Appearance of T$_d^*$ phase across the T$_{d}$-1T$^{\prime}$ phase boundary in Weyl semimetal MoTe$_{2}$

TL;DR

This study investigates the T$_{d}^{*}$ phase in MoTe$_{2}$, revealing its unique stacking order and its emergence during warming from the T$_{d}$ phase, providing insights into phase transitions in Weyl semimetals.

Contribution

It uncovers the detailed stacking sequence and temperature-dependent behavior of the T$_{d}^{*}$ phase in MoTe$_{2}$ using neutron scattering, highlighting its role in phase boundary dynamics.

Findings

T$_{d}^{*}$ phase appears only on warming from T$_{d}$

T$_{d}^{*}$ has an 'AABB' stacking sequence

Diffuse scattering indicates frustrated stacking tendency during cooling

Abstract

Using elastic neutron scattering on single crystals of MoTe$_{2}$ and Mo$_{1-x}$W$_{x}$Te$_{2}$ ($x \lesssim 0.01$), the temperature dependence of the recently discovered T$_{d}^{*}$ phase, present between the low temperature orthorhombic T$_{d}$ phase and high temperature monoclinic 1T$^{\prime}$ phase, is explored. The T$_{d}^{*}$ phase appears only on warming from T$_{d}$ and is observed in the hysteresis region prior to the 1T$^{\prime}$ transition. This phase consists of four layers in its unit cell, and is constructed by an "AABB" sequence of layer stacking operations rather than the "AB" and "AA" sequences of the 1T$^{\prime}$ and T$_{d}$ phases, respectively. Though the T$_{d}^{*}$ phase emerges without disorder on warming from T$_{d}$, on cooling from 1T$^{\prime}$ diffuse scattering is observed that suggests a frustrated tendency toward the "AABB" stacking.

Full text

Many layered materials have structure-property relationships that depend on their layer stacking. For example, the transition metal dichalcogenide MoTe2 is reported to be a type-II Weyl semimetal in its orthorhombic Td phase (with the non-centrosymmetric $Pnm2_{1}$ space group) Sun et al. (2015); Deng et al. (2016), but not in its monoclinic 1T*′* phase (with the centrosymmetric space group $P2_{1}/m$). The two phases have nearly-identical layers and differ mainly by in-plane displacements. Though there is much interest in investigating Weyl semimetals, the properties of MoTe2 are not completely understood. For instance, there is much debate on the origin of the extreme magnetoresistance observed at low temperatures Rhodes et al. (2017); Zhou et al. (2016); Thirupathaiah et al. (2017), the number and location of Weyl points in the Td phase Weber et al. (2018), and the topological nature of the observed surface Fermi arcs that are a necessary but not sufficient condition for a Weyl semimetal Xu et al. (2018). Structural distortions have been known to occur, such as stacking disorder during the phase transition, evidenced by the presence of diffuse scattering observed in neutron Schneeloch et al. (2019) and X-ray Clarke et al. (1978) experiments, and hysteresis effects that extend far beyond the transition region, as seen in resistivity measurements along the thermal hysteresis loop Zandt et al. (2007a). These effects have been largely ignored, though one of the surface Fermi arcs was noted to persist to $\sim$90 K above the transition temperature and to have a history-dependent appearance Weber et al. (2018). In general, structural phase transitions that involve in-plane translations of layers resulting from changes in temperature or pressure have been neglected, but many materials fall in this category, including Ta2NiSe5 Nakano et al. (2018), In2Se3 Ke et al. (2014); Zhao and Yang (2014), $\alpha$-RuCl3 Glamazda et al. (2017), CrX3 (X=Cl, Br, I) McGuire et al. (2015), and MoS2 Hromadová et al. (2013); Chi et al. (2014); Nayak et al. (2014). A better understanding of these types of transitions would not only elucidate these material properties, but could also lead to the discovery of new phases.

