Crystal growth of Dirac semimetal ZrSiS with high magnetoresistance and mobility

High quality single crystal ZrSiS as a theoretically predicted Dirac semimetal has been grown successfully using a vapor phase transport method. The single crystals of tetragonal structure are easy to cleave into perfect square-shaped pieces due to the van der Waals bonding between the sulfur atoms of the quintuple layers. Physical property measurement results including resistivity, Hall coefficient (RH), and specific heat are reported. The transport and thermodynamic properties suggest a Fermi liquid behavior with two Fermi pockets at low temperatures. At T = 3 K and magnetic field of Hǁc up to 9 Tesla, large magneto-resistance up to 8500% and 7200% for Iǁ(100) and Iǁ(110) were found. Shubnikov de Haas (SdH) oscillations were identified from the resistivity data, revealing the existence of two Fermi pockets at the Fermi level via the fast Fourier transform (FFT) analysis. The Hall coefficient (RH) showed hole-dominated carriers with a high mobility of 3.05 × 104 cm2 V−1 s−1 at 3 K. ZrSiS has been confirmed to be a Dirac semimetal by the Dirac cone mapping near the X-point via angle resolved photoemission spectroscopy (ARPES) with a Dirac nodal line near the Fermi level identified using scanning tunneling spectroscopy (STS).


Results and Discussion
The crystal structure of ZrSiS can be described as a typical layered compound of quintuple layers of S-Zr-Si-Zr-S, as shown in Fig. 1(a). Each quintuple layer is centered around the Si which bonds four Zr atoms in tetrahedral coordination, and the S atoms are on the two sides of each quintuple layer, weakly bonding with the neighboring layers via a van der Waals type interaction. Based on the molecular orbital analysis, the electronic structures of the Zr ([Kr]4d 2 5s 2 ) of 8-fold coordination and the S ([Ne]3s 2 3p 4 ) of 4-fold coordination imply imbalanced numbers between the valence electron and coordination number, which strongly suggests the existence of Zr-d and S-p orbital hybridization of intermediate metallicity, in agreement with the calculated band structure for a Dirac semimetal 16,22,25,26 . Figure 1(b) shows a typical image of the as-grown single crystals of ZrSiS. Based on the X-ray diffraction patterns, the crystal surfaces can be identified as the low indexing planes of (100), (110) and (001) and the inset shows the morphology of the as-grown ZrSiS single crystal. Figure 1(c) shows the Rietveld refinement of the X-ray powder diffraction results (Bruker D8) using Cu-K α radiation for the pulverized single crystal sample. All of the diffraction peaks can be indexed with the tetragonal system of space group P4/nmm. The refined lattice parameters are a = b = 3.5440 Å, c = 8.0550 Å, and volume (V) = 101.17Å 3 , which are in good agreement with those reported in the literature 25 . Figure 1(d) shows the typical X-ray diffraction patterns for the single crystal sample with two planes of preferred (00 l) and (110) orientations.
STM measurements were performed on a ZrSiS platelet which was cleaved at room-temperature in a vacuum atmosphere better than 5 × 10 −11 mbar, then quickly transferred into an Omicron LT-STM for measurement at a temperature of 4.5 K. STM measurements were performed using an electrochemically etched tungsten tip. dI/d-V(V) spectroscopy curves were acquired using the lock-in technique with a bias modulation, as stated in the relevant figure caption. The (001)-oriented cleavage plane is expected to be between the two adjacent S atomic layers. Figure 2(a) shows large-scale STM topography of the vacuum-cleaved surface revealing a step-edge of height of 0.81 nm, as shown in Fig. 2(b), consistent with the perpendicular spacing between cleavage planes, i.e. the c-axis lattice parameter. Figure 2(c) reveals the square S surface lattice with no discernible reconstruction. A number of round bumps can be seen, most likely adatoms resting at hollow sites on top of the S surface lattice, which may be debris resulting from the cleavage process. Numerous surface defects are also seen, representing possible H interstitials between S atoms of the surface lattice, and probable substitutions occupying various lattice sites.  Schoop et al. 16 . The dI/dV minimum slightly below E F may correspond to the LDOS minimum associated with the Dirac crossings along both the surface projected -G X and -G M directions. The onset of the bulk conduction bands is seen above E F . Spectroscopic characterization of the single crystal ZrSiS was carried out using angle-resolved photoemission spectroscopy (ARPES). Systematic high-resolution ARPES measurements for the low-energy electronic structure investigation were performed at the SIS-HRPES end station at the SLS, PSI, Switzerland, which is equipped with a high-efficiency R4000 electron analyzer. The energy and momentum resolutions were better than 40 meV and 1% of the Brillouin Zone (BZ), respectively. The samples were cleaved in-situ and measured at 18 K in a vacuum better than 10 −10 torr. The crystals were found to be very stable, exhibiting no degradation for the typical measurement period of 20 hours. Figure 3(a) shows the Fermi surface map measured with incident photon energy of 70 eV at T = 18 K. Our wider BZ mapping reveals multiple Fermi surface pockets on the surface of ZrSiS crystals. The observed pockets include a diamond-shaped Fermi surface, an elliptical-shaped Fermi surface, and a small electron pocket, encircling the zone center (Γ) point, the M point, and the X point of the BZ, respectively (see Fig. 3(a)). Furthermore, a Dirac-like dispersive state mostly originating from the surface is observed at the X point, as shown in Fig. 3(b). We note that these results are consistent with the recently published observations 16,17 . The observed sharp ARPES spectra provide a strong evidence to indicate the high quality of single crystals.
