Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd₃As₂

Plasma-Induced 2D Electron Transport at Hetero-Phase Titanium Oxide Interface

Interfaces of metal oxide heterojunctions display a variety of intriguing physical properties that enable novel applications in spintronics, quantum information, neuromorphic computing, and high-temperature superconductivity. One such LaAlO3 /SrTiO3 (LAO/STO) heterojunction hosts a 2D electron liquid (2DEL) presenting remarkable 2D superconductivity and magnetism. However, these remarkable properties emerge only at very low temperatures, while the heterostructure fabrication is challenging even at the laboratory scale, thus impeding practical applications. Here, a novel plasma-enabled fabrication concept is presented to develop the TiO2 /Ti3 O4 hetero-phase bilayer with a 2DEL that exhibits features of a weakly localized Fermi liquid even at room temperature. The hetero-phase bilayer is fabricated by applying a rapid plasma-induced phase transition that transforms a specific portion of anatase TiO2 thin film into vacancy-prone Ti3 O4 in seconds. The underlying mechanism relies on the screening effect of the achieved high-density electron liquid that suppresses the electron-phonon interactions. The achieved "adiabatic" electron transport in the hetero-phase bilayer offers strong potential for low-loss electric or plasmonic circuits and hot electron harvesting and utilization. These findings open new horizons for fabricating diverse multifunctional metal oxide heterostructures as an innovative platform for emerging clean energy, integrated photonics, spintronics, and quantum information technologies.

High-Mobility Topological Semimetals as Novel Materials for Huge Magnetoresistance Effect and New Type of Quantum Hall Effect

The quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science over recent decades. Recently, the discovery of a novel class of materials-the topological semimetals-has led to a growing interest in the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure, and carrier mobility in recently discovered high carrier mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. Their large magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The possibility of designing novel quantum sensors and devices based on solid-state semimetals is also examined.

SdH Oscillations from the Dirac Surface State in the Fermi-Arc Antiferromagnet NdBi

The recent progress in CuMnAs and Mn3X (X = Sn, Ge, Pt) shows that antiferromagnets (AFMs) provide a promising platform for advanced spintronics device innovations. Most recently, a switchable Fermi-arc is discovered by the ARPES technique in antiferromagnet NdBi, but the knowledge about electron-transport property and the manipulability of the magnetic structure in NdBi is still vacant to date. In this study, SdH oscillations are successfully verified from the Dirac surface states (SSs) with 2-dimensionality and nonzero Berry phase. Particularly, it is observed that the spin-flop transition only appears when the external magnetical field is applied along [001] direction, and features obvious hysteresis for the first time in NdBi, which provides a powerful handle for adjusting the spin texture in NdBi. Crucially, the DFT shows the Dirac cone and the Fermi arc strongly depend on the high-order magnetic structure of NdBi and further reveals the orbital magnetic moment of Nd plays a crucial role in fostering the peculiar SSs, leading to unveil the mystery of the band-splitting effect and to manipulate the electronic transport, high-effectively, in the thin film works in NdBi. It is believed that this study provides important guidance for the development of new antiferromagnet-based spintronics devices based on cutting-edge rare-earth monopnictides.

Gate-Tunable Berry Curvature Dipole Polarizability in Dirac Semimetal Cd_{3}As_{2}

We reveal the gate-tunable Berry curvature dipole polarizability in Dirac semimetal Cd_{3}As_{2} nanoplates through measurements of the third-order nonlinear Hall effect. Under an applied electric field, the Berry curvature exhibits an asymmetric distribution, forming a field-induced Berry curvature dipole, resulting in a measurable third-order Hall voltage with a cubic relationship to the longitudinal electric field. Notably, the magnitude and polarity of this third-order nonlinear Hall effect can be effectively modulated by gate voltages. Furthermore, our scaling relation analysis demonstrates that the sign of the Berry curvature dipole polarizability changes when tuning the Fermi level across the Dirac point, in agreement with theoretical calculations. The results highlight the gate control of nonlinear quantum transport in Dirac semimetals, paving the way for promising advancements in topological electronics.