The Td and 1T*′* phases can be constructed from a stacking pattern of “A” and “B” operations, as shown in Fig. 1(a). The A operation maps one layer of Td to the layer below it, so Td can be built from repeating “AA” sequences. The B operation is the same as for A but followed by a translation of $\pm$0.15 lattice units, with a sign that is alternating layer-by-layer. Thus, 1T*′* can be built from repeating “AB” sequences. We previously reported that diffuse scattering observed in the $H0L$ scattering plane on cooling from 1T*′* towards Td (in particular, the low intensity along $(60L)$) is consistent with a disordered A/B stacking pattern Schneeloch et al. (2019). How the stacking changes with temperature has not been closely examined, though an explanation for the relative stability of the Td and 1T*′* phases via free energy calculations was earlier proposed Kim et al. (2017). Understanding the nature of layer stacking will provide useful insight into how Weyl nodes disappear across the phase boundary.

We performed elastic neutron scattering as a function of temperature to study the mechanism of the structural phase transition between the 1T*′* and Td phases in MoTe2. On warming, the recently discovered T${}_{d}^{*}$ phase Dissanayake et al. (2019) was observed, having a pseudo-orthorhombic structure and a four-layer unit cell, rather than the two-layer unit cells of 1T*′* and Td. The stacking sequence of T${}_{d}^{*}$ can be described by “AABB”, as shown in Fig. 1(a). Upon warming, the Td$\rightarrow$T${}_{d}^{*}$ transition is not accompanied by disorder. Diffuse scattering is observed on further warming from T${}^{*}_{d}$ to 1T*′. On the other hand, on cooling from 1T′* to Td, the T${}_{d}^{*}$ phase is absent and only diffuse scattering is observed that suggests a frustrated tendency toward the “AABB” layer order.

Elastic neutron scattering was performed at Oak Ridge National Laboratory, on the triple axis spectrometers HB1, CG4C, and HB1A at the High Flux Isotope Reactor; and on the time-of-flight spectrometer CORELLI at the Spallation Neutron Source Ye et al. (2018). Though the crystals are monoclinic at room temperature, for simplicity, we use orthorhombic coordinates, with $a\approx 6.3$ Å  $b\approx 3.5$ Å  and $c\approx 13.8$ Å. The collimations were 48*′-40′-S-40′-120′* for HB1 and CG4C, and 40*′-40′-S-40′-80′* for HB1A. Incident neutron energies were 13.5 meV for HB1, 4.5 meV for CG4C, and 14.6 meV for HB1A. Resistance measurements were performed in a Quantum Design Physical Property Measurement System. All crystals were grown in excess Te flux, including the two used for neutron scattering, “MT1” and “MT2”. MT1 has the composition MoTe2, while MT2 has the composition Mo1-xWxTe2 with $x\lesssim 0.01$ as estimated by energy dispersive X-ray spectroscopy and the $c$-axis lattice constant. Details can be found in the Supplemental Materials.

In Figures 1(b-e), neutron scattering intensity scans along $(2,0,L)$ are combined for many temperatures on cooling and warming through the hysteresis. In the 1T*′* phase, the $(202)_{1T^{\prime}}^{D1}$ and $(20\bar{3})_{1T^{\prime}}^{D2}$ Bragg peaks are observed near $L=2.3$ and $L=2.7$, respectively; $D1$ and $D2$ denote each of the two 1T*′* twins. (Since MT1 could not be warmed fully into 1T*′* in Fig. 1(c) for technical reasons, diffuse scattering was present on subsequent cooling from 300 K in Fig. 1(b).) At low temperatures, Td-phase Bragg peaks at $L=2$ and $L=3$ are observed, as indicated in the figure. On warming from Td past $\sim$260 K, a peak appears at L = 2.5, indicating the onset of T${}_{d}^{*}$. The presence of this peak at half-integer $L$ indicates an out-of-plane doubling of the unit cell, so we label this peak $(205)_{T_{d}^{*}}$ (Fig. 1(e)). With additional warming, a gradual transformation into the 1T*′* phase occurs, accompanied by diffuse scattering indicating stacking disorder. Examples of the diffuse scattering can be seen in the individual plots of intensity along $(2,0,L)$ in Fig. 1(f), where 1T*′* is transitioning into Td; and in Fig. 1(g), where T${}_{d}^{*}$ is transitioning into 1T*′*. For MT2, we measured through the hysteresis twice and found the same pattern of diffuse scattering at the same temperatures along the hysteresis, suggesting that the appearance of the diffuse scattering through the hysteresis is reproducible.