The resistivity and magnetoresistance measurement results of single crystal ZrSiS, in magnetic fields of μ 0 H (H‖ c) up to 9 Tesla for current flow along the (100) and (110) directions are shown in Fig. 4(a,b). Metallic behavior is observed for both configurations in the absence of magnetic field, down to a temperature of 3 K. The room temperature resistivities are found to be 15 and 19.4 μΩ-cm, and fall to 0.18 and 0.38 μΩ-cm at 3 K, and their corresponding residual resistivity ratios (RRR = ρ 300K /ρ 3K ) are 83 and 51 for I‖ (100) and I‖ (110), respectively, which attests to the high quality of the grown single crystal sample. The resistivity of ZrSiS at low temperature is lower than the recently reported semimetals WTe 2 27 and NbP 13 . When a field is applied, the resistivity of the sample follows the metallic behavior until it approaches certain temperature called the "crossover" temperature T* (defined by the resistivity minimum) for metallic to semiconducting systems (insets of Fig. 4(a,b)), below which the resistivity begins to increase dramatically, which is similar to the metal-semiconductor transition induced by the magnetic field, as also observed in WTe 2 27 , PdCoO 2 28 , and NbSb 2 29 . Figure 4(c,d) shows the magnetoresistance (MR) measured in the I‖ (100) and I‖ (110) directions as a function of magnetic field up to 9 T at different temperatures. The MR percentage, calculated from [ρ (H) − ρ (0)]/ρ (0)] × 100%, reaches 8500% and 7200% at 3 K without any signature of saturation in a field of 9 T for I‖ (100) and I‖ (110) , respectively. The observed MR at low-temperature is nearly one order lower than those reported for TaAs and WTe 2 3,27 . The large and unsaturated MR of ZrSiS may be interpreted as a quantum effect due to the linear energy dispersion at the band touching point 13 . Upon raising the temperature, the MR of ZrSiS remains almost unchanged at low-temperature and then begins to decrease drastically at higher temperatures for both the I‖ (100) and I‖ (110) directions. Scaling of magnetoresistance (MR) data for different temperatures under Kohler's rule   shows that these curves do not fall into a single curve, indicating the violation of Kohler's rule as shown in Fig. S8(a) and (b). It means that the ZrSiS crystal has more than one type of charge carriers 18,30 .
Strong Shubnikov de Haas (SdH) oscillations are observed in the I‖ (100) and I‖ (110) directions at 3 K, as shown in Fig. 4(c) and (d), providing added evidences for the coexistence of multiple Fermi surfaces. In order to analyze the SdH oscillations, a smoothed background is subtracted from the raw ρ(H, T) data to obtain the oscillatory component ( Fig. 5(a,b). A fast Fourier transform (FFT) analysis is performed to extract the frequency spectrum of the SdH oscillations, as shown in the inset of Fig. 5(a,b). The obtained FFT spectra show two distinct peaks at 14.84 T and 237.31 T for I‖ (110) and 15.67 T and 244.26 T for I‖ (100) , corresponding to two Fermi pockets and the obtained results are consistent with the previous studies 18, 19 . We used FFT filtering to separate the oscillation patterns (denoted as δ ρ ) for the observed frequencies of 244.26 T and 15.67 T for I‖ (100) direction as shown in Fig. 5(c,d), and the insets show the obtained FFT frequencies verified from the extracted δ ρ patterns. Using the Onsager relation, , where the A F is the Fermi surface area cross section perpendicular to the field, F is the frequency of oscillation, and ϕ 0 is the magnetic flux quantum, the Fermi surface cross sections are calculated to be 1. Hall coefficient (R H ) measurements were performed to investigate the carrier mobility and concentration. The temperature dependence of R H is shown in Fig. 6(a) for a ZrSiS single crystal under an applied magnetic field of 5000 Oe. At low temperature R H and field dependent Hall resistivity data at 3 K (inset of Fig. 6(b)) apparently deviates from the linearity indicating the two types of carriers, and the positive value throughout the measured temperature range implies that the conduction mechanism is hole-dominated and decreases with decreasing temperature from 300 K to 60 K until it saturates to a constant.
