Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena

Crystal Structure Design and Synthesis of Noncentrosymmetric Superconductors in Intercalation-Induced Transition Metal Dichalcogenides

In this paper, we have performed a crystal structure screening and properties prediction framework within the noncentrosymmetric AMX2 system, which arises from the intercalation of elements in transition metal dichalcogenides. After rigorous evaluations of thermodynamic and dynamic stability, we have refined our initial structure pool of 504 crystals to a focused set of 48 promising candidates. Analysis of their electronic properties has revealed that 23 of these crystals exhibit semiconducting behavior. The results on electron-phonon coupling and band calculations indicate that most of the remaining 25 crystals are superconducting topological nodal line or Weyl semimetals. Additionally, we find that β-InNbSe2 in the AMX2 family can serve as an excellent candidate to explore topological nodal lines and Lifshitz transitions. Furthermore, we also extended the thermodynamic stability analysis to higher temperatures. Ultimately, we have successfully synthesized β-InNbSe2 with a stoichiometric ratio of 1:1:2 experimentally and characterized its superconducting properties. This study represents a systematic foray into the identification of new superconducting and topological materials within the noncentrosymmetric AMX2 family. This screening framework can be extended to other quasi two-dimensional systems.

Weak antilocalization in the topological semimetal candidate YbAuSb

We report a study of the magnetic and magnetotransport properties of YbAuSb single crystals, which were grown using the bismuth flux. The x-ray diffraction data indicate that YbAuSb crystallizes in LiGaGe-type hexagonal structure with space groupP63mc. Our magnetic measurements revealed that YbAuSb is nonmagnetic with a divalent state of ytterbium ion. The temperature-dependent electrical resistivity exhibits a metallic behavior. A cusp-like feature in transverse and longitudinal magnetoresistance is observed at the low field regime. This cusp-like feature is attributed to the weak antilocalization (WAL) effect, which is more prominent at low temperatures. The transverse magnetoconductivity in low field region follows semiclassical model∼B, which is consistent with the presence of WAL phenomena. The WAL effect in transverse and longitudinal magnetoconductance is well explained using the modified Hikami-Larkin-Nagaoka and generalized Altshuler-Aronov model, respectively. The Hall resistivity shows a linear field dependence with a positive slope, suggesting hole charge carriers dominate in electrical transport. The calculated carrier density and mobility are in the order of 1020 cm-3and 102 cm2 V-1 s-1, respectively.

Phase transitions associated with magnetic-field induced topological orbital momenta in a non-collinear antiferromagnet

Resistivity measurements are widely exploited to uncover electronic excitations and phase transitions in metallic solids. While single crystals are preferably studied to explore crystalline anisotropies, these usually cancel out in polycrystalline materials. Here we show that in polycrystalline Mn3Zn0.5Ge0.5N with non-collinear antiferromagnetic order, changes in the diagonal and, rather unexpected, off-diagonal components of the resistivity tensor occur at low temperatures indicating subtle transitions between magnetic phases of different symmetry. This is supported by neutron scattering and explained within a phenomenological model which suggests that the phase transitions in magnetic field are associated with field induced topological orbital momenta. The fact that we observe transitions between spin phases in a polycrystal, where effects of crystalline anisotropy are cancelled suggests that they are only controlled by exchange interactions. The observation of an off-diagonal resistivity extends the possibilities for realising antiferromagnetic spintronics with polycrystalline materials.

Robust negative longitudinal magnetoresistance and spin-orbit torque in sputtered Pt3Sn and Pt3SnxFe1-x topological semimetal

Contrary to topological insulators, topological semimetals possess a nontrivial chiral anomaly that leads to negative magnetoresistance and are hosts to both conductive bulk states and topological surface states with intriguing transport properties for spintronics. Here, we fabricate highly-ordered metallic Pt₃Sn and Pt₃Sn_xFe_1-x thin films via sputtering technology. Systematic angular dependence (both in-plane and out-of-plane) study of magnetoresistance presents surprisingly robust quadratic and linear negative longitudinal magnetoresistance features for Pt₃Sn and Pt₃Sn_xFe_1-x, respectively. We attribute the anomalous negative longitudinal magnetoresistance to the type-II Dirac semimetal phase (pristine Pt₃Sn) and/or the formation of tunable Weyl semimetal phases through symmetry breaking processes, such as magnetic-atom doping, as confirmed by first-principles calculations. Furthermore, Pt₃Sn and Pt₃Sn_xFe_1-x show the promising performance for facilitating the development of advanced spin-orbit torque devices. These results extend our understanding of chiral anomaly of topological semimetals and can pave the way for exploring novel topological materials for spintronic devices.

Gapless superconductivity in Nb thin films probed by terahertz spectroscopy

Time reversal symmetry (TRS) breaking often generates exotic quantum phases in condensed matter. In superconductors, TRS breaking by an external magnetic field not only suppresses superconductivity but also leads to a novel quantum state called the gapless superconducting state. Here we show that magneto-terahertz spectroscopy provides us with a rare opportunity to access and explore the gapless superconducting state of Nb thin films. We present the complete functional form of the superconducting order parameter for an arbitrary magnetic field, for which a fully self-consistent theory is, surprisingly, yet unavailable. We observe a Lifshitz topological phase transition with a vanishing quasiparticle gap everywhere on the Fermi surface, whereas the superconducting order parameter smoothly crosses over from the gapped to the gapless regime. Our observation of the magnetic pair-breaking effects in Nb challenges traditional perturbative theories and opens a pathway to further exploring and manipulating the exotic state of gapless superconductivity.