Fermi-Arc Metals

We predict a novel metallic state of matter that emerges in a Weyl-semimetal superstructure with spatially varying Weyl-node positions. In the new state, the Weyl nodes are stretched into extended, anisotropic Fermi surfaces, which can be understood as being built from Fermi arclike states. This "Fermi-arc metal" exhibits the chiral anomaly of the parental Weyl semimetal. However, unlike in the parental Weyl semimetal, in the Fermi-arc metal the "ultraquantum state," in which the anomalous chiral Landau level is the only state at the Fermi energy, is already reached for a finite energy window at zero magnetic field. The dominance of the ultraquantum state implies a universal low-field ballistic magnetoconductance and the absence of quantum oscillations, making the Fermi surface "invisible" to de Haas-van Alphen and Shubnikov-de Haas effects, although it signifies its presence in other response properties.

Dominant Two-Dimensional Electron-Phonon Interactions in the Bulk Dirac Semimetal Na3Bi

Bulk Dirac semimetals (DSMs) exhibit unconventional transport properties and phase transitions due to their peculiar low-energy band structure, yet the electronic interactions governing nonequilibrium phenomena in DSMs are not fully understood. Here we show that electron-phonon (e-ph) interactions in a prototypical bulk DSM, Na₃Bi, are predominantly two-dimensional (2D). Our first-principles calculations reveal a 2D optical phonon with strong e-ph interactions associated with in-plane vibrations of Na atoms. We show that this 2D mode governs e-ph scattering and charge transport in Na₃Bi and induces a dynamical phase transition to a Weyl semimetal. Our work advances the quantitative analysis of electron interactions in Na₃Bi and reveals a dominant low-dimensional interaction in a bulk Dirac semimetal.

Correlation-driven organic 3D topological insulator with relativistic fermions

Exploring new topological phenomena and functionalities induced by strong electron correlation has been a central issue in modern condensed-matter physics. One example is a topological insulator (TI) state and its functionality driven by the Coulomb repulsion rather than a spin-orbit coupling. Here, we report a 'correlation-driven' TI state realized in an organic zero-gap system α-(BETS)₂I₃. The topological surface state and chiral anomaly are observed in temperature and field dependences of resistance, indicating a three-dimensional TI state at low temperatures. Moreover, we observe a topological phase switching between the TI state and non-equilibrium Dirac semimetal state by a dc current, which is a unique functionality of a correlation-driven TI state. Our findings demonstrate that correlation-driven TIs are promising candidates not only for practical electronic devices but also as a field for discovering new topological phenomena and phases.

Probing electron-phonon and phonon-phonon coupling in type-II Dirac semi-metal NiTe2via temperature-dependent Raman spectroscopy

We report the temperature-dependent structural characterization of type-II Dirac semimetal NiTe₂in the form of a bulk single crystal and a nanoflake (200 nm thick). Detailed x-ray diffraction study along with Rietveld refinement analysis reveals superior crystallinity and linear thermal expansion coefficient (α_T) of 5.56 × 10^-6and 22.5 × 10^-6K^-1along a or b and c lattice directions, respectively. Temperature evolution of Raman spectra shows non-linear variations in the phonon frequency and full-width half maxima of the out-of-plane A1gand in-plane E_gmodes. Raman mode E2g1, corresponding to an in-plane vibration, disappears on decreasing the thickness from bulk to nanoflake. Quantitative analysis with anharmonic model yields dominating electron-phonon interaction over phonon-phonon interaction mediated by three- and four-phonon processes.

Photodetection and Infrared Imaging Based on Cd3As2 Epitaxial Vertical Heterostructures

Due to the nontrivial electronic structure, Cd₃As₂ is predicted to possess various transport properties and outstanding photoresponses. Photodetectors based on topological materials are mostly made up of nanoplates, yet monolithic in situ heteroepitaxial Cd₃As₂ photodetectors are rarely reported to date owing to the crystal mismatch between Cd₃As₂ and semiconductors. Here, we demonstrate Cd₃As₂/Zn_xCd_1-xTe/GaSb vertical heteroepitaxial photodetectors via molecule beam epitaxy. By constructing dual-Schottky junctions, these photodetectors show high responsivity and external quantum efficiency in a broadband spectrum. Based on the strong and fast photoresponse, we achieved visible light to near-infrared imaging using a one-pixel imaging system with a galvo. Our results illustrate that the integration of three-dimensional Dirac semimetal Cd₃As₂ with semiconductors has potential applications in broadband photodetection and infrared cameras.

