Observation of Dirac surface states in the noncentrosymmetric superconductor BiPd

Materials with strong spin-orbit coupling (SOC) have in recent years become a subject of intense research due to their potential applications in spintronics and quantum information technology. In particular, in systems which break inversion symmetry, SOC facilitates the Rashba-Dresselhaus effect, leading to a lifting of spin degeneracy in the bulk and intricate spin textures of the Bloch wave functions. Here, by combining angular resolved photoemission spectroscopy and low temperature scanning tunneling microscopy measurements with relativistic first-principles band structure calculations, we examine the role of SOC in single crystals of noncentrosymmetric BiPd. We report the detection of several Dirac surface states, one of which exhibits an extremely large spin splitting. Unlike the surface states in inversion-symmetric systems, the Dirac surface states of BiPd have completely different properties at opposite faces of the crystal and are not trivially linked by symmetry. The spin splitting of the surface states exhibits a strong anisotropy by itself, which can be linked to the low in-plane symmetry of the surface termination.

Figure 1

(a) Crystal structure of BiPd, showing the preferred cleaving plane. (b) Schematic representation of the Brillouin zone of BiPd as well as the surface Brillouin zone of the (010) and $\left(0\overline{1}0\right)$ surfaces. (c) Surface Brillouin zone with the cuts shown in panels (d)–(g) in blue. (d) Experimental electronic band structure of a BiPd(010) surface along the $S-\mathrm{\Gamma }$ direction ($\nu =21.2\mathrm{eV}$). (e) Electronic structure measured with $\nu =29\mathrm{eV}$. The photoemission intensities in (d) and (e) and in other photoemission intensity maps in this Rapid Communication are displayed using the color scale shown in (e). (f) and (g) Calculated electronic structure of BiPd in slab geometry including the cuts shown in (d) and (e). The size of the circles is proportional to the spectral weight of Bi $6p$ states in the first (red) and second (blue) layer of the (010) and $\left(0\overline{1}0\right)$ surfaces. The surface states are labeled $\mathrm{SS}n+$ and $\mathrm{SS}n-$, where + and $-$ denote whether they occur on the (010) or $\left(0\overline{1}0\right)$ surface, while $n$ numbers the surface states sequentially with increasing binding energy.

Figure 2

(a) and (b) Intensity maps of the energy and $k$-resolved surface band structure of BiPd measured along the $S-{\mathrm{\Gamma }}^{\prime }$ direction with $\nu =21.2\mathrm{eV}$ and $\nu =29\mathrm{eV}$, respectively. (c) Schematic representation of the surface states. (d) Constant energy cuts obtained at 0.59, 0.7, and 0.83 eV; energies indicated as dashed horizontal lines in (a). Overlaid on the constant energy cuts is a schematic of the surface Brillouin zone.

Figure 3

(a) and (b) Topographies of the $\left(0\overline{1}0\right)$ and (010) terminations, respectively, obtained with the same tip. Blue/red spheres represent Bi atoms and green/purple Pd atoms in the top surface layer [compare Fig. 1]. (c) Line cuts of the two terminations, showing the different corrugations. Line cuts shifted horizontally for clarity. (d) $dI/dV$ spectra obtained on $\left(0\overline{1}0\right)$ and (010) terminations. The surface state on the $\left(0\overline{1}0\right)$ face is at a slightly larger energy than on (010) ($V_{\mathrm{s}}=0.5\mathrm{V}, I_{\mathrm{s}}=2\mathrm{nA}$).

Figure 4

(a) and (b) Cuts in the $S-{\mathrm{\Gamma }}^{\prime }$ and $S-\mathrm{\Gamma }$ directions, respectively, from which the band structure parameters of the SS1+ state have been determined. Solid lines show a fit of the Rashba model [Eq. (1)] to the data. (c) Band structure of the Rashba spin-split surface state at the $S$ point (SS1+) as determined by fitting the Rashba model to the ARPES data. The Rashba spin splitting is highly anisotropic.