Using the two band model 31 , the carrier densities and mobilities can be calculated by fitting the field dependent Hall conductivity (σ xy ) data, , and n e (n h ) and μ e (μ h ) are the carrier concentrations and mobilities of electron and holes, respectively. The resistivity (ρ xx ) of I‖ (100) direction was used for the Hall conductivity calculation. From the fitting results at 3 K as shown in Fig. 6(b), n h = 1.55 × 10 23 cm −3 , n e = 1.12 × 10 23 cm −3 , μ h = 5.9 × 10 4 cm 2 V −1 s −1 and μ e = 0.20 × 10 4 cm 2 V −1 s −1 were obtained. The average mobility, μ = 3.05 × 10 4 cm 2 V −1 s −1 is very close to the already reported data (1.79 × 10 4 cm 2 V −1 s −1 ) 19 of ZrSiS crystal. The carrier concentration of ZrSiS crystal is four orders of magnitude larger than that of the topological Weyl semimetal NbP. The estimated mobility at 3 K is two orders of magnitude lower than the compounds in the same class of semimetals, including Cd 3 As 2 (9 × 10 6 cm 2 /V·s, at 5 K) 7 , NbP(5 × 10 6 cm 2 /V·s, at 1.85 K) 12 , but close to that of TaAs (5 × 10 5 cm 2 /V·s, at 2 K) 3 .
The electronic properties were explored further with the specific heat measurement. Figure 7 shows the specific heat (C P ) of a ZrSiS single crystal from 0 to 200 K. It can be seen that C P starts to saturate at 57 J mol −1 K −1 above ~200 K, which is close to the Dulong-Petit value, and an exponential suppression of specific heat at low temperatures is observed. The solid line is the fit to the Debye model 24 , where θ D is the Debye temperature and R the ideal gas constant. By fitting the above equation, the θ D is obtained to be ~493 K, which is the largest among those observed in the typical Dirac and Weyl semimetals, including Cd 3 As 2 (200 K), TaAs (352 K) and pyrochlore oxides (400 K) 23,24,32,33 . The inset of Fig. 7 shows the C P /T data fitting below 55 K using the expression of γ β = + C T T / P 2 , where the T linear term in C p represents the electronic contribution and the higher order term represents the lattice contribution. The derived Sommerfeld coefficient γ  Inset shows the C P /T data fitted with the expression of γ β = + C T T / is estimated to be 6.84 mJ mol −1 K −2 , which is higher than several other typical semimetals including NbAs (0.09(1) mJ mol −1 K −2 ) 34 , Y 3 Ir 4 Ge 13 (4.3 mJ mol −1 K −2 ) 35 , and YPtBi (4 mJ mol −1 K −2 ) 36 . The phononic contribution is estimated to be β = 5.54 × 10 −5 J mol −

Conclusion
In summary, we have grown high quality single crystals of Dirac semimetal ZrSiS and performed a systematic physical and electronic property characterization to compare with some typical semimetals in the same class.
Tunneling spectroscopy acquired at the cleaved (001) surface, visualized using STM, is consistent with previous ARPES observations of a distinct surface state and a Dirac line node near the Fermi level. Our ARPES measurements revealed the presence of multiple Fermi pockets of three different shaped Fermi surface with dispersion map along the M-X-M momentum space direction to substantiate the quality of the grown crystal sample. The large unsaturated MR up to 9 Tesla is found at 3 K and compared with those reported semimetals of the same class. ZrSiS exhibits strong Shubnikov de Haas (SdH) oscillations observed in magneto-resistance measurements. The positive value of the Hall coefficient observed between 3 and 300 K suggests p type carriers dominating ZrSiS, and the mobility is found to be 3.05 × 10 4 cm 2 V −1 s −1 comparable with that of TaAs.

Experimental Section
Sample Preparation. Single crystals of ZrSiS, as shown in Fig. 1(b), were grown in using a two-step chemical vapor transport process using I 2 as the transport agent. A silica ampoule with length of 20-30 cm and ID/OD of 1.8/2.0 mm was used for the synthesis and growth. In the first step for direct solid state reaction, a stoichiometric amount of 5 N purity precursors of Zr:Si:S = 1:1:1 molar ratio was sealed in an evacuated quartz ampoule. The vacuum-sealed quartz ampoule containing ternary mixtures was treated at 1100 °C for one week and then furnace-cooled to room temperature. The polycrystalline ZrSiS sample was confirmed to be single phase. In the second step, the polycrystalline powder of ZrSiS was mixed with I 2 in weight ratio of 100:1 and vacuum-sealed in a two-zone tube furnace having a thermal gradient of about 1100-950 °C within ~30 cm. After a period of 10 days, single crystals of ZrSiS with size up to 4.0 × 2.9 × 3.0 mm 3 were obtained. The ZrSiS single crystals have shiny cleaved surface with a morphology of well-defined crystal planes indexed as (100), (110), and (001), as shown in the inset of Fig. 1(b).