Low threshold optical bistability based on topological edge state in photonic crystal heterostructure with Dirac semimetal

The special band structure of three-dimensional Dirac semimetal (3D DSM) makes it show strong nonlinear optical characteristics in the terahertz region, which provides a new way to develop terahertz nonlinear devices with low threshold. In this paper, we theoretically study the optical bistability (OB) of transmitted light in a multilayer structure with 3D DSM embedded in two one-dimensional photonic crystals (1D PhC). The topological edge state (TES) excited by the 1D PhC heterostructure significantly enhances the local electric field near the nonlinear 3D DSM, which provides a positive condition for the realization of low threshold OB. Through parameter optimization, we obtain a threshold electric field with an incident electric field of 10⁶ V/m levels. Furthermore, the influences of the Fermi energy and thickness of 3D DSM and the angle of the incident light on the hysteretic behavior as well as the threshold of OB are clarified. 3D DSM-based optical devices with intrinsic OB provide a building block for future integrated optical and all-optical networks.

Synthesis of Weyl Semi-Metal Co3Sn2S2 by Hydrothermal Method and Its Physical Properties

In the field of condensed matter physics, as new quantum materials, topological semimetals have a special topological energy band structure and nontrivial band crossings in the energy band, which will have many excellent topological properties, such as internal insulation of topological insulators and the presence of conduction electrons on the surface; this makes topological semimetals exhibit wider application prospects in electronic devices. So far, the experimental synthesis of topological semimetals was performed using physical methods to synthesize bulk single crystals, which is not conducive to the commercial application of micro and small devices. Weyl semimetal Co3Sn2S2 with shandite structure was successfully synthesized experimentally by a green and environmentally friendly hydrothermal method. Adjusting its reaction temperature, molar atomic ratio of elements and annealing temperature, and other experimental conditions, we analyze the crystal structure and physical properties of Co3Sn2S2, with the nanocrystal size being about 200 nm. We found that the Co3Sn2S2 synthesized by the hydrothermal method has a Curie temperature at 100 K to undergo ferromagnetic transition.

Prediction of topological Dirac semimetal in Ca-based Zintl layered compounds CaM2X2 (M = Zn or Cd; X = N, P, As, Sb, or Bi)

Topological Dirac materials are attracting a lot of attention because they offer exotic physical phenomena. An exhaustive search coupled with first-principles calculations was implemented to investigate 10 Zintl compounds with a chemical formula of CaM₂X₂ (M = Zn or Cd, X = N, P, As, Sb, or Bi) under three crystal structures: CaAl₂Si₂-, ThCr₂Si₂-, and BaCu₂S₂-type crystal phases. All of the materials were found to energetically prefer the CaAl₂Si₂-type structure based on total ground state energy calculations. Symmetry-based indicators are used to evaluate their topological properties. Interestingly, we found that CaM₂Bi₂ (M = Zn or Cd) are topological crystalline insulators. Further calculations under the hybrid functional approach and analysis using k · p model reveal that they exhibit topological Dirac semimetal (TDSM) states, where the four-fold degenerate Dirac points are located along the high symmetry line in-between Г to A points. These findings are verified through Green's function surface state calculations under HSE06. Finally, phonon spectra calculations revealed that CaCd₂Bi₂ is thermodynamically stable. The Zintl phase of AM₂X₂ compounds have not been identified in any topological material databases, thus can be a new playground in the search for new topological materials.

