Vanishing quantum oscillations in Dirac semimetal ZrTe5

Rashba-splitting-induced topological flat band detected by anomalous resistance oscillations beyond the quantum limit in ZrTe5

Topological flat bands - where the kinetic energy of electrons is quenched - provide a platform for investigating the topological properties of correlated systems. Here, we report the observation of a topological flat band formed by polar-distortion-assisted Rashba splitting in the three-dimensional Dirac material ZrTe5. The polar distortion and resulting Rashba splitting on the band are directly detected by torque magnetometry and the anomalous Hall effect, respectively. The local symmetry breaking further flattens the band, on which we observe resistance oscillations beyond the quantum limit. These oscillations follow the temperature dependence of the Lifshitz-Kosevich formula but are evenly distributed in B instead of 1/B at high magnetic fields. Furthermore, the cyclotron mass gets anomalously enhanced about 102 times at fields ~ 20 T. Our results provide an intrinsic platform without invoking moiré or order-stacking engineering, which opens the door for studying topologically correlated phenomena beyond two dimensions.

Quantum-classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering quantum effects under a magnetic field, such as the Landau quantization and quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum-classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of the thermal Green's function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.

Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5

The fine-tuning of topologically protected states in quantum materials holds great promise for novel electronic devices. However, there are limited methods that allow for the controlled and efficient modulation of the crystal lattice while simultaneously monitoring the changes in the electronic structure within a single sample. Here, we apply significant and controllable strain to high-quality HfTe5 samples and perform electrical transport measurements to reveal the topological phase transition from a weak topological insulator phase to a strong topological insulator phase. After applying high strain to HfTe5 and converting it into a strong topological insulator, we found that the resistivity of the sample increased by 190,500% and that the electronic transport was dominated by the topological surface states at cryogenic temperatures. Our results demonstrate the suitability of HfTe5 as a material for engineering topological properties, with the potential to generalize this approach to study topological phase transitions in van der Waals materials and heterostructures.

Anisotropic magnetoresistance and electronic features of the candidate topological compound praseodymium monobismuthide

PrBi, a sister member of the rare-earth monopnictide family, is an excellent candidate for studying extreme magnetoresistance and nontrivial topological electronic states. In this study, we perform angular magnetoresistance measurements as well as bulk and surface band structure calculations on this compound. PrBi's magnetoresistance is revealed to be significantly angle-dependent and shows a fourfold symmetry as always observed in the nonmagnetic isostructural counterparts, including LaSb, LaBi, and LuBi. Its angular magnetoresistance can be reproduced well using the semiclassical two-band model. The deduced parameters suggest that PrBi hosts an elongated electron pocket with a mobility anisotropy of ∼3.13 and is slightly uncompensated in its carrier concentration. Our bulk and surface band structure calculations confirm the anisotropic electronic features. Moreover, we reveal that a nodal-line-shaped surface state appears at the X̄ point, and is associated with the quadratic dispersion along the -X̄ direction, and the linear type-I Dirac dispersion along the X̄-M̄ direction. Owing to the type-I Dirac dispersion feature, PrBi could serve as a promising material platform for studying many unexpected physical properties, such as the highly anisotropic transport and valley polarization of electrons.

Gate-Tunable Multiband Transport in ZrTe5 Thin Devices

Interest in ZrTe₅ has been reinvigorated in recent years owing to its potential for hosting versatile topological electronic states and intriguing experimental discoveries. However, the mechanism of many of its unusual transport behaviors remains controversial: for example, the characteristic peak in the temperature-dependent resistivity and the anomalous Hall effect. Here, through employing a clean dry-transfer fabrication method in an inert environment, we successfully obtain high-quality ZrTe₅ thin devices that exhibit clear dual-gate tunability and ambipolar field effects. Such devices allow us to systematically study the resistance peak as well as the Hall effect at various doping densities and temperatures, revealing the contribution from electron-hole asymmetry and multiple-carrier transport. By comparing with theoretical calculations, we suggest a simplified semiclassical two-band model to explain the experimental observations. Our work helps to resolve the longstanding puzzles on ZrTe₅ and could potentially pave the way for realizing novel topological states in the two-dimensional limit.

Magneto-transport evidence for strong topological insulator phase in ZrTe5

The identification of a non-trivial band topology usually relies on directly probing the protected surface/edge states. But, it is difficult to achieve electronically in narrow-gap topological materials due to the small (meV) energy scales. Here, we demonstrate that band inversion, a crucial ingredient of the non-trivial band topology, can serve as an alternative, experimentally accessible indicator. We show that an inverted band can lead to a four-fold splitting of the non-zero Landau levels, contrasting the two-fold splitting (spin splitting only) in the normal band. We confirm our predictions in magneto-transport experiments on a narrow-gap strong topological insulator, zirconium pentatelluride (ZrTe5), with the observation of additional splittings in the quantum oscillations and also an anomalous peak in the extreme quantum limit. Our work establishes an effective strategy for identifying the band inversion as well as the associated topological phases for future topological materials research.

Fermi level fluctuations, reduced effective masses and Zeeman effect during quantum oscillations in nodal line semimetals

We probe quantum oscillations in nodal line semimetals (NLSM) by considering an NLSM continuum model under strong magnetic field and report the characteristics of the Landau level (LL) spectra and the fluctuations in the Fermi level as the field in a direction perpendicular to the nodal plane is varied through. Based on the results on parallel magnetization, we demonstrate the growth of quantum oscillation with field strength as well as its constancy in period when plotted against 1/B. We find that the density of states (DOS) which show series of peaks in succession, witness bifurcation of those peaks due to Zeeman effect. For field normal to nodal plane, such bifurcations are discernible only if the electron effective mass is considerably smaller than its free value, which usually happens in these systems. Though a reduced effective massm* causes the Zeeman splitting to become small compared to LL spacings, experimental results indicate a manifold increase in the Landegfactor which again amplifies the Zeeman contribution. We also consider magnetic field in the nodal plane for which the DOS peaks do not repeat periodically with energy anymore. The spectra become more spread out and the Zeeman splittings become less prominent. We find the low energy topological regime, that appears with such in-plane field set up, to shrink further with reducedm* values. However, such topological regime can be stretched out in case there are smaller Fermi velocities for electrons in the direction normal to the nodal plane.

