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 magneto-infrared 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 away from the Brillouin zone center. Our work identifies ZrTe5 as a strong TI at liquid helium temperature and provides a new perspective in determining band inversion in layered topological materials.
We study the effects of temperature on the topological nature of ZrTe$_5$, which sits near the phase boundary between strong and weak topological insulating orders. Using first-principles calculations, we show that the band gap and the topological indices of ZrTe$_5$ are extremely sensitive to thermal expansion, and that the electron-phonon interaction accounts for more than a third of the total temperature-dependent effects in ZrTe$_5$. We find that the temperature dependence of the band gap has an opposite sign in the strong and weak topological insulator phases. Based on this insight, we pr…
Topological materials with broken inversion symmetry can give rise to nonreciprocal responses, such as the current rectification controlled by magnetic fields via magnetochiral anisotropy. Bulk nonreciprocal responses usually stem from relativistic corrections and are always very small. Here we report our discovery that ZrTe5 crystals in proximity to a topological quantum phase transition present gigantic magnetochiral anisotropy, which is the largest ever observed to date. We argue that a very low carrier density, inhomogeneities, and a torus-shaped Fermi surface induced by breaking of invers…
ZrTe5 is a layered material that exhibits intricate topological effects. Intensive theoretically and experimental efforts have been devoted to try to understand the physics in this materials. In this paper the temperature dependent magneto-transport properties of ZrTe5 thin flakes are investigated. A characteristic temperature T* is observed in the temperature dependence of three different types of magnetoresistance simultaneously, which are the saturated Hall anomaly, the chiral anomaly and the longitudinal magnetoresistance. Furthermore, the value of T* decreases monotonically from 200K to 1…
In this paper, we give a systematic theoretical study on the Landau levels (LLs) and magneto-optical conductivity Re$(σ_{αα})$ in a gapped Dirac semimetal model with mixed linear and parabolic dispersions under a magnetic field, which was recently proposed by Jiang \textit{et al.} [Phys. Rev. Lett. {\bf125}, 046403 (2020)] to explain the experimental magnetoinfrared spectroscopy in the three-dimensional ZrTe$_5$ crystal. We find that the strong magnetic field can drive the LLs become noninverted and thus the strong topological insulator phase in ZrTe$_5$ turns to be a trivial insulator. In the…
A phase transition between topologically distinct insulating phases involves closing and reopening of the bandgap. Close to this topological phase transition, the bulk energy spectrum is characterized by a massive Dirac dispersion, where the mass plays the role of bandgap. Here we report the observation of a non-monotonic strain dependence of resistivity and negative longitudinal magnetoresistance in ZrTe5, which is known to host massive Dirac Fermions in the bulk. This non-monotonic strain dependence is consistent with the closing and reopening of the bandgap at the Brillouin-zone center, ind…
We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe$_5$. We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D \emph{massless} Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe$_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitt…
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 predictio…
Recent experiments have reported a lot of spectacular transport properties in topological materials, such as quantum oscillations and three-dimensional (3D) quantum Hall effect (QHE) in ZrTe$_5$. In this paper, by using a strong topological insulator model to describe ZrTe$_5$, we study the magnetotransport property of the 3D system. With fixed carrier density, we find that there exists a deferring effect in the chemical potential, which favors distinguishing the saddle points of the inverted LLs. On the other hand, with fixed chemical potential, the features of 3D QHE are demonstrated and we …
Using Landau level spectroscopy, we determine the temperature dependence of the energy band gap in zirconium pentatelluride (ZrTe$_5$). We find that the band gap reaches $E_g=(5 \pm 1)$ meV at low temperatures and increases monotonously when the temperature is raised. This implies that ZrTe$_5$ is a weak topological insulator, with non-inverted ordering of electronic bands in the center of the Brillouin zone. Our magneto-transport experiments performed in parallel show that the resistivity anomaly in ZrTe$_5$ is not connected with the temperature dependence of the band gap.