Materials and possible mechanisms of extremely large magnetoresistance: a review

Magnetoresistance (MR) is a characteristic that the resistance of a substance changes with the external magnetic field, reflecting various physical origins and microstructures of the substance. A large MR, namely a huge response to a low external field, has always been a useful functional feature in industrial technology and a core goal pursued by physicists and materials scientists. Conventional large MR materials are mainly manganites, whose colossal MR (CMR) can be as high as -90%. The dominant mechanism is attributed to spin configuration aligned by the external field, which reduces magnetic scattering and thus resistance. In recent years, some new systems have shown an extremely large unsaturated MR (XMR). Unlike ordinary metals, the positive MR of these systems can reach 10³%-10⁸% and is persistent under super high magnetic fields. The XMR materials are mainly metals or semimetals, distributed in high-mobility topological or non-topological systems, and some are magnetic, which suggests a wide range of application scenarios. Various mechanisms have been proposed for the potential physical origin of XMR, including electron-hole compensation, steep band, ultrahigh mobility, high residual resistance ratio, topological fermions, etc. It turns out that some mechanisms play a leading role in certain systems, while more are far from clearly defined. In addition, the researches on XMR are largely overlapped or closely correlated with other recently rising physics and materials researches, such as topological matters and two-dimensional (2D) materials, which makes elucidating the mechanism of XMR even more important. Moreover, the disclosed novel properties will lay a broad and solid foundation for the design and development of functional devices. In this review, we will discuss several aspects in the following order: (I) introduction, (II) XMR materials and classification, (III) proposed mechanisms for XMR, (IV) correlation with other systems (featured), and (V) conclusions and outlook.

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.

Nontrivial topological states in new two-dimensional CdAs

By using first-principles calculations and symmetry analysis, we propose two topological nontrivial two-dimensional (2D) materials: CdAs-164 and CdAs-187. The results of binding energies, phonon dispersions, mechanical constants and thermodynamic stability demonstrate that the two materials are stable and may be synthesized in future experiments. When spin-orbit coupling (SOC) is not considered, the former is a typical Dirac semimetal with six equivalent Dirac points on the paths of Γ-M. These Dirac points are protected by vertical mirror symmetry. The latter is a nodal ring semimetal with the coexistence of two type-I nodal rings and one type-II nodal ring, and these nodal rings are protected by the horizontal mirror operationσ_h. After SOC is considered, both of the two materials turn into topological insulators withZ₂= 1. Our findings indicate that CdAs-164 and CdAs-187 are excellent candidates to explore the nontrivial topological states of 2D materials.

Strong Anisotropy and Bipolar Conduction-Dominated Thermoelectric Transport Properties in the Polycrystalline Topological Phase of ZrTe5

ZrTe₅ has unique features of a temperature-dependent topological electronic structure and anisotropic crystal structure and has obtained intensive attention from the thermoelectric community. This work revealed that the sintered polycrystalline bulk ZrTe₅ possesses both (020) and (041) preferred orientations. The transport properties of polycrystalline bulk p-type ZrTe₅ exhibits an obvious anisotropic characteristic, that is, the room-temperature resistivity and thermal conductivity, possessing anisotropy ratios of 0.71 and 1.49 perpendicular and parallel to the pressing direction, respectively. The polycrystalline ZrTe₅ obtained higher ZT values in the direction perpendicular to the pressing direction, as compared to that in the other direction. The highest ZT value of 0.11 is achieved at 350 K. Depending on the temperature-dependent topological electronic structure, the electronic transport of p-type ZrTe₅ is dominated by high-mobility electrons from linear bands and low-mobility holes from the valence band, which, however, are merely influenced by valence band holes at around room temperature. Furthermore, external magnetic fields are detrimental to thermoelectric properties of our ZrTe₅, mainly arising from the more prominent negative effects of electrons under fields. This research is instructive to understand the transport features of ZrTe₅ and paves the way for further optimizing their ZTs.

Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups

Having the chiral anomaly (CA) induced magneto-transport phenomena extensively studied in single Weyl semimetal as characterized by topological charge n = 1, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where n > 1. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with external magnetic field, electric field and temperature gradient. Starting from the low-energy model, we show analytically that at zero temperature both LMC and PHC vary cubically with topological charge as n ³ while the finite temperature (T ≠ 0) correction is proportional to (n + n ²)T ². Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge as n ² and the PNC is found to vary non-monotonically as a function of n. Our study hence clearly suggests that the inherent properties of m-WSMs indeed show up distinctly through the CA and the chiral magnetic effect induced transport coefficients in two different setups. Moreover, in order to obtain an experimentally realizable picture, we simultaneously verify our analytical findings through the numerical calculations using the lattice model of m-WSMs.