Orbit topology analyzed from π phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal

With the emergence of Dirac fermion physics in the field of condensed matter, magnetic quantum oscillations (MQOs) have been used to discern the topology of orbits in Dirac materials. However, many previous researchers have relied on the single-orbit Lifshitz-Kosevich (LK) formula, which overlooks the significant effect of degenerate orbits on MQOs. Since the single-orbit LK formula is valid for massless Dirac semimetals with small cyclotron masses, it is imperative to generalize the method applicable to a wide range of Dirac semimetals, whether massless or massive. This report demonstrates how spin-degenerate orbits affect the phases in MQOs of three-dimensional massive Dirac semimetal, NbSb2 With varying the direction of the magnetic field, an abrupt π phase shift is observed due to the interference between the spin-degenerate orbits. We investigate the effect of cyclotron mass on the π phase shift and verify its close relation to the phase from the Zeeman coupling. We find that the π phase shift occurs when the cyclotron mass is half of the electron mass, indicating the effective spin gyromagnetic ratio as g s = 2. Our approach is not only useful for analyzing MQOs of massless Dirac semimetals with a small cyclotron mass but also can be used for MQOs in massive Dirac materials with degenerate orbits, especially in topological materials with a sufficiently large cyclotron mass. Furthermore, this method provides a useful way to estimate the precise g s value of the material.

Anisotropic magnetotransport in tilted magnetic topological semimetals

We systematically investigate the anisotropic magneto-conductivity and planar Hall effect in tilted magnetic topological semimetals in the frame of Kubo formula by considering the vertex correction of velocity. The nonzero anisotropic magneto-conductivity is due to the intrinsic magnetization by magnetic doping rather than the external magnetic field previously studied in literatures. In the scenario, tilt, which is common in band structure, plays a key role in this anisotropic magneto-conductivity. This anisotropic magneto-conductivity completely originates from the band anisotropy. The vertex correction only amends the magnitude, but does not change the qualitative behavior of the longitudinal conductivity. However, the planar Hall conductivity is always zero for tilt along bothxandydirections in vivid contrast to the case arising from an external magnetic field. Our work offers a route to understand the anisotropic magneto-conductivity effect in tilted Weyl semimetals with Zeeman field. It will be helpful to get a deeper understanding of the transport characteristic in tilted topological semimetals.

Electronic and topological properties of group-10 transition metal dichalcogenides

The group 10 transition metal dichalcogenides (TMDs) (MX ₂: M = Ni, Pd, Pt; X = S, Se, Te) have attracted much attention in the last few decades because of observation of exotic phases and phenomena such as superconductivity (SC), topological surface states (TSSs), type II Dirac fermions, helical spin texture, Rashba effect, 3D Dirac plasmons, metal-insulator transitions, charge density waves (CDW) etc. In this review, we cover the experimental and theoretical progress on the physical phenomena influenced by the strong electron-electron correlation of the group-10 TMDs from the past to the present. We have especially emphasized on the SC and topological phases in the bulk as well as in atomically thin materials.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Unraveling the Topological Phase of ZrTe_{5} via Magnetoinfrared Spectroscopy

For materials near the phase boundary between weak and strong topological insulators (TIs), their band topology depends on the band alignment, with the inverted (normal) band corresponding to the strong (weak) TI phase. Here, taking the anisotropic transition-metal pentatelluride ZrTe_{5} as an example, we show that the band inversion manifests itself as a second extremum (band gap) in the layer stacking direction, which can be probed experimentally via magnetoinfrared spectroscopy. Specifically, we find that the band anisotropy of ZrTe_{5} features a slow dispersion in the layer stacking direction, along with an additional set of optical transitions from a band gap next to the Brillouin zone center. Our work identifies ZrTe_{5} as a strong TI at liquid helium temperature and provides a new perspective in determining band inversion in layered topological materials.

Observation of a thermoelectric Hall plateau in the extreme quantum limit

The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here, we demonstrate that the thermoelectric Hall conductivity αxy in the three-dimensional Dirac semimetal ZrTe5 acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields.

Anomalous Thermoelectric Effects of ZrTe_{5} in and beyond the Quantum Limit

Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. We study the thermoelectric effects of ZrTe_{5} in a magnetic field. The presence of the nontrivial electrons leads to the anomalous Nernst effect and quasilinear field dependence of thermopower below the quantum limit. In the strong-field quantum limit, both the thermopower and Nernst signal exhibit exotic peaks. At higher magnetic fields, the Nernst signal has a sign reversal at a critical field where the thermopower approaches zero. We propose that these anomalous behaviors can be attributed to the gap closing of the zeroth Landau bands in topological materials with the band inversion. Our understanding to the anomalous thermoelectric properties in ZrTe_{5} opens a new avenue for exploring Dirac physics in topological materials.

Fast and controlled growth of two-dimensional layered ZrTe3 nanoribbons by chemical vapor deposition

We first demonstrated ZrTe₃ nanoribbons can be grown directly by chemical vapor deposition method, which exhibit intriguing magnetic properties.