Quasiparticle interference of Fermi arc states in the type-II Weyl semimetal candidate $\mathrm{WT}{\mathrm{e}}_2$

Weyl semimetals possess linear dispersions through pairs of Weyl nodes in three-dimensional momentum spaces, whose hallmark arclike surface states are connected to Weyl nodes with different chirality. $\mathrm{WT}{\mathrm{e}}_2$ was recently predicted to be a new type of Weyl semimetal. Here, we study the quasiparticle interference (QPI) of its Fermi arc surface states by combined spectroscopic-imaging scanning tunneling spectroscopy and density functional theory calculations. We observed the electron scattering on two types of $\mathrm{WT}{\mathrm{e}}_2$ surfaces unambiguously. Its scattering signal can be ascribed mainly to trivial surface states. We also address the QPI feature of nontrivial surface states from theoretical calculations. The experimental QPI patterns show some features that are likely related to the nontrivial Fermi arc states, whose existence is, however, not conclusive. Our study provides an indispensable clue for studying the Weyl semimetal phase in $\mathrm{WT}{\mathrm{e}}_2$.

Figure 1

Sample morphology and defect states. (a) Top view (top) and side view (bottom) of the crystal structure of $1T$ ′-$\mathrm{WT}{\mathrm{e}}_2$, showing two types of surfaces. The W atoms, the Te atoms of the top surfaces, and the Te atoms of the bottom surfaces are depicted with blue, yellow, and orange balls, respectively. (b),(c) STM topography of the bottom (b) and top (c) surfaces of $\mathrm{WT}{\mathrm{e}}_2$. A high-resolution STM image shows the atomic resolution of $\mathrm{WT}{\mathrm{e}}_2$, whose unit cell is marked with a black rectangle [inset of (c)]. (d) Magnified view of the three types of defects observed on the top and bottom surface, respectively. The scale bar for all images in (c),(d) is 5 nm. (e) Tunneling spectra of the three types of defects and bare $\mathrm{WT}{\mathrm{e}}_2$ surface. The spectra have been shifted by 0.02 nS for each curve, whose zero conductance values have been marked with horizontal line segments. Imaging conditions: $V_{\mathrm{s}}=30\mathrm{mV}$, $I_{\mathrm{t}}=100\mathrm{pA}$ for (b),(c); $V_{\mathrm{s}}=120\mathrm{mV}$, $I_{\mathrm{t}}=100\mathrm{pA}$ for [(b), inset]; $V_{\mathrm{s}}=30\mathrm{mV}$, $I_{\mathrm{t}}=100\mathrm{pA}$ for (d).

Figure 2

Experimental QPI of $\mathrm{WT}{\mathrm{e}}_2$ at 40 mV and its DFT simulation. (a),(b) Topography of the bottom surface $\mathrm{WT}{\mathrm{e}}_2$ (a) and its $\mathrm{d}I$/$\mathrm{d}V$ conductance map at 40 mV (b). Imaging conditions for (a): $V_{\mathrm{s}}=300\mathrm{mV}$, $I_{\mathrm{t}}=50\mathrm{pA}$. Set point conditions for (b): $V_{\mathrm{s}}=180\mathrm{mV}$, $I_{\mathrm{t}}=600\mathrm{pA}$. (c) Symmetrized FFT of the $\mathrm{d}I$/$\mathrm{d}V$ map in (b). (d) Calculated (black and red curves) and measured (blue curve) $\mathrm{d}I$/$\mathrm{d}V$ spectra of the two surfaces. (e),(g) Calculated SWCEC at 20 meV of the bottom surface and its corresponding SSP map. (f),(h) CECs of the trivial surface arc states extracted from (e) and its corresponding SSP map (h). The yellow rectangles in (c),(g),(h) mark the same size of the $q$ space. The interpocket scattering configurations are marked in (e)–(h).

Figure 3

Comparison between QPI patterns and SSP maps of bottom surface at various energies. (a)–(d) Calculated SWCECs of the bottom surface at −20, 20, 70, and 120 meV. (e–h) CECs of the surface states extracted from (a)–(d). The topological arcs are seen as two dots (indicated with green arrows) adjacent to the large trivial arc in the magnified view of the rectangle in (g). (i)–(l) SSP maps of the SWCEC in (a)–(d). (m)–(p) SSP maps of the CEC of (e)–(h). (q)–(t) QPI patterns measured at 0, 40, 90, and 140 mV. The rectangle areas in (m)–(t) mark the comparison between the SSP maps and the experimental QPI patterns. A green arrow in (q) marks the scattering between surface states and bulk states. The scattering pattern between topological arcs and the trivial arcs is marked as a blue cross in (o) and (s). (u),(v) Energy dispersion along the $q_x$ direction extracted from the SSP map of the SWCECs (u) and from the QPI pattern (v), respectively. (w) Derivative image of (v). The green lines in (u)–(w) mark the range of the $q_x$ vectors associated to interarc scattering, which are extracted from the SSP maps of the trivial surface state. Set point conditions for (q)–(t): $V_{\mathrm{s}}=180\mathrm{mV}$, $I_{\mathrm{t}}=600\mathrm{pA}$.

Figure 4

Comparison between QPI patterns and SSP maps of top surface at various energies. (a)–(d) Calculated SWCECs of the top surface at −20, 20, 70, and 120 meV. (e)–(h) CECs of the trivial surface states extracted from (a)–(d). (i)–(l) SSP maps of the SWCECs in (a)–(d). (m)–(p) SSP maps of the CECs of (e)–(h). (q)–(t) QPI patterns measured at 0, 40, 90, and 140 mV. The rectangle areas in (m)–(t) mark the comparison between the SSP maps and the experimental QPI patterns. A green arrow in (q) marks the scattering between trivial surface states and bulk states. (u),(v) Energy dispersion along the $q_x$ direction extracted from the SSP map of the SWCECs (u) and from the QPI pattern (v), respectively. (w) Derivative image of (v). The green lines in (u)–(w) mark the range of the $q_x$ vectors associated to interarc scattering, which are extracted from the SSP maps of the trivial surface state. Set point conditions for (q)–(t): $V_{\mathrm{s}}=150\mathrm{mV}$, $I_{\mathrm{t}}=430\mathrm{pA}$.