Surface Termination Dependent Quasiparticle Scattering Interference and Magneto-transport Study on ZrSiS

Dirac nodal line semimetals represent a new state of quantum matters in which the electronic bands touch to form a closed loop with linear dispersion. Here, we report a combined study on ZrSiS by density functional theory calculation, scanning tunneling microscope (STM) and magneto-transport measurements. Our STM measurements reveal the spectroscopic signatures of a diamond-shaped Dirac bulk band and a surface band on two types of cleaved surfaces as well as a spin polarized surface band at ${\bar{\Gamma}}$ at E~0.6eV on S-surface, consistent with our band calculation. Furthermore, we find the surface termination does not affect the surface spectral weight from the Dirac bulk bands but greatly affect the surface bands due to the change in the surface orbital composition. From our magneto-transport measurements, the primary Shubnikov de-Haas frequency is identified to stem from the hole-type quasi-two-dimensional Fermi surface between {\Gamma} and X. The extracted non-orbital magnetoresistance (MR) contribution D($\theta$, H) yields a nearly H-linear dependence, which is attributed to the intrinsic MR in ZrSiS. Our results demonstrate the unique Dirac line nodes phase and the dominating role of Zr-d orbital on the electronic structure in ZrSiS and the related compounds.


Introduction
The study on Dirac-like systems has progressed greatly in the past decade. While two-dimensional (2D) Dirac fermions were found in graphene [1] and on the surfaces of topological insulators [2], threedimensional (3D) Dirac fermions that are protected by inversion symmetry and time reversal symmetry were demonstrated experimentally in Na3Bi [3] and Cd3As2 [4]. Weyl fermions that stem from Dirac fermions due to the broken inversion symmetry or broken time reversal symmetry were also observed e.g.
in TaAs [5]. Furthermore, it has been predicted that Dirac nodal line semimetal phase exists when the nondegenerate conduction and valence bands cross each other to form a closed loop [6]. Experimentally, several Dirac nodal line semimetals, within which their linear bands crossings connect to form continuous lines or arcs, were observed in PbTaSe2 [7], PtSn4 [8] and ZrSiS family [9][10][11][12][13]. However, it has been revealed that both PbTaSe2 [7,14] and PtSn4 [8] exhibit the complex band structure, making them difficult to study the Dirac nodal bands separately. In contrast, the electronic band structure of ZrSiS is relatively simple. Indeed, recent ARPES studies on ZrSiS revealed the existence of non-symmorphic symmetry protected line nodes [9][10][11][12][13], which was first predicted by Kane and Young in 2015 [15]. In addition, there also exist a Dirac surface band at X ̅ and a diamond-shaped Dirac band at Γ ̅ from ARPES [9][10][11][12][13]16] and scanning tunnelling microscope (STM) study [17,18]. Both Dirac bands are also shown to disperse linearly up to few hundred meV even above EF by quasiparticle scattering interference (QPI) imaging [17,18], from which ZrSiS exhibits strongly band-selective scattering depending on impurity lattice site [17].
Moreover, transport measurements revealed extremely large, non-saturated and anisotropic magnetoresistance (MR) in ZrSiS [16,[19][20][21]. Several Shubnikov-de-Haas (SdH) oscillations measurements reported a major peak at ~240 T, which is attributed to the quasi-2D Fermi surface [16,19,[21][22][23][24][25] while a peak at ~600 T observed by thermoelectric power [23] and high field SdH [24] measurement is assigned to a 3D Fermi surface. Recently, frequency independent flat optical conductivity [25], the rapid relaxation rate after photoexcitation [26] and Ag tip induced superconductivity [27] are also reported in ZrSiS. Thus, these fascinating phenomena demonstrated that the ZrSiS family is a great system for studying the Dirac nodal-lines [11,12,28,29]. However, the experimental investigations on the detail electronic band structure above EF and the orbital contribution are still inadequate. In addition, a proper model to extract the non-orbital MR contribution is needed to reveal the intrinsic MR contribution due to the Dirac fermions.
In this paper, we investigate the surface and bulk electronic structures in Dirac nodal line semimetal, ZrSiS, by density function theory (DFT) calculations, STM and magneto-transport measurements. Our bulk calculation reveals that the Fermi surface of ZrSiS primarily consists of a 3D diamond-shaped Dirac band at Γ and a quasi-2D tubular band between Γ and X. The slab calculation shows a surface band exists at X ̅ with linear dispersion over several hundred meV. A fully spin-polarized surface state at E ~ 0.6 eV is found to connect the diamond-shaped Dirac band and the bulk conduction band and is completely separated from the bulk bands. Our STM measurements reveal both S-and Si-surfaces and we deduce the observed atoms to be Zr, independent of the surface terminations. Our data from QPI imaging support the band structure from our DFT calculation. Our further analysis suggests that different surface terminations have negligible effect on the surface spectral weight from the Dirac bulk bands in ZrSiS but that of the surface bands can be greatly reduced due to the change in orbital composition. The enhanced surface spectral weight from the diamond-shaped band produces a stronger QPI pattern than that from the surface band. Our finding suggests an unusual scattering selection rule and highlights the important role of Zr-d orbitals. On the other hand, multiple SdH frequencies are clearly identified from the magneto-transport measurements. A model is proposed and applied on the angular dependent MR data to separate the dominant orbital MR contribution and the non-orbital MR that is likely associated with the Dirac bands.
Our results thus demonstrate that ZrSiS and its related compounds are a valuable platform for exploring Dirac line nodes physics and their future applications.

