Session L51: Dirac and Weyl Semimetals: Materials and Modeling---Type II Weyl Semimetals and Beyond

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We have shown that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation, and time-reversal symmetry. We determined that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window [G. Chang et al. Nature Materials 17, 978-985 (2018)]. Among all the materials, we predicted the RhSi family to exhibit the ideal topological band structures, displaying the largest possible momentum separation of compensative chiral fermions, the largest proposed topologically nontrivial energy window, and the longest possible Fermi arcs on its surface [G. Chang et al. PRL 119, 206401 (2017)]. We present the theory of exotic nonlinear optical responses of topological chiral crystals, including quantized photogalvanic effect in RhSi [G. Chang et al. PRL 119, 206401 (2017)] and robust photocurrents from Fermi arc surface states [G. Chang et al. PRL 124, 166404 (2020)]. We also discuss the experimental discovery of the RhSi family as topological chiral crystals [D. S. Sanchez et al. Nature 567, 500-505 (2019) & T. A. Cochran et al. arXiv:2004.11365 (2020)] and additional experiments that our discovery has enabled. (This work is in collaboration with D. S. Sanchez, I. Belopolski, T. A. Cochran, B. J. Wieder, F. Schindler, J. Yin, S. S. Zhang, S. Huang, B. Singh, T. Chang, A. Bansil, T. Neupert, S.-Y. Xu, H. Lin, and M. Zahid Hasan)   

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Layered transition metal dichalcogenides MoTe₂ and WTe₂ are suggested to be Weyl semimetals in their orthorhombic T_d phase. These materials exist in bulk forms as stacks of strongly in-plane bonded layers with weak van der Waals interlayer interaction and their properties often vary with stacking changes. For example, MoTe₂ exhibits a first order structural phase transition at ∼260K from a low-temperature orthorhombic T_d phase to a high-temperature monoclinic 1T' phase, with an intermediate pseudo-orthorhombic T_d* phase seen only on warming. In contrast, it is long believed that WTe₂ has only the T_d phase at ambient pressure since the material was first structurally characterized decades ago. We performed elastic neutron scattering measurements at the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) on a WTe₂ single crystal and observed a T_d-1T’ structural phase transition at ~565K. The transition proceeds without any hysteresis or intermediate phase. The observation of the 1T' phase in WTe₂ at ambient pressure adds details to the structural behavior of the Mo_1-xW_xTe₂ family, and gives new insights into re-examination of theories that lack a transition in WTe₂.   

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Along with the observation of type-II Weyl semimetallic (WSM) phase, multiple novel quantum phenomena such as pressure-induced superconductivity, extremely large magnetoresistance, and various kinds of Hall responses, have been observed in the Td phase of WTe2 and MoTe2. Interestingly, it has been reported that W_1-xMo_xTe₂ also hosts type-II WSM phase [1,2]. Therefore, a systematically study of the electronic structure of Td-WTe2 as a function of Mo substitution is quintessential to understand the subtle changes occurring in the electronic topology near the Fermi level. In this work, we use density-functional theory calculations to investigate the electronic structure of W_1-xMo_xTe₂ (x=0, 0.25, 0.5, 0.75, and 1.0). We find that the total number of Weyl nodes and their location, Fermi arcs, and surface states are very sensitive to the chemical composition. We will discuss the structural stability, the number of Weyl points, Fermi arcs, etc. as x varies.

[1] BelopolskiI et al.; Phys. Rev. B 94, 085127 (2016).
[2] Chang et al.; Nat. Commun. 7, 10639 (2016).   

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Strong anisotropic behavior of Raman modes has been detected in polarized Raman spectroscopy of a ternary compound NbIrTe₄ nanoflake. 19 Raman modes of A₁ and A₂ symmetries were detected and were consistent with DFT calculations. By rotating the sample the Raman spectroscopy probes different directions of the crystal structure. These measurements were implemented so that the polarization direction of the incident and scattered beams are parallel and perpendicular, respectively. Through analysis of this angular dependence one can extract the Raman tensor elements which depend on electron-phonon coupling. By exciting at 633 nm and 514 nm, it is possible to observe the sensitivity of the tensor elements to excitation energy for 19 Raman modes. We find that the mode excitation sensitivity depend strongly on their frequency which indicates that some modes couple much more strongly to electronic states than others.   