The T${}_{d}^{*}$ phase structure can be deduced from the following observations: First, T${}_{d}^{*}$ appears to be orthorhombic, but has additional peaks at half-integer $L$ values relative to Td, indicating a four-layer unit cell. Second, the 1T*′* and Td phases can be built from A/B stacking sequences, so we presume the same is true for T${}_{d}^{*}$. There are only two possible pseudo-orthorhombic stacking sequences: “AABB” and “ABBA”, which are twins of each other. Since this structure, with highest possible symmetry P21/m, appears to have an orthorhombic unit cell but has atomic positions incompatible with orthorhombic space groups, we refer to it as pseudo-orthorhombic.

To verify the predicted AABB stacking structure of T${}_{d}^{*}$, we carried out single-crystal neutron diffraction measurements on the MT1 crystal on CORELLI, and the data are shown in Figures 2(a,c). The data were taken on warming to 300 K, and the presence of peaks at half-integer $L$ in the $2KL$ plane in Fig. 2(c) confirm the presence of the T${}_{d}^{*}$ phase. The diffuse scattering streaks along $L$ are from stacking disorder that was already present on warming from 240 K, possibly due to not cooling sufficiently into Td beforehand. (There is a discrepancy between the detection of T${}_{d}^{*}$ in MT1 at 300 K on CORELLI and up to $\sim$280 K on HB1A. The cause of the temperature discrepancy is unknown, but may be related to the presence of stacking disorder before warming.) Figures 2(b,d) show simulated intensity maps. To match the data, it was necessary to consider a 47.8% volume fraction of Td as well as 28.2% and 24.0% volume fractions of the two T${}_{d}^{*}$ twins. The volume fractions were obtained by fitting the intensities of Bragg peaks within $-1\leq H\leq 8$, $-1\leq K\leq 1$, and $-20\leq L\leq 20$ with the calculated peak intensities of the ideal “AA”, “AABB”, and “ABBA” stacking sequences of Td and the two T${}_{d}^{*}$ twins, respectively. These structures were built from layers having the coordinates in Ref. Qi et al. (2016). As can be seen in Figures 2(a-d), the patterns of peak intensities in these scattering planes match those arising from our model.

Stringent constraints on possible T${}_{d}^{*}$ structures follow from the lack of change in $(00L)$ and $(01L)$ peak intensities between the Td phase at 240 K and the T${}_{d}^{*}$ phase at 300 K (as seen from the near-unity intensity ratios in Fig. 2(e). For context, intensity ratios for $(20L)$ and $(30L)$ peaks are also included.) A lack of change in $0KL$ peak intensities implies a lack of change in atomic positions along the $b$- and $c$-directions, but is consistent with layer displacements along the $a$-direction, as is the case between 1T*′* and Td Schneeloch et al. (2019). The AABB structure should be centrosymmetric, since it can be transformed from the centrosymmetric AB-stacked 1T*′* phase by a centrosymmetric series of translations (see Supplementary Materials). Inversion symmetry centers for the AABB structure are depicted in Fig. S2 in the Supplemental Materials. Barring small non-centrosymmetric distortions, which are unlikely given that first-principles calculations have shown that MoTe2 layers isolated from the non-centrosymmetric Td environment tend to become centrosymmetric Heikes et al. (2018), we conclude that T${}_{d}^{*}$ is centrosymmetric with P$2_{1}/m$ symmetry. A structural refinement assuming P$2_{1}/m$ symmetry was performed (see Supplementary Materials), with rough agreement between the refined and ideal coordinates, though the absence of visible $0KL$ peaks in our data (apart from those with even $K+L$) indicates that the true T${}_{d}^{*}$ structure is closer to the ideal AABB stacking than our refined coordinates.