Band structure calculation
Our ZrSiS single crystals are grown by two-step chemical vapour transport process as described in detail elsewhere [30] and have the PbFCl-type crystal structure in tetragonal space group P4/nmm, as showed in figure 1(a). The lattice constants, determined by x-ray diffraction, are a = 3.544 Å and c = 8.055 Å . In ZrSiS, square Zr2S2 layers are alternatively stacked along the c-axis with double layers of Si atoms.
We calculate the electronic structure based on DFT theory. The bulk band structure without and with SOC is shown in figures 1(b) and 1(c), respectively. Several Dirac bands can be found in the bulk band structure without SOC (circled in red and blue). The Dirac band crossings also form two one-dimensional (1D) line nodes between R and X at E ~ -0.45 eV to -0.67 eV and also between A and M at E ~ -2.2 eV. When the SOC is taken into account in the calculation, the Dirac bands near the Fermi level (marked as red circles in figures 1(b) and 1(c)) open a small gap (~37 meV) but their dispersion remains linear as illustrated in figure 1(c). In contrast, the 1D line nodes (marked as blue circles in figures 1(b) and 1(c)) in the occupied states remain degenerate due to the protection from non-symmorphic symmetry [9-13, 17, 31]. These Dirac points are connected to form a 3D diamond-shaped Fermi surface at Γ. Moreover, quasi-2D tubular Fermi surface is also found along X as shown in figure 1(f). These results are consistent with recent ARPES [9-13, 16, 31] and SdH [16,19,21,22,24,25] measurements on ZrSiS. To better compare the theoretical calculation with STM and ARPES measurements, we also carry out a slab calculation and the resultant band structure with the surface component is shown in figure 1(d). By comparing the electronic structure of ZrSiS from the bulk and slab calculations, we find the surface states with linear dispersion around ̅ at EF, and this is consistent with previous ARPES [9][10][11][12][13] and STM [17] experiments.
Interestingly, we also find that the SOC opens a gap of ~100 meV (orange circles in figure 1(b) and (c)) on the Dirac crossings around E ~ 0.6 eV and a surface state emerges to connect the top of inner Dirac band and the bottom of conduction bands (orange arrow along Γ ̅̅̅̅ in figure 1(d)). Our DFT calculation also shows that this surface state is fully spin-polarized and the spins are all aligned in-plane clockwise as showed in figure 1(e). The surface state is still protected by time reversal symmetry but not by topology since our calculation shows ZrSiS is topologically trivial. From the calculated band structure, the linear dispersion of all Dirac bands in ZrSiS extends over a wide energy range of several hundred meV, which has a great advantage over other Dirac semimetals with linear dispersion of much smaller energy range.