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Recent results have shown an emergence of CDW order in SrAl4 at 243K, together with a hysteretic structural transition at 87K from a tetragonal to potentially monoclinic structure. The tetragonal structure of BaAl4 with lattice parameters very close to SrAl4 invites a chemical substitution study to track the reported transitions. We have performed electrical resistivity and magnetic susceptibility measurements, along with x-ray and neutron scattering on the Ba1-xSrxAl4 family. All samples have been grown in self-flux and produce large single-crystals, seemingly limited by crucible size.   

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A robust methodology to detect Dirac-Weyl fermions in topological semimetals by transport or thermodynamic measurements remains an open problem. It is often argued that a π-phase in quantum oscillations directly corresponds to the nontrivial Berry phase of topological semimetals. However, the oscillation phase is complicated by multiple contributing factors including the orbital magnetic moment, rendering such correspondences ambiguous for a substantial fraction of topological semimetals. Here, we propose to utilize the temperature dependence of the frequency, F(T), rather than the oscillation phase, as a hallmark signature of topology in quantum oscillations. At temperatures that are comparable to the cyclotron energy, F(T) encodes the energy-derivative of the cyclotron mass - a quantity that vanishes for conventional Schroedinger-type fermions, yet equals the inverse square of the Fermi velocity for Dirac-Weyl fermions. Cd₃As₂, Bi₂O₂Se and LaRhIn₅ serve as testing grounds confirming our methodology. Our approach requires no ab-initio calculation as input, and is able to identify topological Fermi pockets which are small compared to the Brillouin-zone volume - both attributes being ideally suited to identify topological heavy-fermion materials.   

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A robust methodology to detect Dirac-Weyl fermions in topological semimetals by transport or thermodynamic measurements remains an open problem. It is often argued that a $\pi$ phase in quantum oscillations directly corresponds to the nontrivial Berry phase of topological semimetals. However, the oscillation phase is complicated by multiple contributing factors including the orbital magnetic moment, rendering such correspondences ambiguous for a substantial fraction of topological semimetals. Here, we propose to utilize the temperature dependence of the frequency, F(T), rather than the oscillation phase, as a hallmark signature of topology in quantum oscillations. At temperatures that are comparable to the cyclotron energy, F(T) encodes the energy-derivative of the cyclotron mass - a quantity that vanishes for conventional Schroedinger-type fermions, yet equals the inverse square of the Fermi velocity for Dirac-Weyl fermions. Cd$_3$As$_2$, Bi$_2$O$_2$Se and LaRhIn$_5$ serve as testing grounds confirming our methodology. Our approach requires no ab-initio calculation as input, and is able to identify topological Fermi pockets which are small compared to the Brillouin-zone volume - both attributes being ideally suited to identify topological heavy-fermion materials.   

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Weyl semimetals (WSM) are an important class of quantum materials in which the low-energy quasi-particle excitations of electrons mimic the features of massless Weyl fermions. Pair creation/annihilation of Weyl fermions has been a subject of much research interest in recent years. In this work, by means of the density-functional theory calculations, we study the role of external pressure and Mo substitution in the widely studied WSM T_d-WTe₂, i.e., W_0.5Mo_0.5Te₂. We find that Weyl nodes slightly shift in the energy space away from the Fermi level as external pressure gradually increases up to 2 GPa. We notice that new pairs of Weyl nodes start appearing through pair-creation mechanism in 2-20 GPa pressure range, yielding as many as 44 Weyl nodes at 20 GPa. Beyond 20 GPa pressure, some pairs of opposite Weyl nodes start annihilating systematically leaving only 16 Weyl points at 35 GPa, which remains invariant until 45 GPa pressure.   

