Exploring the Dirac nature of ${\mathrm{RbBi}}_2$

Characteristics of topological semimetals such as a nonsaturating magnetoresistance (MR), a field-induced metal to semiconducting crossover and a robust resistivity plateau are observed under a magnetic field in type-I ${\mathrm{RbBi}}_2$ bulk superconductor with $T_{\mathrm{c}}=4.15$ K. The MR exhibits a notable 3500% increase at 2 K and 9 T and the resistivity follows a power law temperature dependence, while the MR $\propto H^{1.26}$, indicating weak carrier compensation. First principles calculations provided insights into the dynamical stability of the cubic structure at 0 K. Both hole and electron pockets are observed at the Fermi surface. The electron-phonon interaction constant indicates weak coupling strength ($<1$) that leads to a maximum predicted $T_{\mathrm{c}}$ of 2.852 K. Just below the Fermi level, ${\mathrm{E}}_F$, the electronic band structure consists of linear band crossings at the $X$ points in the Brillouin zone (BZ) corresponding to massless, symmetry-protected Dirac fermions.

Figure 1

(a) The unit cell showing the cubic crystal structure of ${\mathrm{RbBi}}_2$. (b) The Bi sublattice forming a hyperkagome structure on a plane perpendicular to the threefold (111) axis. (c) The fourfold screw $S_4$ and twofold $C_2$ rotations of the lattice. Number indicates the fractional part of the vertical positions of the atoms (in units of the lattice constant $a$). (d) Brillouin zone and high symmetry points.

Figure 2

(a) The electrical resistivity as a function of applied magnetic field in the range 0–9 T. (b) Temperature dependence of resistivity at low temperatures in the presence of applied field H = 9 T. The solid line shows the power law fit $\rho ={\rho }_0+A{T}^2+B{T}^3+C{T}^5$ to the data at low temperatures. (c) The low temperature resistivity behavior at applied fields measured on a quenched sample of ${\mathrm{RbBi}}_2$ above the critical field. (d) The residual resistivity at 2 K plotted as a function of the applied magnetic field. (e) The magnetoresistance (MR) of ${\mathrm{RbBi}}_2$ is compared between data collected at 2 and 5 K. (f) MR fitted with $MR=\alpha {(H/{\rho }_0)}^m$ at 2 K and 5K showing the Kohler scaling.

Figure 3

Phonon dispersion curves of ${\mathrm{RbBi}}_2$ along the high-symmetry directions using (a) Linear-response theory and (b) Finite displacement method. The high symmetry points are marked in the Brillouin zone in Fig. 1.

Figure 4

Electronic band structures of ${\mathrm{RbBi}}_2$ (a) without SOC (scalar relativistic) and (b) with SOC (fully relativistic). The Fermi energy (${\mathrm{E}}_{\text{F}}$) is set at 0 eV. (c) Dirac point at X at $-0.4187$ eV below the Fermi level. For the two pairs of bands that cross the Fermi level, the degenerate pair with lower (higher) energy are bands No. 5 and No. 6 (No. 7 and No. 8).

Figure 5

(a)–(d) Fermi surface without SOC for ${\mathrm{RbBi}}_2$. Four bands cross the ${\mathrm{E}}_{\text{F}}$, whose Fermi surface is shown here. The Brillouin zone showing the high symmetry points is shown in Fig. 1.

Figure 6

( a)–(d) Fermi surface and corresponding Fermi velocity of ${\mathrm{RbBi}}_2$ with SOC. The high symmetry points are labeled.