Positive longitudinal magnetoconductivity induced by chiral magnetic effect in mercury selenide

A negative longitudinal magnetoresistance without any sign of saturation was found in a non-centrosymmetric Weyl semimetal (WSM) candidate mercury selenide in an electron concentration range of 5.5 × 10¹⁵-1.7 × 10¹⁷cm^-3and a temperature range of 0.33-150 K. The magnitude of the effect varies with a sample from≈10% up to≈30% in a magnetic field of 12 T atT= 150 K. Moreover, the positive contribution to magnetoconductivity has a characteristic quadratic dependence on the magnetic field, increasing with a charged center concentration atT= 150 K. The most likely explanation for the discovered longitudinal magnetoconductivity feature lies in the chiral magnetic effect, which is inherent to WSMs. The role of the Dyakonov-Perel mechanism in inter-nodal spin relaxation is discussed in regard to HgSe.

Skin effect as a probe of transport regimes in Weyl semimetals

SignificanceWeyl semimetals are a class of three-dimensional materials, whose low-energy excitations mimic massless fermions. In consequence they exhibit various unusual transport properties related to the presence of chiral anomalies, a subtle quantum phenomenon that denotes the breaking of the classical chiral symmetry by quantum fluctuations. In this work we present a universal description of transport in weakly disordered Weyl semimetals with several scattering mechanisms taken into account. Our work predicts the existence of a new anomaly-induced transport regime in these materials and gives a crisp experimental signature of a chiral anomaly in optical conductivity measurements. Finally, by also capturing the hydrodynamic regime of quasiparticles, our construction bridges the gap between developments in electronic fluid mechanics and three-dimensional semimetals.

Two-Dimensional Weak Antilocalization Signatures Due to Quantum Coherent Transport in Nanocrystalline SnTe

Nanostructured topological crystalline insulators (TCIs) in the presence of exotic surface states with spin momentum locking reported in individual nanostructures are predicted to hold a great promise for spintronics and quantum computing applications. However, practical application demands a strategy with large-scale production and integration for device applications. In this work, we demonstrate through prominent signatures of weak antilocalization (WAL), arising predominantly from destructive quantum interference on robust surface states, that a correlated TCI phase is possible in the nanobulk assembly of carefully nanostructured quasi-two-dimensional SnTe (edge-to-edge length ∼ 382 nm) synthesized by a simple, rapid, and scalable microwave-assisted solvothermal method. Hikami-Larkin-Nagaoka analysis (T^-0.71), as well as the temperature dependence of resistivity, illustrates an interplay of both conductions from 2D channels and 3D EEI effects as the precursor for the observed WAL at low temperatures (2-6 K). Interestingly, the enhanced thermoelectric power of the sample of ∼45 μV/K, with a p-type carrier concentration of ∼10¹⁸/cm³ at 300 K, makes this SnTe nanocrystalline assembly more attractive as a multifunctional material for large-scale technological applications.

Weak antilocalization, spin–orbit interaction, and phase coherence length of a Dirac semimetal Bi0.97Sb0.03

The present study develops a general framework for weak antilocalization (WAL) in a three-dimensional (3D) system, which can be applied for a consistent description of longitudinal resistivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xx} \left( B \right)$$\end{document}ρxxB and Hall resistivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xy} \left( B \right)$$\end{document}ρxyB over a wide temperature (T) range. Compared to the previous approach Vu et al. (Phys Rev B 100:125162, 2019), which assumes infinite phase coherence length (l_ϕ) and a zero spin–orbit scattering length (l_SO), the present framework is more general, covering high T and the intermediate spin–orbit coupling strength. Based on the new approach, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xx} \left( B \right)$$\end{document}ρxxB and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xy} \left( B \right)$$\end{document}ρxyB of the Dirac semimetal Bi_0.97Sb_0.03 was analyzed over a wide T range from 1.7 to 300 K. The present framework not only explains the main features of the experimental data but also enables one to estimate l_ϕ and l_SO at different temperatures. The l_ϕ has a power-law T dependence at high T and saturates at low T. In contrast, the l_SO shows negligible T dependence. Because of the different T dependence, a crossover occurs from the l_SO-dominant low-T to the l_ϕ-dominant high-T regions. Accordingly, the hallmark features of weak antilocalization (WAL) in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xx} \left( B \right)$$\end{document}ρxxB and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{xy} \left( B \right)$$\end{document}ρxyB are gradually suppressed across the crossover with increasing T. The present theory describes both low-T and high-T regions successfully, which is impossible in the previous approximate approach. This work offers insights for understanding quantum electrical transport phenomena and their underlying physics, particularly when multiple WAL length scales are competing.