For a closer look at how the transition proceeds, in Fig. 3(a,b) we plot intensities for four Bragg peaks as a function of temperature. The integrated intensities were obtained from fits of the data shown in Figures 1(d) and 1(e). On cooling below $\sim$280 K (Fig. 3(a)), there is a steady decrease in the intensity of the 1T*′* peaks in the hysteresis region. The peaks eventually become difficult to resolve from the diffuse scattering, and fitting was not done within the region indicated by the pink shaded bar. On further cooling, the Td peaks appear.

In contrast, on warming the intensities of the Td peaks in Fig. 3(b) remain constant until a sudden change is observed around 260 K. At this temperature, the T${}_{d}^{*}$ peaks appear (magenta symbols) at the expense of the Td peaks. On further warming, the Td and T${}_{d}^{*}$ peak intensities both decrease and disappear by 280 K. Again, diffuse scattering is observed (pink shaded region) prior to the crystal transforming fully into 1T*′. Though a coherent, long-range T${}_{d}^{*}$ phase only appears on warming, the intensity shift toward $(2,0,2.5)$ on cooling as seen in Fig. 1(b) and 1(d) suggests a tendency toward the AABB stacking, though frustrated and not resulting in an ordered structure. On both cooling into Td* or warming into 1T*′, there is a gradual increase in the intensity of the Td* and 1T*′* peaks, which occurs with a decrease in diffuse scattering (see Fig. S3 of the Supplemental Materials). This lingering diffuse scattering is probably related to the long residual hysteresis commonly observed in the resistivity measurements (e.g., in Ref. Zandt et al. (2007b), or Fig. S4 in the Supplemental Materials.)

To investigate the boundary between the Td and T${}_{d}^{*}$ regions, in Fig. 3(c), intensity integrated near $(2,0,2.5)$ is plotted for two different thermal hysteresis loops for the MT2 crystal. The narrow hysteresis loop (black symbols) corresponds to the sample warming into T${}_{d}^{*}$, then cooling back to Td without entering 1T*′. Fig. 3(d) is a plot of the data used to calculate the narrow hysteresis loop intensities. The $(205)_{T_{d}^{*}}$ peak intensity rises and falls through the hysteresis loop. Diffuse scattering is not present even at a temperature a few Kelvin below the T${}_{d}^{*}$ peak’s disappearance on cooling. Thus, T{}_{d}^{*}$$\rightarrowTd* likely proceeds without disorder. In contrast, a wider hysteresis loop (green symbols) is observed when the sample is allowed to warm into 1T*′*. This is coupled to the substantial diffuse scattering present on cooling, as shown earlier in Fig. 1(d,e). Nevertheless, for both narrow and wide hysteresis loops, a sudden drop of intensity near $(2,0,2.5)$ appears on cooling below 255 K, though more gradually for the wide hysteresis loop.

A similar pattern can be seen in the resistance data of Fig. 3(e), taken on a MoTe2 crystal with residual resistance ratio $\sim$460 through consecutive narrow (black; 200 to 265 K) and wide (green; 200 to 350 K) hysteresis loops. On cooling, the resistance decreases quickly and in a symmetric manner (for cooling vs. warming) for the narrow hysteresis loop, but more slowly and asymmetric for the wide hysteresis loop. Even so, the temperature at which both loops begin to bend on cooling is similar, as seen from $dR/dT$ in Fig. 3(f), though slightly lower for the wide hysteresis loop. The kink seen on warming (near 258 K) is likely the onset of T${}_{d}^{*}$ and not 1T*′*, judging from the temperature and the similarities between the resistance and neutron scattering hysteresis loops.