Emergent superconductivity by Re doping in type -II Weyl semimetal NiTe2

Recently topological semimetals emerge as a new platform to realise topological superconductivity. Here we report the emergent superconductivity in single-crystals of Re doped type-II Weyl semimetal NiTe₂. The magnetic and transport measurements highlight that Re substitution in Ni-site induces superconductivity at a maximum temperature of 2.36 K. Hall effect and specific heat measurements indicate that Re substitution is doping hole and facilitates the emergence of superconductivity by phonon softening and enhancing the electron-phonon coupling.

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.

Phase Controlled Growth of Cd3As2 Nanowires and Their Negative Photoconductivity

The bottom-up synthesis process often allows the growth of metastable phase nanowires instead of the thermodynamically stable phase. Herein, we synthesized Cd₃As₂ nanowires with a controlled three-dimensional Dirac semimetal phase using a chemical vapor transport method. Three different phases such as the body centered tetragonal (bct), and two metastable primitive tetragonal (P4₂/nbc and P4₂/nmc) phases were identified. The conversion between three phases (bct → P4₂/nbc → P4₂/nmc) was achieved by increasing the growth temperature. The growth direction is [110] for bct and P4₂/nbc and [100] for P4₂/nmc, corresponding to the same crystallographic axis. Field effect transistors and photodetector devices showed the nearly same electrical and photoelectrical properties for three phases. Differential conductance measurement confirms excellent electron mobility (2 × 10⁴ cm²/(V s) at 10 K). Negative photoconductance was first observed, and the photoresponsivity reached 3 × 10⁴ A/W, which is ascribed to the surface defects acting as trap sites for the photogenerated electrons.

Strain tuning of closed topological nodal lines and opposite pockets in quasi-two-dimensional α-phase FeSi2

Following topological nodal point semimetals, topological nodal line semimetals with one dimensional (1D) topological elements have recently aroused great interest worldwide in the fields of quantum chemistry and condensed matter physics. In this study, by means of first-principles, we predict that quasi-two-dimensional (2D) α-FeSi2 with a P4/mmm space group is a topological nodal line semimetal with two nodal lines close to the Fermi level, in the kz = 0 and kz = π planes. Usually, topological nodal line semimetals can be classified into type I, type II, and hybrid-type categories, each type with different physical properties. Importantly, for the first time, we find that type I, type II, and hybrid-type nodal lines can be realized in a realistic material, i.e., quasi-2D α-FeSi2, by strain switching. The realization of tunable nodal line types occurs because quasi-2D α-FeSi2 has special opposite-pocket-behaving bands around the Fermi level. The results presented herein reflect that α-FeSi2 is a valuable candidate for spintronics application by utilization of type I, type II, and hybrid-type topological nodal line semimetals in a single material tuned by mechanical strain.

Drift velocity saturation and large current density in intrinsic three-dimensional Dirac semimetal cadmium arsenide

Transport of electrons at high electric fields is investigated in intrinsic three-dimensional Dirac semimetal cadmium arsenide, considering the scattering of electrons from acoustic and optical phonons. Screening and hot phonon effect are taken in to account. Expressions for the hot electron mobility μ and power loss P are obtained as a function of electron temperature T _e. The dependence of drift velocity v _d on electric field E and electron density n _e has been studied. Hot phonon effect is found to set in the saturation of v _d at relatively low E and to significantly degrade its magnitude. The drift velocity is found to saturate at a value v _ds ∼ 10⁷ cm s^-1 and it is weakly dependent on n _e. A large saturation current density ∼ 10⁶ A cm^-2 is predicted.

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.

