Unconventional Superconductivity in YPtBi and Related Topological Semimetals

Abstract

YPtBi, a topological semimetal with very low carrier density, was recently found to be superconducting below Tc = 0.77 K. In the conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would therefore not allow for superconductivity. Based on relativistic density functional theory calculations of the electron-phonon coupling in YPtBi it is found that carrier concentrations of more than 10 21 cm −3are required to explain the observed critical temperature with the conventional pairing mechanism, which is several orders of magnitude larger than experimentally observed. It is very likely that an unconventional pairing mechanism is responsible for the superconductivity in YPtBi and related topological semimetals with the Half-Heusler structure.A series of Half-Heusler compounds with heavy elements were predicted to have topologically non-trivial band order [1][2][3]. These compound have high cubic symmetry, however without inversion symmetry. The normal band order with the s-like, twofold degenerate Γ 6 state sitting above the p-like, fourfold degenerate Γ 8 -state is inverted in some of these compounds due to spin-orbit coupling. In their natural state, the cubic symmetry leads to a band degeneracy at Γ around the Fermi level, rendering them semimetals with topologically non-trivial band order (topological semimetals) and very low density of states (DOS) at the Fermi level D(E F ). By breaking the cubic symmetry with some amount of uniaxial strain, the compounds can be made insulating, so they could become 3D topological insulators [4]. They would exhibit metallic surface states with Dirac-like dispersion, i.e., the electrons behave as massless particles with ultrahigh mobility, while at the same time being insulating in the bulk. These surface states are topologically protected as long as time-reversal symmetry is preserved, i.e., they are protected against scattering from non-magnetic impurities. Indeed, for some of these materials there is experimental evidence for topologically nontrivial bandstructures and the presence of Dirac surface states [5][6][7], although none were found to be insulating in the bulk. Some compounds from this class were found to be superconductors with critical temperatures up to 1.8 K, e.g. LaPtBi, LuPtBi, LuPdBi, YPtBi,. Compounds of the type RPdBi (R is a lanthanide with an open 4f shell) that show coexisiting local moment antiferromagnetism as well as superconductivity were found, pointing to the presence of spin triplet Cooper pairs [12], which is allowed due to the missing structural inversion symmetry [13]. Due to the topologically nontrivial band structure, novel collective excitations are possible, in particular surface Majorana fermions [14]. These could provide the basis for low-decoherence quantum processing [15].Superconducting semiconductors such as GeTe and SnTe are long known [16,17] and their superconductivity can be explained [17] with the Eliashberg theory of electron-phonon mediated superc...

Crystal growth of Dirac semimetal ZrSiS with high magnetoresistance and mobility

“…7 shows the C P /T data fitting below 55  K using the expression of , where the T linear term in C p represents the electronic contribution and the higher order term represents the lattice contribution. The derived Sommerfeld coefficient γ is estimated to be 6.84 mJ mol −1   K −2 , which is higher than several other typical semimetals including NbAs (0.09(1) mJ mol −1  K −2 )34, Y 3 Ir 4 Ge 13 (4.3 mJ mol −1  K −2 )35, and YPtBi (4 mJ mol −1  K −2 )36. The phononic contribution is estimated to be β  = 5.54 × 10 −5  J mol −1   K −3 .…”

Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals

“…[11,23]. In the present work, we instead consider this self-consistent equation in terms of the barred gap functionφ ± φ ± (iω n , k) ≡ kF ± (iω n , k), (9) such that the linearized Eliashberg equation becomes a symmetric eigenvalue equation of the form ρφ = S φ (see Appendix A) :…”

“…For most of these materials, such as diamond and silicon, experimental data and ab-initio calculations [2][3][4] point towards a conventional pairing mechanism mediated by phonons [5,6]. However, this picture does not seem to hold for some dilute semiconductors such as SrTiO 3 [7], PbTe [8] and bismuth-based half-Heusler materials like YPtBi [9] where other pairing mechanisms have been suggested [10][11][12][13]. In various works it is proposed that YPtBi is a three-dimensional (3D) quadratic bandtouching Luttinger semimetal [13][14][15], where the quasiparticles are characterized by a pseudospin j = 3/2 due to the strong spin-orbit coupling [13,[16][17][18].…”

Interacting Majorana modes at surfaces of noncentrosymmetric superconductors

“…(27) for all plaquettes, we extend the definitions in Eqs. (23) and (24) such that for x ≤ 0 or y ≤ 0 the product is understood as equaling 1.…”