Berry curvature induced anisotropic magnetotransport in a quadratic triple-component fermionic system

Triple-component fermions (TCFs) are pseudospin-1 quasiparticles hosted by certain three-band semimetals in the vicinity of their band-touching nodes (2019Phys. Rev.B100235201). The excitations comprise of a flat band and two dispersive bands. The energies of the dispersive bands areE±=±αn2k⊥2n+vz2kz2withk⊥=kx2+ky2andn= 1, 2, 3. In this work, we obtain the exact expression of Berry curvature, approximate form of density of states and Fermi energy as a function of carrier density for any value ofn. In particular, we study the Berry curvature induced electrical and thermal magnetotransport properties of quadratic (n= 2) TCFs using semiclassical Boltzmann transport formalism. Since the energy spectrum is anisotropic, we consider two orientations of magnetic field (B): (i)Bapplied in thex-yplane and (ii)Bapplied in thex-zplane. For both the orientations, the longitudinal and planar magnetoelectric/magnetothermal conductivities show the usual quadratic-Bdependence and oscillatory behavior with respect to the angle between the applied electric field/temperature gradient and magnetic field as observed in other topological semimetals. However, the out-of-plane magnetoconductivity has an oscillatory dependence on angle between the applied fields for the second orientation but is angle-independent for the first one. We observe large differences in the magnitudes of transport coefficients for the two orientations at a given Fermi energy. A noteworthy feature of quadratic TCFs which is typically absent in conventional systems is that certain transport coefficients and their ratios are independent of Fermi energy within the low-energy model.

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-Bdependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin-orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

Emergence of topological superconductivity in doped topological Dirac semimetals under symmetry-lowering lattice distortions

Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials.

Anomalous negative longitudinal magnetoresistance and violation of Ohm's law deep in the topological insulating regime in Bi[Formula: see text]Sb[Formula: see text]

Bi[Formula: see text]Sb[Formula: see text] is a topological insulator (TI) for [Formula: see text]-0.20. Close to the Topological phase transition at [Formula: see text], a magnetic field induced Weyl semi-metal (WSM) state is stabilized due to the splitting of the Dirac cone into two Weyl cones of opposite chirality. A signature of the Weyl state is the observation of a Chiral anomaly [negative longitudinal magnetoresistance (LMR)] and a violation of the Ohm's law (non-linear [Formula: see text]). We report the unexpected discovery of Chiral anomaly-like features in the whole range ([Formula: see text]) of the TI state. This points to a field induced WSM state in an extended x range and not just near the topological transition at [Formula: see text]. Surprisingly, the strongest Weyl phase is found at [Formula: see text] with a non-saturating negative LMR much larger than observed for [Formula: see text]. The negative LMR vanishes rapidly with increasing angle between B and I. Additionally, non-linear I-V is found for [Formula: see text] indicating a violation of Ohm's law. This unexpected observation of a strong Weyl state in the whole TI regime in Bi[Formula: see text]Sb[Formula: see text] points to a gap in our understanding of the detailed crystal and electronic structure evolution in this alloy system.

Chiral Anomaly Induced Negative Magnetoresistance and Weak Anti-Localization in Weyl Semimetal Bi0.097Sb0.03 alloy

Experimental access to massless Weyl fermions through topological materials promises substantial technological ramifications. Here, we report magneto-transport properties of Bi1- xSbx alloy near the quantum critical point x = 3% and 3.5%. The two compositions that are synthesized and studied are single crystals of Bi0.97Sb0.03 and Bi0.965Sb0.035. We observe a transition from semimetal to semiconductor with the application of magnetic field in both specimen. An extremely large transverse magnetoresistance (MR) 1.8×105 % and 8.2×104 % at 2.5K and 6T is observed in Bi0.97Sb0.03 and Bi0.965Sb0.035, respectively. Kohler scaling of transverse MR reveals the crossover of low field quadratic MR to a high field linear MR at low temperatures in both samples. A decrease in longitudinal MR (LMR) is observed only in Bi0.97Sb0.03 that implies the presence of chiral anomaly associated with the Weyl state at the crossover point (x=0.03) in Bi1-xSbx system. The chiral anomaly is absent for the sample Bi0.965Sb0.035. A sharp increase in longitudinal resistivity for Bi0.97Sb0.03 close to zero magnetic fields indicates the weak anti-localization effect in Bi0.97Sb0.03. Extremely high carrier concentrations and high mobilities have been recorded for both the samples.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Index Theorem on Chiral Landau Bands for Topological Fermions

Topological fermions as excitations from multidegenerate Fermi points have been attracting increasing interest in condensed matter physics. They are characterized by topological charges, and magnetic fields are usually applied in experiments for their detection. Here we present an index theorem that reveals the intrinsic connection between the topological charge of a Fermi point and the in-gap modes in the Landau band structure. The proof is based on mapping fermions under magnetic fields to a topological insulator whose topological number is exactly the topological charge of the Fermi point. Our Letter lays a solid foundation for the study of intriguing magnetoresponse effects of topological fermions.