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We characterize ultrafast optical anisotropy in type-II Weyl semimetals WTe₂ and NbIrTe₄, using polarized transient reflectance. We study single nanoflakes excited by an ultrafast (140 fs) 800 nm pulse, and monitor the dynamic reflectance of a tunable polarized NIR-MIR probe pulse. CW polarized reflectance measurements establish the biaxial symmetry of a flake's optical anisotropy. A half-wave plate sweeps the probe polarization between critical optical axes and records the dynamic response as a function of angle. The intensity and phase of the transient signal sensitively depends on the probe polarization in both materials, whereas characteristic lifetimes show no clear correlation. In WTe_2, we observe a rapid ~1.0 ps decay followed by a slow nanosecond-scale relaxation. Likewise in NbIrTe₄, we observe a fast ~0.6 ps initial decay followed by a slower nanosecond process. We interpret these results in the context of carrier thermalization and lattice cooling in topological semimetals.   

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Weyl semimetals are topological systems that have generated considerable interest due to their transport properties as well as their nonlinear response to light. Due to the topological nature of the Weyl cones, these systems are very sensitive to nonlinear responses such as the shift and injection current response to polarized light. Optical experiments done on various Weyl semimetals have already shown large photocurrent responses, but so far investigation into enhancement of nonlinear responses due to excitations from the Weyl node has been quite limited. These measurements are experimentally difficult due to the low energy requirement to excite about the node, however excitations between Weyl nodes and the Fermi surface may be a way to avoid this challenge. Here we report on mid-IR photocurrent measurements performed on the type-II Weyl semimetal WP2. Polarization and wavelength dependence of the response shows a room temperature injection current response resonant with the energy of one of the Weyl nodes.   

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Dirac fermions with highly-dispersive linear bands are usually considered weakly correlated, due to relatively large bandwidths (W) compared to Coulomb interactions (U). With the discovery of nodal-line semimetals, the notion of Dirac point has been extended to lines and loops in the momentum space [1]. The anisotropy associated with nodal-line structure gives rise to greatly reduced kinetic energy along the line. However, experimental evidence for anticipated enhanced correlations in nodal-line semimetals is sparse. Here we report on prominent correlation effects in a nodal-line semimetal compound ZrSiSe [2] through a combination of optical spectroscopy and density-functional-theory calculations. We observed two fundamental spectroscopic hallmarks of electronic correlations: strong reduction (1/3) of the free carrier Drude weight and of the Fermi velocity compared to predictions of density functional band theory. The renormalization of Fermi velocity can be further controlled with external magnetic field. ZrSiSe therefore offers the rare opportunity to investigate correlation-driven physics in a Dirac system.

[1] Y. Shao, Z. Sun, et al, Proceedings of the National Academy of Sciences 116,1168 (2019)
[2] Y. Shao et al, Nature Physics 16, 636–641 (2020)   

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In this work, we have applied ¹²⁵Te nuclear magnetic resonance (NMR) spectroscopy combined with density functional theory (DFT) to characterize the electronic structure of a single crystal sample of ZrSiTe. Both the NMR shift and the spin-lattice relaxation rate (1/T₁) clearly show minima at 20 K. The observed T-dependence corresponds to the chemical potential crossing an ungapped 2D Dirac nodal line, which corresponds to the symmetry-protected R-X nodal line in ZrSiTe. From the orientation dependence we show that diamagnetism of electrons along this nodal line dominates the low-T shifts, and the results indicate very small or zero nodal line energy dispersion. 1/T₁ is also dominated by these carriers, with the results agreeing with a model for fluctuating local fields due to very high mobility quasi-2D Dirac electrons. At higher temperatures, additional extrema reflect the topology of the bands connecting the protected node to the network of nodal loops in ZrSiTe, and these provide direct evidence of temperature-driven Lifshitz transitions.   

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Exotic multifold topological excitations have been predicted and were recently observed in transition metal silicides like β-RhSi. We report that interesting topological features of RhSi are also observed in its orthorhombic α phase, which displays multiple types of Dirac nodes very close to the Fermi level ε_F . We discuss the symmetry analysis, band connectivity along high-symmetry lines using group representations, band structure, the nature of the Dirac points and of a nodal line occurring near ε_F which is protected by the crystalline symmetry. The de Haas–van Alphen effect indicates a Fermi surface in agreement with the calculations. We find an elliptically shaped nodal line very close to ε_F around and near the S point on the k_y-k_z plane that results from the intersection of two upside-down Dirac cones. Both Dirac points of the participating Kramers degenerate bands are only 5 meV apart; hence, an accessible magnetic field might induce a crossing between Dirac sub-bands.