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Topological semimetals with protected surface states mark a new paradigm of research beyond the early landmarks of band-structure engineering, allowing fabrication of efficient catalyst to harness the rich metallic surface states to activate specific chemical processes. Herein, we demonstrate a facile solid-phase method for in-situ doping of Ir at the Os sites in the Os3Sn7, an alloy with topological states, which significantly improves the photocatalytic performance for the reduction of CO2 to CO and CH4. Experimental evidence combined with theoretical calculations reveal that the nontrivial topological surface states greatly accelerate charge-separation/electron-enrichment and adsorption/activation of CO2 molecules, rendering highly efficient reaction channels to stimulate the formation of *COOH and *CO, as well CHO*. This work shows the promise of achieving high photocatalytic performances with synthesizing topological catalysts and provides hints on the design of novel topological catalysts with superior photoactivity towards the CO2 reduction reaction., Comment: 33 Pages, 6 Figures, 1 Table

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 show a commonly observed positive MR in a perpendicular magnetic field, distinct from other Dirac materials, we observe a sharp negative MTP. In a parallel magnetic field, we still observe a negative longitudinal MR, however, a remarkable positive MTP is observed for the fields parallel to the thermal gradients. Our theoretical calculations suggest that this anomalous magneto-thermoelectric behavior can be attributed to the screened Coulomb scattering. This work demonstrates the significance of impurity scattering in the electron transport of topological materials and provides deep insight into the novel magneto-transport phenomena in Dirac materials.

Recently, log-periodic quantum oscillations have been detected in topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with DSI feature, resembling the artificial supercritical atom collapse. The density of states of these quasi-bound states are enhanced and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy (STM/S). By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible, meanwhile the energies of quasi-bound states move gradually towards the Fermi energy (EF). These features are consistent with the theoretical prediction of a magnetic-field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

In disordered transition-metal dichalcogenide (TMD) superconductor, both the strong spin-orbit coupling (SOC) and disorder show remarkable effects on superconductivity. However, the features of SOC and disorder were rarely detected directly. Here we report the quantum transport behaviors arising from the interplay of SOC and disorder in the TMD superconductor 1T-NbSeTe. Before entering the superconducting state, the single crystal at low temperature shows a resistivity upturn, which is T1/2 dependent and insensitive to the applied magnetic fields. The magnetoresistance (MR) at low temperatures shows a H1/2 dependence at high magnetic fields. The characteristics are in good agreement with the electron-electron interaction (EEI) in a disordered conductor. In addition, the upturn changes and MR at low magnetic fields suggest the contribution of weak antilocalization (WAL) effect arising from the strong SOC in the material. Moreover, the quantitative analyses of the transport features in different samples imply anomalous disorder-enhanced superconductivity that needs to be further understood. The results reveal the disorder enhanced EEI and the strong SOC induced WAL effect in 1T-NbSeTe, which illustrate the resistivity minimum in the widely studied doped superconductors. The work also provides insights into the disorder effect on the superconductivity.

This study demonstrates the design and synthesis of Cu0.5Ir1-xZrxTe2 system by partial substitution of Ir with Zr acting as a negative chemical pressure. With the doping of Zr, the cell parameters significantly expand, signifying an effective negative chemical pressure. The experimental results found evidence that the charge density wave (CDW)-like order is immediately quenched by subtle Zr substitution for Ir and a classical dome-shape Tc(x) that peaked at 2.80 K can be observed. The optimal Cu0.5Ir0.95Zr0.05Te2 compound is a BCS-type superconductor and exhibits type-II SC. However, high Zr concentration can provoke disorder, inducing the reappearance of CDW order. The present study shows that the Cu0.5Ir1-xZrxTe2 system may provide a new platform for further understanding of multiple electronic orders in transition metal dichalcogenides., Comment: 29 pages, 8 figures, 2 tables; The manuscript with the same title will be published by J. Phys. Chem. C

Saddle point approximations, extremely important in a wide variety of physical contexts, require the analytical continuation of canonically conjugate quantities to complex variables in quantum mechanics. An important component of this approximation's implementation is arriving at the phase correction attributable to caustics, which involves determinantal prefactors. The common prescription of using the inverse of half a certain determinant's total accumulated phase sometimes leads to sign errors. The root of this problem is traced to the zeros of the determinants at complex times crossing the real time axis. Deformed complex time contours around the zeros can repair the sign errors that sometimes occur, but a much more practical way is given that links saddles back to associated real trajectories and avoids the necessity of locating the complex time zeros of the determinants.

Semiclassical methods are extremely important in the subjects of wave packet and coherent state dynamics. Unfortunately, these essentially saddle point approximations are considered nearly impossible to carry out in detail for systems with multiple degrees of freedom due to the difficulties of solving the resulting two-point boundary value problems. However, recent developments have extended the applicability to a broader range of systems and circumstances. The most important advances are first to generate a set of real reference trajectories using appropriately reduced dimensional spaces of initial conditions, and second to feed that set into a Newton-Raphson search scheme to locate the $exposed$ complex saddle trajectories. The arguments for this approach were based mostly on intuition and numerical verification. In this paper, the methods are put on a firmer theoretical foundation and then extended to incorporate saddles $hidden$ from Newton-Raphson searches initiated with real trajectories. This hidden class of saddles is relevant to tunneling-type processes, but a hidden saddle can sometimes contribute just as much as or more than an exposed one. The distinctions between hidden and exposed saddles clarifies the interpretation of what constitutes tunneling for wave packets and coherent states in the time domain.