Quantum transport evidence of Weyl fermions in an epitaxial ferromagnetic oxide

Magnetic Weyl semimetals have novel transport phenomena related to pairs of Weyl nodes in the band structure. Although the existence of Weyl fermions is expected in various oxides, the evidence of Weyl fermions in oxide materials remains elusive. Here we show direct quantum transport evidence of Weyl fermions in an epitaxial 4d ferromagnetic oxide SrRuO₃. We employ machine-learning-assisted molecular beam epitaxy to synthesize SrRuO₃ films whose quality is sufficiently high to probe their intrinsic transport properties. Experimental observation of the five transport signatures of Weyl fermions—the linear positive magnetoresistance, chiral-anomaly-induced negative magnetoresistance, π phase shift in a quantum oscillation, light cyclotron mass, and high quantum mobility of about 10,000 cm²V⁻¹s⁻¹—combined with first-principles electronic structure calculations establishes SrRuO₃ as a magnetic Weyl semimetal. We also clarify the disorder dependence of the transport of the Weyl fermions, which gives a clear guideline for accessing the topologically nontrivial transport phenomena.

Despite various predictions, the evidence of Weyl fermions in oxide materials remains elusive. Here, the authors show evidence of Weyl fermions in quantum transport measurements in an epitaxial ferromagnetic oxide SrRuO₃.

Topological electronic state and anisotropic Fermi surface in half-Heusler GdPtBi

Half-Heusler alloys possess unique and desirable physical properties due to their thermoelectricity, magnetism, superconductivity, and weak antilocalization effects. These properties have become of particular interest since the recent discovery of topological Weyl semimetal state for which the electronic bands are dispersed linearly around one pair of Weyl nodes, with opposite chirality (i.e., chiral anomaly). Here, we report the transport signatures of topological electronic state in a half-Heusler GdPtBi single crystal. We show that the non-trivial π Berry phase, negative magnetoresistance and giant planner Hall effect arise from the chiral anomaly and that the Shubnikov-de Haas oscillation frequency in GdPtBi is angle-dependent with an anisotropic Fermi surface (FS). All transport signatures not only demonstrate the topological electronic state in half-Heusler GdPtBi crystals, but also describe the shape of the anisotropy FS.

Magnetotransport properties of noncentrosymmetric CaAgBi single crystal

We report on the single crystal growth and transport properties of a topological semimetal CaAgBi which crystallizes in the hexagonal ABC-type structure with the non-centrosymmetric space groupP63mc(No. 186). The transverse magnetoresistance measurements with current in the basal plane of the hexagonal crystal structure reveal a value of about 30% forI∥[10̄0] direction and about 50% forI∥[1̅10] direction at 10 K in an applied magnetic field of 14 T. The magnetoresistance shows a cusp-like behavior in the low magnetic field region, suggesting the presence of weak antilocalization effect for temperatures less than 100 K. The Hall measurements reveal that predominant charge carriers are p-type, exhibiting a linear behavior at high fields. The magnetoconductance of CaAgBi is analyzed based on the modified Hikami-Larkin-Nagaoka model. Our first-principle calculations within a density-functional theory framework reveal that the Fermi surface of CaAgBi consists of both the electron and hole pockets and the size of the hole pocket is much larger than electron pockets suggesting the dominant p-type carriers in accordance with our experimental results.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a double degeneracy of the electronic bands (Kramers degeneracy). By lifting the degeneracy, spin textures manifest themselves in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is difficult to observe directly. Here, we use quantum interference measurements to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL is fitted using a single interference channel at low doping, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement.

Pseudo chiral anomaly in zigzag graphene ribbons

As the three-dimensional analogs of graphene, Weyl semimetals display signatures of chiral anomaly which arises from charge pumping between the lowest chiral Landau levels of the Weyl nodes in the presence of parallel electric and magnetic fields. In this work, we study the pseudo chiral anomaly and its transport signatures in graphene ribbon with zigzag edges. Here 'pseudo' refers to the case where the inverse of width of zigzag graphene ribbon plays the same role as magnetic field in three-dimensional Weyl semimetals. The valley chiral bands in zigzag graphene ribbons can be introduced by edge potentials, giving rise to the nonconservation of chiral current, i.e. pseudo chiral anomaly, in the presence of a longitudinal electric field. Further numerical results reveal that pseudo magnetoconductivity of zigzag graphene ribbons is positive and has a nearly quadratic dependence on the pseudofield, which is regarded as the transport signature of pseudo chiral anomaly.

Planar Hall effect induced by anisotropic orbital magnetoresistance in type-II Dirac semimetal PdTe2

We measure planar Hall effect (PHE) and longitudinal anisotropic magnetoresistance (AMR) with a magnetic field rotating in the a-b plane in the type-II Dirac semimetal PdTe₂. The measured PHE and AMR curves can be fitted by the theoretical equations; however, a detailed analysis of the extracted data demonstrates that the parameter related to PHE and AMR has no relationship with the chiral anomaly due to the absence of negative longitudinal magnetoresistance (MR) when the electric and magnetic fields are parallel to each other. Meanwhile, we prove that the origin of PHE in PdTe₂ is the anisotropic orbital MR. Our work suggests that negative longitudinal MR is necessary to identify chiral anomaly, and we cannot in general use PHE as a signal for the presence of the chiral anomaly in Dirac/Weyl semimetals.