We next discuss how these structural transitions proceed and the kinds of interlayer interactions that may be responsible, beginning from the observation that the onset to Td occurs at a similar temperature whether cooling from the ordered T${}_{d}^{*}$ phase, or from the frustrated T${}_{d}^{*}$ region accessed on cooling from 1T*′. Since the onset temperature to Td* does not appear to vary substantially with overall stacking disorder, we suggest that short-range rather than long-range interlayer interactions determine the onset temperatures (into 1T*′* or T${}_{d}^{*}$ as well as Td). (Though we use the term “interlayer interactions”, we emphasize that these are effective interactions. Whether an interlayer boundary shifts from A$\rightarrow$B depends on the free energy, which depends on the surrounding environment, which is specified by the A/B stacking sequence. “Interlayer interactions” represent the dependence of an interlayer boundary’s contribution to the free energy on the surrounding stacking, and can be indirect, involving changes to band structure, phonon dispersion, etc.)

In contrast, long-range interlayer interactions may govern the gradual decrease in diffuse scattering and increase in Bragg peak intensities on warming into 1T*′* or cooling into Td. What kind of stacking faults causing this diffuse scattering persist on cooling into Td, even when short-range interlayer interactions favor an ordered phase? At twin boundaries, shifts of A$\rightarrow$B or B$\rightarrow$A (e.g., AAAABBB…$\rightarrow$AAABBBB…) would not change the short-range environment, and could only be induced by changes in long-range interlayer interactions. The decrease in diffuse scattering in Td on cooling can be explained by the annihilation of these twin boundaries, either by joining in pairs or by exiting a crystal surface. The lack of change on subsequent warming can be explained by the relaxation of conditions that, on cooling, had driven twin boundaries to annihilate.

Previous studies on MoTe2 should be re-examined in light of the existence of the T${}_{d}^{*}$ phase. First, the hysteresis loop in resistivity (first reported in Ref. Hughes and Friend (1978)) has been interpreted as indicating the transition between Td and 1T*′, but in view of the current data, most of the change in the resistance occurs between Td* and T${}_{d}^{*}$ on warming. Second, second harmonic generation (SHG) intensity measurements, expected to be zero for inversion symmetry and nonzero otherwise, show abrupt (within $<$4 K) changes on both heating and cooling through the hysteresis loop Sakai et al. (2016). Since the transition to 1T*′* occurs gradually, and since T${}_{d}^{*}$ appears to be centrosymmetric, the abrupt warming transition seen in SHG may be due to the Td$\rightarrow$T${}_{d}^{*}$ rather than Td$\rightarrow$1T*′* transition. The abrupt transition on cooling is harder to explain, but it is possible that the loss of inversion symmetry on cooling into Td occurs suddenly even as the transition proceeds with disorder. Our findings may also inform proposed applications, such as the photoinduced ultrafast topological switch in Ref. Zhang et al. (2019); since the Td$\rightarrow$T{}_{d}^{*}$$\rightarrowTd transition occurs without disorder and with only a $\sim$5 K hysteresis, and since T${}_{d}^{*}$ appears to be centrosymmetric, a topological switch may more efficiently use T${}_{d}^{*}$ rather than 1T*′*.

In conclusion, using elastic neutron scattering, we mapped the changes in stacking that occur in the thermal hysteresis between the Td and 1T*′* phases in MoTe2. On warming from the orthorhombic Td, T${}_{d}^{*}$ arises without diffuse scattering and corresponds to an “AABB” sequence of stacking operations. Diffuse scattering is present on further warming from T${}_{d}^{*}$ to 1T*′, and on cooling from 1T′* to Td, where a frustrated tendency toward the “AABB” stacking is seen. Thus, the 1T*′-Td* transition has complex structural behavior and deserves further study.

Acknowledgements

This work has been supported by the Department of Energy, Grant number DE-FG02-01ER45927. A portion of this research used resources at the High Flux Isotope Reactor and the Spallation Neutron Source, which are DOE Office of Science User Facilities operated by Oak Ridge National Laboratory.