STM experiments
We first investigate the surface electronic structure with STM measurements, which are carried out in a homemade low temperature ultra-high vacuum STM system at T = 4.5 K with electrochemically etched tungsten tips [33]. The STM tips are cleaned and reshaped first by field-emission on the gold surface. The ZrSiS single crystal is in situ cleaved at the sample stage of the STM head at around T = 5 K right before STM measurements. Due to the nature of a layered crystal structure with a glide plane between S layers, it is generally assumed that the cleavage should occur naturally here and yield large flat and charge neutral S-surface. Interestingly, we find that ZrSiS can also be cleaved to reveal Si-surface. Figure 2 Fermi level is the lowest due to Dirac crossing in the band structure but not zero. The measured tunnelling spectra appear to be in excellent agreement with our orbital-projected density of states (PDOS) calculation, as displayed in figure 2(f), in which Zr-d orbital dominates the LDOS near EF over S-p and Si-p orbitals on the surface. This explains why it is easier to observe Zr atoms than S or Si atoms in STM topographic images and confirms the previous impurities study of ZrSiS by STM and DFT study [17]. The simulated STM images also support this view [17]. A dip exists at E ~ 0.6 eV in PDOS calculation and is also observed in tunnelling spectrum at E ~ 0.74 eV, which could be related to the change in energy dispersion as indicated by black and orange arrows in figure 1(d). This dip feature will also allow us to better compare the experimental data with DFT results at the high energy in the following section.
To further investigate the dependence of the electronic structure on differently terminated surfaces, we utilize Fourier transform-scanning tunnelling spectroscopy (FT-STS), which can relate the real space characteristic wavevectors resulting from QPI to the band structure in momentum space. First, energy resolved differential tunnelling conductance maps, dI/dV(r, E = eV) are taken in a field of view (FOV) of 60  60nm 2 on S-and Si-surfaces as shown in figure 3(a)-(e) and (k)-(o), respectively. The standing waves due to QPI are visible around the defects and impurities and show very similar patterns at the same energy.
The main difference is that many impurities on the Si-surface do not contribute to any QPI (possibly S clusters, as shown in appendix A4) and the QPI signals diminish at E < ~125 meV. We then take FT of the dI/dV(r, E) maps and obtain the corresponding dI/dV(q, E) maps on S-and Si-surfaces, as shown in figure 3(f)-(j) and (p)-(t), respectively (the movies also available in supplementary materials, are available online at stacks.iop.org/NJP/20/ 103025/mmedia). Three pronounced dispersive C4-symmetric q-vectors (q 1 , q 2 and q 3 ) can be observed in the dI/dV(q, E) maps (figure 3). After analysing the direction, wavelength and energy dispersion of q-vectors and comparing with the calculated band structure, we can identify q 1 as the intra-pocket scattering between the diamond-shaped band at Γ ̅ , q 2 as the intra-pocket scattering of the surface band at X ̅ and q 3 as the inter-pocket scattering between the surface bands at X ̅ as shown in figure 4(a). Our q-vectors assignments are consistent with previous QPI studies on ZrSiS [17,18].
However, on the Si-surface, all q-vectors become weaker with decreasing energy and the QPI from the surface bands (q 2 and q 3 ) diminished at E < ~125 meV. This is mainly because the disorder from the large amount of impurities on the Si-surface suppresses the QPI. In addition, the surface band near X ̅ has significant S-p orbital contribution and the dispersion towards Γ ̅ and ̅ is linked to a change in its Zr-d orbitals [31], which reduces the spectral weight on the surface bands and in term, weakens the QPI near X ̅ on the Si-surface. To quantify the QPI data, we then extract q 1  To verify the existence of the predicted spin-polarized surface at higher energy, we take dI/dV(r, E) maps between 500 and 1000 meV with higher q-resolution on the same FOV of the S-surface (figure 3(a)) because it will be difficult to resolve smaller q 1  Thus, we can conclude that the disappearance of q 1 is consistent with the time reversal symmetry protection from the predicted fully spin-polarized surface band in figure 1(d) and (e). We are unable to make the comparison with data from Si-surface because of the large background at q = 0 due to the large amount of surface impurities. Although such a surface state is not protected by the non-symmorphic symmetry nor the band topology, its full in-plane spin polarization with time reversal protection may be useful in a related compound that has the Fermi level within its proximity.