Here we report a systematic investigation on the evolution of the structural and physical properties, including the charge density wave and superconductivity of the polycrystalline CuIr2Te4-xIx. X-ray diffraction results indicate that both of a and c lattice parameters increase linearly. The resistivity measurements indicate that the charge density wave is destabilized with slight x but reappears when x is large than 0.9. Meanwhile, the superconducting transition temperature enhances as x raises and reaches a maximum value of around 2.95 K for the optimal composition CuIr2Te3.9I0.1 followed by a slight decrease with higher iodine doping content. The specific heat jump for the optimal composition CuIr2Te3.9I0.1 is approximately 1.46, which is close to the Bardeen Cooper Schrieffer value which is 1.43, indicating it is a bulk superconductor. The results of thermodynamic heat capacity measurements under different magnetic fields, magnetization and magneto-transport measurements further suggest that CuIr2Te4-xIx bulks are type II superconductors. Finally, an electronic phase diagram for this CuIr2Te4-xIx system has been constructed. The present study provides a suitable material platform for further investigation of the interplay of the CDW and superconductivity., Comment: The manuscript with the same title will be published by Chinese Physics Letters, 2021

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 experiments. In this work, we investigate the Hall effect of ZrTe5 and HfTe5 thin flakes in static ultrahigh magnetic fields up to 33 T. We find the AHE saturates to 55 (70) Ohm^-1*cm^-1 for ZrTe5 (HfTe5) thin flakes above ~ 10 T. Combining detailed magnetotransport experiments and Berry curvature calculations, we clarify that the splitting of massive Dirac bands without Weyl points can be responsible for AHE in non-magnetic topological materials ZrTe5 and HfTe5 thin flakes. This model can identify our thin flake samples to be weak topological insulators and serve as a new tool to probe the band structure topology in topological materials.

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials., Comment: Accepted by npj Quantum Materials

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 Berry curvature in a tilted Weyl semimetal. Our work not only enriches the Hall family but also provides new insights into the Berry phase effect in topological materials., Comment: National Science Review, 2020

Discrete scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity which can be rarely observed in quantum systems. Here we report the log-periodic quantum oscillations in the magnetoresistance (MR) and the Hall traces of HfTe5 crystals, which reveals the appearance of DSI. The oscillations show the same logB-periodicity in the behavior of MR and Hall, indicating an overall effect of the DSI on the transport properties. Moreover, the DSI feature in the Hall resistance signals its close relation to the carriers. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. Our work evidences the universality of the DSI in the Dirac materials and paves way for the full understanding of the novel phenomenon.

Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport phenomena in Dirac and Weyl semimetals. Section 1 is a brief introduction to the topological semimetals (TSMs). In Section 2 and Section 3, the intriguing transport phenomena in Dirac semimetals (DSMs) and Weyl semimetals (WSMs) are reviewed, respectively. The most widely studied Cd3As2 and the TaAs family are selected as representatives to show the typical properties of DSMs and WSMs, respectively. Beyond these systems, the advances in other TSM materials, such as ZrTe5 and the MoTe2 family, are also introduced. In Section 4, we provide perspectives on the study of TSMs especially on the magnetotransport investigations.

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 responsible for the DSI feature. Our work provides a new perspective on the ground state of topological materials beyond the QL.

The main objective of this paper is to address the instability and dynamical bifurcation of the Dean problem. A nonlinear theory is obtained for the Dean problem, leading in particular to rigorous justifications of the linear theory used by physicists, and the vortex structure. The main technical tools are the dynamic bifurcation theory [15] developed recently by Ma and Wang., Comment: 16 pages,1figure

Recently, we presented a paper about the tip-induced superconducting phase on TaAs single crystal (arXiv:1607.00513). A conductance plateau with double conductance peaks at finite bias, sharp double dips and a zero bias conductance peak were observed in the point contact spectra (PCS). These three features in one PCS suggest the possibility of p-wave like superconductivity and Majorana zero modes in the surface. Soon after our paper posted on arXiv, Gayen el al. (arXiv:1607.01405) questioned the underlying mechanism of our observations based on their experimental measurements in conventional superconductors(Pb and Nb) and conclusively indicated that the superconductivity observed in our TaAs crystal is conventional. We disagree with their quick conclusion without any specific study on the TaAs materials. We will explain in the following that for the clean (Z=0) point contact (PC) in ballistic limit, the superconducting transition feature in temperature dependence of PC resistance is expected. And the critical current effect claimed by Gayen el al. cannot explain the observed PCS in our paper.

Weyl fermion is a massless Dirac fermion with definite chirality, which has been long pursued since 1929. Though it has not been observed as a fundamental particle in nature, Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum space, which are topologically protected against small perturbations. Here, we report for the first time the tip induced superconductivity on TaAs crystal by point contact spectroscopy. A conductance plateau and sharp double dips are observed in the point contact spectra, indicating p-wave like unconventional superconductivity. Furthermore, the zero bias conductance peak in low temperature regime is detected, suggesting potentially the existence of Majorana zero modes. The experimentally observed tunneling spectra can be interpreted with a novel mirror-symmetry protected topological superconductor induced in TaAs, which can exhibit zero bias and double finite bias peaks, and double conductance dips in the measurements. Our work can open a broad avenue in search for new topological superconducting phases from topological Weyl materials and trigger intensive investigations for pursuing Majorana fermions.

HfTe5 is predicted to be a promising platform for studying topological phases. Here through an electrical transport study, we present the first observation of chiral anomaly and ultrahigh mobility in HfTe5 crystals. Negative magneto-resistivity in HfTe5 is observed when the external magnetic and electrical fields are parallel (B//E) and quickly disappears once B deviates from the direction of E. Quantitative fitting further confirms the chiral anomaly as the underlying physics. Moreover, by analyzing the conductivity tensors of longitudinal and Hall traces, ultrahigh mobility and ultralow carrier density are revealed in HfTe5, which paves the way for potential electronic applications.