Ca3P2and other topological semimetals with line nodes and drumhead surface states

Abstract

As opposed to ordinary metals, whose Fermi surfaces are two dimensional, topological (semi-)metals can exhibit protected one-dimensional Fermi lines or zero-dimensional Fermi points, which arise due to an intricate interplay between symmetry and topology of the electronic wavefunctions. Here, we study how reflection symmetry, time-reversal symmetry, SU(2) spin-rotation symmetry, and inversion symmetry lead to the topological protection of line nodes in three-dimensional semi-metals. We obtain the crystalline invariants that guarantee the stability of the line nodes in the bulk and show that a quantized Berry phase leads to the appearance of protected surfaces states, which take the shape of a drumhead. By deriving a relation between the crystalline invariants and the Berry phase, we establish a direct connection between the stability of the line nodes and the drumhead surface states. Furthermore, we show that the dispersion minimum of the drumhead state leads to a van Hove singularity in the surface density of states, which can serve as an experimental fingerprint of the topological surface state. As a representative example of a topological semi-metal, we consider Ca3P2, which has a line of Dirac nodes near the Fermi energy. The topological properties of Ca3P2 are discussed in terms of a low-energy effective theory and a tight-binding model, derived from ab initio DFT calculations. Our microscopic model for Ca3P2 shows that the drumhead surface states have a rather weak dispersion, which implies that correlation effects are enhanced at the surface of Ca3P2.

Triple Point Topological Metals

“…In type-A TPTMs the crossing of conduction and valence (occupied and unoccupied) bands occurs on a high-symmetry line and is quadratic, while for the type-B phase this quadratic touching point splits into two points, where the bands cross linearly. The presence of nodal lines with nontrivial Berry phase, as is the case for type B, is generally associated with the appearance of surface states [26,27]. The merging and subsequent annihilation of nodal lines is similar to the nexus point discussed in the context of 3 He-A and Bernal-stacked graphite with neglected spin-orbit coupling (SOC) [28][29][30][31].…”

Photovoltaic anomalous Hall effect in line-node semimetals

“…Weyl semimetals have become a hot topic because the real Weyl semimetal materials has been theoretically proposed 9,10 and experimentally discovered in the inversion symmetry breaking TaAs class crystal [11][12][13][14] . Differently from the Dirac/Weyl semimetals where the conduction band touches the valence band at discrete points in the momentum space, the conduction and valence bands in topological line-node semimetals touch each other on closed lines and symmetry protected drumhead surface states emerge 3,4,[15][16][17] . Recently, several theoretical proposals [18][19][20][21][22][23][24][25][26][27] and experimental studies [26][27][28][29][30][31][32] appeared on line-node materials.…”

Circular dichroism and radial Hall effects in topological materials

“…For instance, TI's possess protected Kramers degeneracies on their surfaces [1][2][3], whereas Dirac and Weyl semimetals have discrete point singularities in their bulk [4][5][6][7][8][9][10][11][12][13][14][15][16]. Intriguingly, the band-crossing can also form a symmetry-protected 1D loop [16][17][18][19][20][21][22][23][24][25][26][27][28]. Upon symmetry breaking, the loop can be reduced to Weyl points or a full gap [19].…”