Unusual Dirac Fermions on the Surface of a Noncentrosymmetric $\alpha$-BiPd Superconductor

Combining multiple emergent correlated properties such as superconductivity and magnetism within the topological matrix can have exceptional consequences in garnering new and exotic physics. Here, we study the topological surface states from a noncentrosymmetric $\alpha$-BiPd superconductor by employing angle-resolved photoemission spectroscopy and first-principles calculations. We observe that the Dirac surface states of this system have several interesting and unusual properties, compared to other topological surface states. The surface state is strongly anisotropic and the in-plane Fermi velocity varies rigorously on rotating the crystal about the $y$ axis. Moreover, it acquires an unusual band gap as a function of $k_y$, possibly due to hybridization with bulk bands, detected upon varying the excitation energy. The coexistence of all the functional properties in addition to the unusual surface state characteristics make this an interesting material.

Figure 1

(a) Crystal structure of $\alpha$-BiPd (left), 3D Brillouin zone (top right), and 2D Brillouin zone (bottom right) projected onto the (010) plane in which we locate the respective positions of the high-symmetry points. Top surface layer (TSL) and bottom surface layer (BSL) are shown on the crystal structure. Preferable cleavage plane of the crystal is between any two Bi layers. The lattice parameters are given by $a=7.33\AA$, $b=10.86\AA$, and $c=8.82\AA$. In (b) we schematically show a typical measuring geometry in which $s$- and $p$-plane polarized lights are defined with respect to the analyzer entrance slit and the scattering plane (SP). Note here that $k_x$ and $k_z$ represent in-plane momentum vectors, while $k_y$ is the out-of-plane momentum vector. (c),(d) Energy distribution maps (EDMs) measured using $p$- and $s$-polarized lights, respectively along the $\mathrm{\Gamma }\text{−}X$ high-symmetry line with a photon energy of 75 eV. Similarly, panel (e) shows the EDM measured using $p$-polarized light along the $\mathrm{\Gamma }\text{−}Z$ high-symmetry line with 75 eV photon energy. (f) 3D view of the Dirac surface state from DFT calculations along $k_x$ and $k_z$.

Figure 2

DFT-GGA band structure calculations. (a) Bulk band structure without the spin-orbit coupling (SOC) for Bi $p_y$ orbital character (top left) and for Pd $d_{xy}$ (bottom left). Similarly, the bulk band structure with spin-orbit coupling is shown for $p_y$ (top right) and for Pd $d_{xy}$ (bottom right). (b) Slab calculations for the surface band structure along the high-symmetry lines $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}Z$ from the top and bottom surface layers with SOC for Bi $p_y$ and Pd $d_{xy}$ orbitals.

Figure 3

(a) Top panels show representative photon-energy-dependent EDMs taken along the $\mathrm{\Gamma }\text{−}X$ direction with 60, 75, and 100 eV measured using $p$-polarized light. (b) Energy distribution curves (EDCs) taken at $k_{\parallel }=0$ from the EDMs shown in (a). In (b) the black curve is a fit to the EDCs using double Lorentzian functions. (c) Experimentally obtained photon-energy-dependent band gaps ($E_g$) at the Dirac node. (d) DFT band structure calculated without magnetic order (black) and with the imposed magnetic moments on the surface Pd atoms (red), in which we could notice a band gap ($E_g$) opening at the Dirac node in the presence of magnetic order.