Quasiparticle interference in ZrSiS: Strongly band-selective scattering depending on impurity lattice site

Scanning tunneling microscopy visualizations of quasiparticle interference (QPI) enable powerful insights into the $k$-space properties of superconducting, topological, Rashba, and other exotic electronic phases, but their reliance on impurities acting as scattering centers is rarely scrutinized. Here, we investigate QPI at the vacuum-cleaved (001) surface of the Dirac semimetal ZrSiS. We find that interference patterns around impurities located on the Zr and S lattice sites appear very different, and can be ascribed to selective scattering of different subsets of the predominantly Zr $4d$-derived band structure, namely, the $m=0$ and $\pm 1$ components. We show that the selectivity of scattering channels requires an explanation beyond the different bands' orbital characteristics and their respective charge density distributions over Zr and S lattice sites. Importantly, this result shows that the usual assumption of generic scattering centers allowing observations of quasiparticle interference to shed light indiscriminately and isotropically upon the $q$ space of scattering events does not hold, and that the scope and interpretation of QPI observations can therefore be be strongly contingent on the material defect chemistry. This finding promises to spur new investigations into the quasiparticle scattering process itself, to inform future interpretations of quasiparticle interference observations, and ultimately to aid the understanding and engineering of quantum electronic transport properties.

Figure 1

Overview of STM and QPI observations at the cleaved ZrSiS(001) surface. (a) Crystal structure of ZrSiS, with a cleavage plane between adjacent S square nets indicated. Also shown, in (b), is the top-down view of the (001) surface, and the relative alignment between the Zr, Si, and S atomic sublattices. (c) Macroscopic view of ZrSiS single crystals, showing large, flat, and reflective (001) primary facets. (d) Typical STM topography (taken at $V=0.2$ V, $I=0.3$ nA), showing a square surface lattice with various types of impurities. (e) A conductance map at $V=0.5$ eV in the same field of view, showing highly directional QPI modulations around impurity sites. Impurities of different types clearly cause QPI modulations of different directionality and wave vector. The inset shows the 2D FFT image with Bragg peaks and QPI signals clearly discernible.

Figure 2

Identification of observed surface lattice and impurity sites. A typical scanning tunneling spectroscopy curve, shown in (a), corresponds well with the calculated surface projected LDOS, shown in (b). The element-resolved LDOS indicates tunneling measurements, including topography maps, are dominated by Zr-derived states. Voltage-dependent topography maps, taken using $I=1$ nA, and at $V=0.5$ and $-0.25$ eV respectively, are shown in (c) and (d). Taking point defects as a position reference shows that the predominant topographic corrugation belongs to the same atomic sublattice in each case. Zoom-in views of a $5\times 5$ unit-cell array at each voltage, (e) and (f), compare well with the corresponding simulated STM images, (g) and (h), in which the atomic positions are known, showing that the most prominent observed corrugation corresponds to the Zr atomic layer. The common types of point defect shown in the topography maps in (i) and (j) can then be identified as $D_{\text{Zr}}$ and $D_{\text{S}}$, respectively. Simulated STM images of possible candidates for $D_{\text{Zr}}$ and $D_{\text{S}}$ (modeled as ${\mathrm{S}}_{\text{Zr}}$ and ${\mathrm{Si}}_{\text{S}}$ substitutions, respectively) are shown in the insets, and reproduce the qualitative features observed in experimental STM maps.

Figure 3

Local QPI observations around $D_{\text{Zr}}$ and $D_{\text{S}}$ impurities. (a) A conductance map ($V=0.5$ V, $I=1$ nA) showing QPI modulations stemming from a defect centered at a Zr lattice site, with the topography image of the defect pattern shown in the inset ($V=0.2$ V, $I=0.3$ nA). (b) The corresponding 2D FFT image. (c), (d) The corresponding conductance and 2D FFT images for a defect centered at a S lattice site, taken using the same parameters as in (a) and (b). Clearly different sets of scattering wave vectors are seen, labeled ${\mathit{q}}_1$ and ${\mathit{q}}_2$ for $D_{\text{Zr}}$, and ${\mathit{q}}_3$ for $D_{\text{S}}$.

Figure 4

Dispersive behavior of QPI phenomena. (a) The $q$ vectors described in Fig. 3 are identified within the CEC of the surface-projected bands. The axes of interest are $\overline{MXM}$ and $\overline{M\mathrm{\Gamma }M}$. The surface band diagrams (derived from the top three atomic layers) along these axes are shown in (b) and (c), respectively, indicating electronlike dispersion for ${\mathit{q}}_1$ and holelike dispersion for ${\mathit{q}}_3$. Experimental QPI dispersion plots along the $\overline{\mathrm{\Gamma }X}$ and $\overline{\mathrm{\Gamma }M}$ cuts are shown in (d) and (e). A comparison of the experimental QPI peaks determined using Lorentzian fitting of $dI/dV$($\mathit{q}$) = $g$($\mathit{q}$) shown in (d) and (e), with the expected dispersion behavior obtained from the peak along $\overline{\mathrm{\Gamma }X}$ and $\overline{\mathrm{\Gamma }M}$ of $N$($\mathit{q}$) at each energy, are shown in (f) and (g). The good agreement between measurement and calculation allows us to attribute the $q$ vectors of interest to scattering within particular bands.

Figure 5

Relation of defect-site-dependent QPI selectivity to the orbital character of bands. (a) Total CEC, and orbital-resolved CECs for (b) $m=0$ and (c) $m=\pm 1$, at $E-E_F=0.5\mathrm{eV}$, with the prominent scattering wave vectors ${\mathit{q}}_{1,2,3}$ marked. (d)–(f) The corresponding $N$($\mathit{q}$) for the total ($m$-conserving) and orbital-resolved CECs. (g)–(i) Experimental QPI patterns acquired over the large area shown in Fig. 1, and locally around $D_{\text{Zr}}$ and $D_{\text{S}}$, respectively, as shown in Fig. 3. The QPI measured over a large area gives the aggregate scattering effects of all impurities, which is likely a linear combination of the scattering effects of $D_{\text{Zr}}$ and $D_{\text{S}}$.

Figure 6

Spatial distribution of partial charge densities for $m=0$ and $\pm 1$ dominated $k$ points ($P_0$ and $P_1$ in Fig. 5). (a) Calculated charge densities as a function of depth for the slab model. The charge density sampled from the $m=0$ dominated $k$ point $P_0$ shows the clear characteristics of a surface state, vanishing within the interior of the slab. (b) Zoom-in charge densities in the vicinity of the surface, showing a lack of any particular dominance by either partial charge component around the $z$ positions of either the S or Zr lattice sites. (c), (d) Planar projections of each partial charge component at the $z$ height of the S (Zr) lattice site for the $m=0$ ($m=\pm 1$) dominated component. Both components appear to have higher intensities around the Zr site.