Breaking Lattice Symmetry in Highly Strained Epitaxial VO2 Films on Faceted Nanosurface

The lattice symmetry of strongly correlated oxide heterostructures determines their exotic physical properties by coupling the degrees of freedom between lattices and electrons, orbitals, and spin states. Systematic studies on VO₂, a Mott insulator, have previously revealed that lattice distortion can be manipulated by the interfacial strain and electronic phase separation can emerge. However, typical epitaxial film-substrate interface strain provides a very limited range for exploring such interface-engineered phenomena. Herein, epitaxially grown VO₂ thin films on asymmetrically faceted m-plane sapphire substrates with the hill-and-valley type surfaces have been demonstrated. Interestingly, lattice symmetry breaking has been proven based on the large residual strain from the different faceted planes. By this lattice symmetry breaking, electronic phase separation and metal-insulator transition in the VO₂ films are modulated, and anisotropy in optical responses is exhibited. These results on asymmetrical interfacial engineering in oxide heterostructures open up new routes for novel functional materials design and functional electro/optic device nanofabrication.

Observation of quantum topological Hall effect in the Weyl semimetal candidate HgSe

The magnetoresistance (MR) and Hall effect of a single HgSe crystal with an extremely low electron concentration of 8.8  ×  10¹⁵ cm^-3 were studied in a quantising magnetic field applied both along and across the direction of the electric current. As the result, a broad plateau was discovered in the ordinary (transverse) Hall resistance in the quantum limit. Within a framework of quantum spin Hall effect for an inversion breaking Weyl semimetal, we associate this plateau with a contribution to Hall conductivity from Chern insulator edge states when only a zero Landau level is occupied. In addition to the plateau in the quantum limit, we also detected a well-developed plateau-like behaviour in a phenomenologically-introduced 'longitudinal' Hall resistivity. In the 'longitudinal' Hall conductivity, a step-like behaviour was revealed, which we identify with the discovery of half-integer quantum spin Hall effect in HgSe. This effect, being purely topological in origin, supplements the non-trivial Weyl semimetal physics and may serve as a promising magnetotransport method for the detection of Weyl nodes in a studied material.

Band Topology of Bismuth Quantum Films

Bismuth has been the key element in the discovery and development of topological insulator materials. Previous theoretical studies indicated that Bi is topologically trivial and it can transform into the topological phase by alloying with Sb. However, recent high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements strongly suggested a topological band structure in pure Bi, conflicting with the theoretical results. To address this issue, we studied the band structure of Bi and Sb films by ARPES and first-principles calculations. The quantum confinement effectively enlarges the energy gap in the band structure of Bi films and enables a direct visualization of the Z 2 topological invariant of Bi. We find that Bi quantum films in topologically trivial and nontrivial phases respond differently to surface perturbations. This way, we establish experimental criteria for detecting the band topology of Bi by spectroscopic methods.

Quantum Interference Theory of Magnetoresistance in Dirac Materials

Magnetoresistance in many samples of Dirac semimetals and topological insulators displays nonmonotonic behavior over a wide range of magnetic fields. Here a formula of magnetoconductivity is presented for massless and massive Dirac fermions in Dirac materials due to quantum interference of Dirac fermions in scalar impurity scattering potentials. It reveals a striking crossover from positive to negative magnetoresistivity, uncovering strong competition between weak localization and weak antilocalization in multiple Cooperon channels at different chemical potentials, effective masses, and finite temperatures. This work sheds light on the important role of strong coupling of the conduction and valence bands in the quantum interference transport in topological nontrivial and trivial Dirac materials.

Spin-dependent scattering induced negative magnetoresistance in topological insulator Bi2Te3 nanowires

Studies of negative magnetoresistance in novel materials have recently been in the forefront of spintronic research. Here, we report an experimental observation of the temperature dependent negative magnetoresistance in Bi₂Te₃ topological insulator (TI) nanowires at ultralow temperatures (20 mK). We find a crossover from negative to positive magnetoresistance while increasing temperature under longitudinal magnetic field. We observe a large negative magnetoresistance which reaches −22% at 8 T. The interplay between negative and positive magnetoresistance can be understood in terms of the competition between dephasing and spin-orbit scattering time scales. Based on the first-principles calculations within a density functional theory framework, we demonstrate that disorder (substitutional) by Ga⁺ ion milling process, which is used to fabricate nanowires, induces local magnetic moments in Bi₂Te₃ crystal that can lead to spin-dependent scattering of surface and bulk electrons. These experimental findings show a significant advance in the nanoscale spintronics applications based on longitudinal magnetoresistance in TIs. Our experimental results of large negative longitudinal magnetoresistance in 3D TIs further indicate that axial anomaly is a universal phenomenon in generic 3D metals.

