Fermiology and Superconductivity of Topological Surface States in ${\mathrm{PdTe}}_2$

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor ${\mathrm{PdTe}}_2$ by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing ${\mathrm{PdTe}}_2$ with its sister compound ${\mathrm{PtSe}}_2$, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding $p$-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Figure 1

(a) ARPES Fermi surface of ${\mathrm{PdTe}}_2$ ($E_F\pm 5\mathrm{meV}$; $h\nu =107\mathrm{eV}$; p-pol, probing close to an $A$ plane along $k_z$). (b) In-plane dispersion along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction [$h\nu =24\mathrm{eV}$, probing a similar $k_z$ value as in (a)]. (c) Corresponding supercell calculations of the dispersion over an extended energy range, projected onto the top two unit cells of ${\mathrm{PdTe}}_2$. (d) Out-of-plane bulk band dispersions along the $\mathrm{\Gamma }-A$ direction of the Brillouin zone from DFT calculations, projected onto the chalcogen $p_{x,y}$ (red) and $p_z$ (cyan) orbitals. (e)–(h) Equivalent measurements and calculations for ${\mathrm{PtSe}}_2$ (ARPES measurements: $h\nu =107\mathrm{eV}$; p-pol). Topological surface states (TSS), bulk Dirac points (BDP), and inverted band gaps (IBG) are labeled.

Figure 2

(a) Three-component spin-resolved ARPES Fermi surface measured ($h\nu =24\mathrm{eV}$) over the range shown in (b). Here $⟨S_x⟩$ and $⟨S_y⟩$ are perpendicular to and along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction, respectively. $⟨S_z⟩$ is the out-of-plane spin component. (b) Near-$E_F$ constant energy contours measured from spin-integrated ARPES ($h\nu =24\mathrm{eV}$) over the portion of the surface Brillouin zone where the topological states reside. (c) Schematic representation of the global Fermi surface spin texture throughout the surface Brillouin zone that is deduced from our measurements. (d) The in-plane spin texture (arrows) determined directly from the spin-resolved measurements and shown atop the measured spin-integrated Fermi surface segment. (e) ARPES-measured dispersion ($h\nu =24\mathrm{eV}$) and (f) corresponding supercell calculation, cutting through the TSS Fermi surfaces along the dashed line indicated in (b). $k_z$-dependent bulk band calculations are overlaid in (e) and visible as diffuse spectral weight in (f), demonstrating how small projected band gaps control the dispersion of the TSS (see also Supplemental Material, Fig. S2 [35]).

Figure 3

(a) Surface topography of ${\mathrm{PdTe}}_2$ measured at $T=8\mathrm{K}$ of a $8.5\times 8.5{\mathrm{nm}}^2$ region (bias voltage: $V=10\mathrm{mV}$, tunneling current set point: $I=0.4\mathrm{nA}$). (b) ARPES spectra (top; $T=5\mathrm{K}$, $h\nu =24\mathrm{eV}$, integrated along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction of the Brillouin zone) and differential conductance spectra measured using STM at $T=8\mathrm{K}$ (middle) and $T=40\mathrm{mK}$ (bottom). (c) Low-energy spectra measured at 40 mK and performed with a normal ($N$, top) and superconducting ($S$, bottom) tip. The NS-junction (SS-junction) spectra are averaged over a $5.4\times 5.4{\mathrm{nm}}^2$ ($10\times 10{\mathrm{nm}}^2$) area and are normalized to the conductance at 0.6 mV. The dashed lines show the result of Dynes fits, incorporating thermal broadening of 100 mK [21]. For the NS junction, a lock-in amplitude of $25\mu \mathrm{V}$ was used, with the fit yielding a sample superconducting gap size of $\mathrm{\Delta }=215\mu \mathrm{V}$ with a Dynes broadening parameter of $\mathrm{\Gamma }=65\mu \mathrm{V}$. For the SS junction, a lock-in amplitude of $30\mu \mathrm{V}$ was used with Dynes broadenings of 18 and $4\mu \mathrm{V}$ for sample and tip, respectively. The obtained superconducting gap of the sample and tip is $240\mu \mathrm{V}$. (d) Radially averaged decay of zero bias conductance (ZBC) with distance ($R$) from the centre of a vortex core, measured with a superconducting tip in a magnetic field of $7\pm 2\mathrm{mT}$. The inset shows the real-space image of the vortex via its enhanced ZBC. (e) The radial dependence of the full superconducting gap structure with distance from the center of the vortex core, obtained using $V=8\mathrm{mV}$, $I=0.4\mathrm{nA}$ and a lock in amplitude of $30\mu \mathrm{V}$.