GPa where it undergoes a structural transition from the hexagonal phase to body-centered tetragonal phase. Above 50 GPa, the system is more likely to be topologically trivial. Further, we also investigate its phonon spectra, which reveals a gradual depletion of the negative phonon modes with pressure, consistent with the more three-dimensional Fermi surface in the high-pressure phase.Our work may provide a useful guideline for further experimental search and the band engineering of the topologically nontrivial fermions in this intriguing state of matter.

Exact solutions of Kondo problems in higher-order fermions

“…The left picture of Fig. 2 shows the case for the cubic fermion model in three dimensions (22), which suffices to illustrate our framework). As shown in Fig.…”

“…In particular, most recently, even more exotic Weyl and Dirac semimetals which exhibit effective fermions with higher-order dispersion relations have been proposed. These higher-order dispersion relations take a form that is linear in one direction, but quadratic or cubic in the orthogonal plane [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . Such materials are named quadratic and cubic Weyl/Dirac semimetals respectively 12,17,22 , with their corresponding emergent fermions referred to as quadratic and cubic Weyl/Dirac fermions respectively 11,12,15 , and they are classified as Weyl/Dirac according to their 2-fold/4fold band degeneracies at their band crossings 12,13,15 .…”

“…These higher-order dispersion relations take a form that is linear in one direction, but quadratic or cubic in the orthogonal plane [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . Such materials are named quadratic and cubic Weyl/Dirac semimetals respectively 12,17,22 , with their corresponding emergent fermions referred to as quadratic and cubic Weyl/Dirac fermions respectively 11,12,15 , and they are classified as Weyl/Dirac according to their 2-fold/4fold band degeneracies at their band crossings 12,13,15 . For example, in three dimensions, the cubic Weyl/Dirac semimetals display the dispersion relation, in its simplest form,…”

“…A number of materials for the quadratic and cubic Weyl/Dirac semimetals have been recently proposed and extensively studied. Examples of quadratic Weyl/Dirac semimetals include HgCr 2 Se 4 , SiSr 2 , bandinverted α−Sn and PdSb 2 11,14,16 , and examples of cubic Weyl/Dirac semimetals include LiO S O 3 and quasi-onedimensional molybdenum monochalcogenide compounds A I (MoX VI ) 3 , where A I = Na, K, Rb, In or Tl, X VI = S, Se or Te 17,19,22,23 . Moreover, various novel quantum phenomena are predicted to take place in these semimetals, such as charge density wave, non-Fermi liquid, and topological superconductivity 12,18,19,[22][23][24][26][27][28][29][30][31][32][33][34][35] .…”

“…Examples of quadratic Weyl/Dirac semimetals include HgCr 2 Se 4 , SiSr 2 , bandinverted α−Sn and PdSb 2 11,14,16 , and examples of cubic Weyl/Dirac semimetals include LiO S O 3 and quasi-onedimensional molybdenum monochalcogenide compounds A I (MoX VI ) 3 , where A I = Na, K, Rb, In or Tl, X VI = S, Se or Te 17,19,22,23 . Moreover, various novel quantum phenomena are predicted to take place in these semimetals, such as charge density wave, non-Fermi liquid, and topological superconductivity 12,18,19,[22][23][24][26][27][28][29][30][31][32][33][34][35] . It is therefore timely and of theoretical importance to study Kondo problems in these higher-order fermion (KHOF) systems, in particular, using analytically exact methods.…”