Non-saturating quantum magnetization in Weyl semimetal TaAs

Detecting the spectroscopic signatures of relativistic quasiparticles in emergent topological materials is crucial for searching their potential applications. Magnetometry is a powerful tool for fathoming electrons in solids, by which a clear method for discerning relativistic quasiparticles has not yet been established. Adopting the probes of magnetic torque and parallel magnetization for the archetype Weyl semimetal TaAs in strong magnetic field, we observed a quasi-linear field dependent effective transverse magnetization and a non-saturating parallel magnetization when the system enters the quantum limit. Distinct from the saturating magnetic responses for non-relativistic quasiparticles, the non-saturating signals of TaAs in strong field is consistent with our newly developed magnetization calculation for a Weyl fermion system in an arbitrary angle. Our results establish a high-field thermodynamic method for detecting the magnetic response of relativistic quasiparticles in topological materials.

Quantum Oscillations of the Positive Longitudinal Magnetoconductivity: A Fingerprint for Identifying Weyl Semimetals

Weyl semimetals (WSMs) host charged Weyl fermions as emergent quasiparticles. We develop a unified analytical theory for the anomalous positive longitudinal magnetoconductivity (LMC) in a WSM, which bridges the gap between the classical and ultraquantum approaches. More interestingly, the LMC is found to exhibit periodic-in-1/B quantum oscillations, originating from the oscillations of the nonequilibrium chiral chemical potential. The quantum oscillations, superposed on the positive LMC, are a remarkable fingerprint of a WSM phase with a chiral anomaly, whose observation is a valid criteria for identifying a WSM material. In fact, such quantum oscillations were already observed by several experiments.

Observation of an Odd-Integer Quantum Hall Effect from Topological Surface States in Cd_{3}As_{2}

The quantum Hall effect (QHE) in a 3D Dirac semimetal thin film is attributed to either the quantum confinement induced bulk subbands or the Weyl orbits that connect the opposite surfaces via bulk Weyl nodes. However, it is still unknown whether the QHE based on the Weyl orbit can survive as the bulk Weyl nodes are gapped. Moreover, there are closed Fermi loops rather than open Fermi arcs on the Dirac semimetal surface, which can also host the QHE. Here we report the QHE in the 3D Dirac semimetal Cd_{3}As_{2} nanoplate by tuning the gate voltage under a fixed 30 T magnetic field. The quantized Hall plateaus at odd filling factors are observed as a magnetic field along the [001] crystal direction, indicating a Berry's phase π from the topological surface states. Furthermore, even filling factors are observed when the magnetic field is along the [112] direction, indicating the C_{4} rotational symmetry breaking and a topological phase transition. The results shed light on the understanding of QHE in 3D Cd_{3}As_{2}.

Negative longitudinal magnetoresistance in gallium arsenide quantum wells

Negative longitudinal magnetoresistances (NLMRs) have been recently observed in a variety of topological materials and often considered to be associated with Weyl fermions that have a defined chirality. Here we report NLMRs in non-Weyl GaAs quantum wells. In the absence of a magnetic field the quantum wells show a transition from semiconducting-like to metallic behaviour with decreasing temperature. We observe pronounced NLMRs up to 9 Tesla at temperatures above the transition and weak NLMRs in low magnetic fields at temperatures close to the transition and below 5 K. The observed NLMRs show various types of magnetic field behaviour resembling those reported in topological materials. We attribute them to microscopic disorder and use a phenomenological three-resistor model to account for their various features. Our results showcase a contribution of microscopic disorder in the occurrence of unusual phenomena. They may stimulate further work on tuning electronic properties via disorder/defect nano-engineering.

The attribution of negative longitudinal magnetoresistance (NLMR) in Weyl metals to a chiral anomaly is already challenged. Here, NLMR resembling that of Weyl metals is demonstrated in a non-Weyl-metal GaAs quantum well originating from different types of disorder.

Simulation and Manipulation of Tunable Weyl-Semimetal Bands Using Superconducting Quantum Circuits

We simulated highly tunable Weyl-semimetal bands using superconducting quantum circuits. Driving the superconducting quantum circuits with microwave fields, we mapped the momentum space of a lattice to the parameter space, realizing the Hamiltonian of a Weyl semimetal. By measuring the energy spectrum, we directly imaged the Weyl points, whose topological winding numbers were further determined from the Berry curvature measurement. In addition, we manipulated the band structure with an additional pump microwave field, producing a momentum-dependent Weyl-point energy together with an artificial magnetic field, which are indispensable for generating chiral magnetic topological currents in some special Weyl semimetals and may have significant impact on topological physics.

NMR diagnosis of pseudo-scalar superconductivity in 3D Dirac materials

Recently observed 4π periodic Andreev bound states in 3D Dirac materials are attributed to conventional superconducting pairing. Our alternative explanation in terms of a novel form of parity breaking pseudo-scalar superconducting order can be sharply diagnosed by nuclear magnetic resonance relaxation rate. The left-right symmetry breaking of the pseudo-scalar superconductivity can be directly probed as an anti-peak structure below T _C in sharp contrast to the conventional Hebel-Slichter peak.