Topological Dirac semimetal is a newly discovered class of materials and has attracted intense attentions. This material can be viewed as a three-dimensional (3D) analogue of graphene and has linear energy dispersion in bulk, leading to a range of exotic transport properties. Here we report direct quantum transport evidence of 3D Dirac semimetal phase of layered material ZrTe5 by angular dependent magnetoresistance measurements under high magnetic fields up to 31 Tesla. We observed very clear negative longitudinal magnetoresistance induced by chiral anomaly under the condition of the magnetic …
Symmetry protected Dirac semimetals can be transformed into Weyl semimetals by breaking the protecting symmetry, leading to many exotic quantum phenomena such as chiral anomaly and anomalous Hall effect. Here we show that, due to the large Zeeman g factor and small band width along b-axis in Dirac semimetal ZrTe5, a magnetic field of about 8 T along b-axis direction may annihilate the Weyl points and open up a two-dimensional (2D) Dirac mass gap, when the Zeeman splitting exceeds the band width along b-axis. This is manifested by a sharp drop of magnetoresistance (MR) above 8 T, which is proba…
The layered material ZrTe$_5$ appears to exhibit several exotic behaviors which resulted in significant interest recently, although the exact properties are still highly debated. Among these we find a Dirac/Weyl semimetallic behavior, nontrivial spin textures revealed by low temperature transport, and a potential weak or strong topological phase. The anomalous behavior of resistivity has been recently elucidated as originating from band shifting in the electronic structure. Our work examines magnetotransport behavior in ZrTe$_5$ samples in the context of multicarrier transport. The results, in…
A 40-year-old puzzle in transition metal pentatellurides ZrTe$_5$ and HfTe$_5$ is the anomalous peak in the temperature dependence of the longitudinal resistivity, which is accompanied by sign reverses of the Hall and Seebeck coefficients. We give a plausible explanation for these phenomena without assuming any phase transition or strong interaction effect. We show that due to intrinsic thermodynamics and diluteness of the conducting electrons in these materials, the chemical potential displays a strong dependence on the temperature and magnetic field. With that, we compute resistivity, Hall a…
Researches on anomalous Hall effect (AHE) have been lasting for a century to make clear the underlying physical mechanism. Generally, the AHE appears in magnetic materials, in which extrinsic process related to scattering effects and intrinsic contribution connected with Berry curvature are crucial. Recently, AHE has been counterintuitively observed in non-magnetic topological materials and attributed to the existence of Weyl points. However, the Weyl point scenario would lead to unsaturated AHE even in large magnetic fields and contradicts the saturation of AHE in several tesla (T) in experim…
Transition metal pentatelluride ZrTe5 is a versatile material in condensed-matter physics and has been intensively studied since the 1980s. The most fascinating feature of ZrTe5 is that it is a 3D Dirac semimetal which has linear energy dispersion in all three dimensions in momentum space. Structure-wise, ZrTe5 is a layered material held together by weak interlayer van der Waals force. The combination of its unique band structure and 2D atomic structure provides a fertile ground for more potential exotic physical phenomena in ZrTe5 related to 3D Dirac semimentals. However the physical properti…
Recently, perovskite related BaPbO$_3$ has attracted attention due to its hidden topological properties and, moreover, has been used as a thin layer in heterostructures to induce two-dimensional superconductivity. Here we investigate the normal state electronic transport properties of thin films of BaPbO$_3$. Temperature and magnetic field dependent sheet resistances are strongly affected by two-dimensional quantum effects. Our analysis decodes the interplay of spin--orbit coupling, disorder, and electron--electron interaction in this compound. Similar to recently discussed topological materia…
Extensive studies of electron transport in Dirac materials have shown positive magneto-resistance (MR) and positive magneto-thermopower (MTP) in a magnetic field perpendicular to the excitation current or thermal gradient. In contrast, measurements of electron transport often show a negative longitudinal MR and negative MTP for a magnetic field oriented along the excitation current or thermal gradient; this is attributed to the chiral anomaly in Dirac materials. Here, we report a very different magneto-thermoelectric transport behavior in the massive Dirac material ZrTe5. Although thin flakes …
Wireless technology relies on the conversion of alternating electromagnetic fields to direct currents, a process known as rectification. While rectifiers are normally based on semiconductor diodes, quantum mechanical non-reciprocal transport effects that enable highly controllable rectification have recently been discovered. One such effect is magnetochiral anisotropy (MCA), where the resistance of a material or a device depends on both the direction of current flow and an applied magnetic field. However, the size of rectification possible due to MCA is usually extremely small, because MCA rel…
Quantum oscillations are usually the manifestation of the underlying physical nature in condensed matter systems. Here we report a new type of log-periodic quantum oscillations in ultra-quantum three-dimensional topological materials. Beyond the quantum limit (QL), the log-periodic oscillations involving up to five oscillating cycles (5 peaks and 5 dips) are observed on the magnetoresistance (MR) of high quality single-crystal ZrTe5, virtually showing the clearest feature of discrete scale invariance (DSI). Further theoretical analyses show that the two-body quasi-bound states can be responsib…
Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe5 flakes when in-plane magnetic field is parallel and perpendicular to the current. Surprisingly, both symmetric and antisymmetric components with respect to magnetic field are detected in the in-plane Hall resistivity. Further theoretical analysis suggests that the magnetotransport properties originate from the anomalous velocity induced by Be…