Magneto-transport measurements
To further study the bulk electronic structure and transport properties, we carry out magneto-transport measurements by standard four-probe geometry. The resistivity equals about 9 μΩcm at room temperature and gradually decreases with decreasing temperature, showing a metallic behavior (figure 6(a)). Below 20 K, the resistivity is nearly independent of the temperature with a residual resistivity of ~ 0.23 μΩcm, giving a residual resistivity ratio (RRR ≡ 300 / 10 ) of ~ 38.8. Figure 6 We note that, as ≥ 30 o , the major frequency F1 appears to get broader and then split into multiple peaks, where the peak separation grows larger as increases. This behaviour may be related to the fine structures in the 2D tubular Fermi surface shown as the blue area in figure 1(f). The observed major SdH frequency F1 agrees with several previous reports [24,29,34], but we do note that the 3D diamond-shaped band (the green area in figure 1(f)) was not seen in our SdH measurements, which is likely due to its reported unusual mass enhancement [29,35] and our limited field strength.
The presence of multiple bands conduction in ZrSiS is evident from the non-linear field dependence of Hall resistivity (not shown here), and multiple SdH frequencies. In addition, the calculated band structure also suggests the existence of both electron and hole bands at the Fermi level. To find out the intrinsic MR from the bulk bands, we carry out the following analysis. According to the two-band model, the corresponding orbital MR contribution can be expressed as where 1(2) and 1 (2) are the mobility and density, respectively, of the first (second) band.

(Δ / )
is only sensitive to the perpendicular component of the field, and it scales as ( 0 ⊥ ) 2 in lower fields. Based on the Matthiessen's rule, the total MR can thus be expressed as where (Δ / ) = (θ) ( 0 ) 2 , (θ) is a θ-dependent prefactor and ( , ) term represents the non-orbital contribution to the MR. Assuming that ( , ) term grows with field at an exponent less than 2, the value of (Δ / )( , )/ ( 0 ) 2 should gradually approach C(θ) in higher fields, where ( , )/ ( 0 ) 2 term becomes vanishingly small. Figure 8 figure 8(d). The exponent α is found to be close to 1.0 and nearly independent of the values, which also justifies the assumption we made earlier (α <2) for the analysis using Eq. (2). We do note the failure of H-linearity in ( , ) for 0 > 4 Tesla as can be seen in figure 8(c), where we attribute such deviation from H-linearity to the additional contribution from quantum oscillations in the quantum regime. Therefore, the intrinsic MR from the bulk band effect is likely to be best revealed in the low field regime as shown in figure 8(b).
The H-linear MR phenomenon has been observed in topological Dirac and Weyl semimetals, such as Dirac semimetal Cd3As2 [36] and Weyl semimetal NbP [37,38]. Combining the observation of linear dispersion band from QPI analysis and also special Dirac line node in the calculated band in ZrSiS, the observed H-linear ( , ) may provide further support for the existence of the Dirac-like bulk band from the magneto-transport measurements. Nevertheless, the correct theoretical description for the H-linear MR due to Dirac-like band remains a debatable issue [38][39][40][41]. On the other hand, it is also suggested that similar H-linear MR effect can be observed in a narrow band gap semiconductor with inhomogeneous conductivity [40,41]. As shown in figure 8(b), ( , ) appears to be at maximum at = 0 o , and the slope d ( , )/dH seems to roughly scales as cos , which may rule out the possible Zeeman-like spin spitting effects on Dirac electrons [38]. We also note that the H-linear in ( , ) remains valid down to weak field regime, suggesting the quantum MR due to the filling of single Landau level may not apply either [39]. Further investigation is needed to elucidate the intrinsic mechanism for the H-linear MR effect in ZrSiS.

Summary
In summary, we have reported a combined study on the bulk and surface electronic structures of ZrSiS