Theory for the negative longitudinal magnetoresistance in the quantum limit of Kramers Weyl semimetals

Negative magnetoresistance is rare in non-magnetic materials. Recently, negative magnetoresistance has been observed in the quantum limit of β-Ag₂Se, where only one band of Landau levels is occupied in a strong magnetic field parallel to the applied current. β-Ag₂Se is a material that hosts a Kramers Weyl cone with band degeneracy near the Fermi energy. Kramers Weyl cones exist at time-reversal invariant momenta in all symmorphic chiral crystals, and at a subset of these momenta, including the Γ point, in non-symmorphic chiral crystals. Here, we present a theory for the negative magnetoresistance in the quantum limit of Kramers Weyl semimetals. We show that, although there is a band touching similar to those in Weyl semimetals, negative magnetoresistance can exist without a chiral anomaly. We find that it requires screened Coulomb scattering potentials between electrons and impurities, which is naturally the case in β-Ag₂Se.

Proximity-Induced Superconductivity with Subgap Anomaly in Type II Weyl Semi-Metal WTe2

Due to the nontrivial topological band structure in type II Weyl semi-metal tungsten ditelluride (WTe₂), unconventional properties may emerge in its superconducting phase. While realizing intrinsic superconductivity has been challenging in the type II Weyl semi-metal WTe₂, the proximity effect may open an avenue for the realization of superconductivity. Here, we report the observation of proximity-induced superconductivity with a long coherence length along the c axis in WTe₂ thin flakes based on a WTe₂/NbSe₂ van der Waals heterostructure. Interestingly, we also observe anomalous oscillations of the differential resistance during the transition from the superconducting to the normal state. Theoretical calculations show excellent agreement with experimental results, revealing that such a subgap anomaly is the intrinsic property of WTe₂ in superconducting state induced by the proximity effect. Our findings enrich the understanding of the superconducting phase of type II Weyl semi-metals and pave the way for their future applications in topological quantum computing.

Three-Dimensional Chiral Lattice Fermion in Floquet Systems

We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of the low-energy subspace is decoupled from the high-energy subspace, we show that the bulk dynamics in the low-energy subspace can be described by Floquet bands with extra left- or right-handed Weyl points, despite the no-go theorem. Assuming adiabatic evolution of two bands, we show that the difference of the number of right-handed and left-handed Weyl points equals twice the winding number of the adiabatic Floquet operator over the Brillouin zone. Based on these findings, we propose a realization of purely left- or right-handed Weyl particles on a 3D lattice using a Hamiltonian obtained through dimensional reduction of a four-dimensional quantum Hall system. We argue that the breakdown of the adiabatic approximation on the surface facilitates unusual closed orbits of wave packets in an applied magnetic field, which traverse alternatively through the low-energy and high-energy sector of the spectrum.

Pressure-induced phase transitions and superconductivity in a black phosphorus single crystal

We report a thorough study of the transport properties of the normal and superconducting states of black phosphorus (BP) under magnetic field and high pressure with a large-volume apparatus that provides hydrostatic pressure to induce transitions from the layered A17 phase to the layered A7 phase and to the cubic phase of BP. Quantum oscillations can be observed at P ≥ 1 GPa in both resistivity and Hall voltage, and their evolutions with pressure in the A17 phase imply a continuous enlargement of Fermi surface. A significantly large magnetoresistance (MR) at low temperatures is observed in the A7 phase that becomes superconducting below a superconducting transition temperature Tc ∼ 6-13 K. Tc increases continuously with pressure on crossing the A7 to the cubic phase boundary. The strong MR effect can be fit by a modified Kohler's rule. A correlation between Tc and fitting parameters suggests that phonon-mediated interactions play dominant roles in driving the Cooper pairing, which is further supported by our density functional theory (DFT) calculations. The change of effective carrier mobility in the A17 phase under pressure derived from the MR effect is consistent with that obtained from the temperature dependence of the quantum oscillations. In situ single-crystal diffraction under high pressure indicates a total structural reconstruction instead of simple stretching of the A17 phase layers in the A17-to-A7-phase transition. This finding helps us to interpret transport properties on crossing the phase transition under high pressure.

4π-periodic Andreev bound states in a Dirac semimetal

Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi_1-xSb_x. Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb-Bi_0.97Sb_0.03-Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone's very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd)

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (μSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

Fano Interference between Bulk and Surface States of a Dirac Semimetal Cd_{3}As_{2} Nanowire

Dirac semimetals possess Fermi-arc surface states, which will be a set of discrete surface subbands in a nanowire due to the quantum confinement effect. Here, we report a tunable Fano effect induced by the interference between the discrete surface states and continuous bulk states of a Dirac semimetal Cd_{3}As_{2} nanowire. The discrete surface bands lead to a zero bias peak in conductance as the Femi level is tuned to across the surface subbands. The Fano resonance results in an asymmetric line shape in the differential conductance dI/dV spectrum. Furthermore, the Fano interference would introduce an additional phase into the Weyl orbits and lead to a modification of the oscillation frequency. The results are valuable for further understanding the exotic quantum transport properties of topological semimetals.

