Topological surface states above the Fermi level in ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$

We report a detailed experimental study of the band structure of the recently discovered topological material ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$. Using the combination of scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy with surface K doping, we probe the band structure of ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$ with energy and momentum resolution above the Fermi level. Our experiments show the presence of multiple surface states with a linear Dirac-like dispersion, consistent with the predictions from previously reported band-structure calculations. In particular, scanning tunneling spectroscopy measurements provide experimental evidence for the strong topological surface state predicted at $460\mathrm{meV}$, which stems from the band inversion between Hf-$d$ and Te-$p$ orbitals. This band inversion comprised of more localized $d$ states could result in a better surface-to-bulk conductance ratio relative to more traditional topological insulators.

Figure 1

(a) Crystal structure of ${\mathrm{Hf}}_2{\mathrm{Te}}_2\mathrm{P}$. (b) STM topography taken at $-120\mathrm{mV}$ sample bias and $700\mathrm{pA}$ current set point. (c) Fermi surface of a pristine sample measured by ARPES. (d) STS measured $dI/dV$ spectrum with current and bias set points of $450\mathrm{pA}$ and $-1.5\mathrm{V}$.

Figure 2

(a)–(e) ARPES measured constant-energy contours of the K-doped sample for different positive energy values. (f) Band structure of the undoped sample along $\mathrm{\Gamma }\text{−}M$. (g) Band structure of the doped sample along $\mathrm{\Gamma }\text{−}M$. (h) Region highlighted by the gray box in (g) showing the $Q$ vectors (cyan lines) associated with the hole pocket centered at $\mathrm{\Gamma }$ for four different energies. (i) Band structure along the direction of the dotted line in (a). (j) Region highlighted by the gray box in (i) showing the $Q$ vectors (green lines) for five different energies. The appearance of duplicate bands in the K-doped data, when compared to the undoped sample, (f) and Fig. 1, can be attributed to multiple facets of the cleaved surface [21].

Figure 3

(a)–(c) STS maps showing the real-space LDOS near $170\mathrm{meV}$. (d)–(f) Fourier transforms of (a)–(c). (g)–(i) STS maps near $420\mathrm{meV}$. (j)–(l) Fourier transforms of (g)–(i). (m)–(o) Line cuts along $[Q_x=0,Q_y]$. The bias and current values were set to $800\mathrm{mV}$ and $500\mathrm{pA}$, respectively, and the $dI/dV$ signal was measured via a lock-in technique with a modulation amplitude of $10\mathrm{mV}$.

Figure 4

(a) Fourier transform of the STS map at $240\mathrm{mV}$. (b) Line cut of (a) along $[Q_x=0,Q_y]$, showing a distinct peak at $Q_y=0.09(1/\AA )$. (c) QPI dispersion maps along the $\mathrm{\Gamma }\text{−}M$ and $\mathrm{\Gamma }\text{−}K$ directions. The ARPES measured $Q$ vectors are overlaid by cyan and green dots (with solid line error bars) for the dispersion curves displayed in Figs. 2 and 2, respectively. $Q$-vector dispersions from the band-structure calculations along $\mathrm{\Gamma }\text{−}M$ are represented by the red and blue lines [9].