Generation of a Nernst Current from the Conformal Anomaly in Dirac and Weyl Semimetals

We show that a conformal anomaly in Weyl and Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material. We discuss the experimental feasibility of the proposed phenomenon.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Anomalous DC Hall response in noncentrosymmetric tilted Weyl semimetals

Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by [Formula: see text] and the anomalous DC Hall conductivity [Formula: see text] is proportional to [Formula: see text] at charge neutrality. For finite doping there are additive corrections to [Formula: see text] which depend on the chemical potential as well as on the tilt ([Formula: see text]) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount [Formula: see text]. This introduces further changes in [Formula: see text] and we provide simple analytic formulas for these modifications for both type I ([Formula: see text]) and type II ([Formula: see text], overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to [Formula: see text] is proportional to the chemical potential μ and completely independent of the energy shift [Formula: see text]. When instead the tilts are parallel, the correction is linear in [Formula: see text] and μ drops out. For type II the corrections involve both μ and [Formula: see text], are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite [Formula: see text].

Evidence for topological type-II Weyl semimetal WTe2

Recently, a type-II Weyl fermion was theoretically predicted to appear at the contact of electron and hole Fermi surface pockets. A distinguishing feature of the surfaces of type-II Weyl semimetals is the existence of topological surface states, so-called Fermi arcs. Although WTe₂ was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe₂ is a type-II Weyl semimetal by observing two unique transport properties simultaneously in one WTe₂ nanoribbon. The negative magnetoresistance induced by a chiral anomaly is quite anisotropic in WTe₂ nanoribbons, which is present in b-axis ribbon, but is absent in a-axis ribbon. An extra-quantum oscillation, arising from a Weyl orbit formed by the Fermi arc and bulk Landau levels, displays a two dimensional feature and decays as the thickness increases in WTe₂ nanoribbon.

Exotic transport properties of type-II Weyl semimetals have been predicted but are yet to be experimentally evidenced. Here, Li et al. report evidences of an anisotropy of negative magnetoresistance and a quantum oscillation arising from the predicted Weyl orbit in the type-II Weyl semimetal WTe₂.

Violation of Ohm's law in a Weyl metal

Ohm's law is a fundamental paradigm in the electrical transport of metals. Any transport signatures violating Ohm's law would give an indisputable fingerprint for a novel metallic state. Here, we uncover the breakdown of Ohm's law owing to a topological structure of the chiral anomaly in the Weyl metal phase. We observe nonlinear I-V characteristics in Bi_0.96Sb_0.04 single crystals in the diffusive limit, which occurs only for a magnetic-field-aligned electric field (E∥B). The Boltzmann transport theory with the charge pumping effect reveals the topological-in-origin nonlinear conductivity, and it leads to a universal scaling function of the longitudinal magnetoconductivity, which completely describes our experimental results. As a hallmark of Weyl metals, the nonlinear conductivity provides a venue for nonlinear electronics, optical applications, and the development of a topological Fermi-liquid theory beyond the Landau Fermi-liquid theory.

Negative Magnetoresistance without Chiral Anomaly in Topological Insulators

An intriguing phenomenon in topological semimetals and topological insulators is the negative magnetoresistance (MR) observed when a magnetic field is applied along the current direction. A prevailing understanding to the negative MR in topological semimetals is the chiral anomaly, which, however, is not well defined in topological insulators. We calculate the MR of a three-dimensional topological insulator, by using the semiclassical equations of motion, in which the Berry curvature explicitly induces an anomalous velocity and orbital moment. Our theoretical results are in quantitative agreement with the experiments. The negative MR is not sensitive to temperature and increases as the Fermi energy approaches the band edge. The orbital moment and g factors also play important roles in the negative MR. Our results give a reasonable explanation to the negative MR in 3D topological insulators and will be helpful in understanding the anomalous quantum transport in topological states of matter.

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

Negative longitudinal magnetoresistance (NLMR) is shown to occur in topological materials in the extreme quantum limit, when a magnetic field is applied parallel to the excitation current. We perform pulsed and dc field measurements on Pb_{1-x}Sn_{x}Se epilayers where the topological state can be chemically tuned. The NLMR is observed in the topological state, but is suppressed and becomes positive when the system becomes trivial. In a topological material, the lowest N=0 conduction Landau level disperses down in energy as a function of increasing magnetic field, while the N=0 valence Landau level disperses upwards. This anomalous behavior is shown to be responsible for the observed NLMR. Our work provides an explanation of the outstanding question of NLMR in topological insulators and establishes this effect as a possible hallmark of bulk conduction in topological matter.

Localization Effects on Magnetotransport of a Disordered Weyl Semimetal

We study longitudinal magnetotransport in a disordered Weyl semimetal taking into account localization effects in the vicinity of a Weyl node exactly. In a magnetic field, a single chiral Landau level coexists with a number of conventional nonchiral levels. Disorder scattering mixes these topologically different modes leading to very strong localization effects. We derive the average conductance as well as the full distribution function of transmission probabilities along the field direction. Remarkably, we find that localization of the nonchiral modes is greatly enhanced in a strong magnetic field with the typical localization length scaling as 1/B. Technically, we use the nonlinear sigma-model formalism with a topological term describing the chiral states. The problem is solved exactly by mapping to an equivalent transfer matrix Hamiltonian.