Pressure effect on the magnetoresistivity of topological semimetal RhSn

RhSn is a topological semimetal with chiral fermions. At ambient pressure, it exhibits large positive magnetoresistance (MR) and field-induced resistivity upturn at low temperatures. Here we report on the electrical transport properties of RhSn single crystal under various pressures. We find that with increasing pressure the temperature-dependent resistivityρ(T) of RhSn varies minutely, whereas the value of MR at low temperatures decreases significantly. Theρ(T) data was fitted with the Bloch-Grüneisen model and the Debye temperature was extracted. Analyses of the nonlinear Hall conductivity with two-band model indicate that the carrier concentrations do not change significantly with pressure, but the mobilities for both electron and hole carriers are reduced monotonically, which can account for the significant reduction of MR under high pressures.

Thermoelectric transport properties in 3D Dirac semimetal Cd3As2

Thermoelectric transport properties, namely, electrical conductivity, electronic thermal conductivity, and diffusion thermopower are theoretically investigated in 3D Dirac semimetal Cd₃As₂. We employ Boltzmann transport formalism and consider the electron scattering by charged impurities, short-range disorder, acoustic phonons, and optical phonons. The Boltzmann transport equation is solved using the Ritz iteration technique to obtain the first-order perturbation distribution function for the interaction of electrons with inelastic polar optical phonons scattering. The numerical results are presented in the temperature range 2-300 K with the electron concentration in the range (0.1-10)  ×  10¹⁸ cm^-3. It is found that, at low temperature  <  ~70 K transport coefficients are dominated by charged impurity scattering and at higher temperature the phonon scattering is found to be dominant. The validity of Wiedemann-Franz law is examined. Recently observed experimental results are explained by our theory.

Interlayer quantum transport in Dirac semimetal BaGa2

The quantum limit is quite easy to achieve once the band crossing exists exactly at the Fermi level (EF) in topological semimetals. In multilayered Dirac fermion systems, the density of Dirac fermions on the zeroth Landau levels (LLs) increases in proportion to the magnetic field, resulting in intriguing angle- and field-dependent interlayer tunneling conductivity near the quantum limit. BaGa2 is an example of a multilayered Dirac semimetal with its quasi-2D Dirac cone located at EF, providing a good platform to study its interlayer transport properties. In this paper, we report the negative interlayer magnetoresistance induced by the tunneling of Dirac fermions between the zeroth LLs of neighboring Ga layers in BaGa2. When the field deviates from the c-axis, the interlayer resistivity ρzz(θ) increases and finally results in a peak with the applied field perpendicular to the c-axis. These unusual interlayer transport properties are observed together in the Dirac semimetal under ambient pressure and are well explained by the model of tunneling between Dirac fermions in the quantum limit.

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.

Superconductivity and Shubnikov - de Haas effect in polycrystalline Cd3As2 thin films

In this study we observed the reproducible superconducting state in Cd₃As₂ thin films without any external stimuli. Comparison with our previous results reveals similar qualitative behavior for films synthesized by different methods, while the difference in the values of the critical parameters clearly shows the possibility to control this state. The X-ray diffraction measurements demonstrate the presence of the tetragonal Cd₃As₂ crystal phase in studied films. Measurements of high-field magnetoresistance reveal pronounced Shubnikov - de Haas oscillations. The analysis of these oscillations suggests that, due to high carrier concentration in studied Cd₃As₂ films, the initial Dirac semimetal phase may be partially suppressed, which, however, does not contradict with possible topological nature of the observed superconductivity.

De Haas-van Alphen study on three-dimensional topological semimetal pyrite PtBi2

We present the systematic de Haas-van Alphen (dHvA) quantum oscillations studies on the recently discovered topological Dirac semimetal pyrite PtBi₂ single crystals. Remarkable dHvA oscillations are emerged at a low field about 1.5 T. From the analyses of the dHvA oscillations, we extract the high quantum mobilities, light effective masses and phase shift factors for the Dirac fermions in pyrite PtBi₂. From the angular dependence of the dHvA oscillations, we map out the topology of the Fermi surface. Furthermore, we identify two additional oscillation frequencies that are not probed by the SdH oscillations, which provides us with opportunities to further understand its Fermi surface topology.

Magnetotransport Properties of Layered Topological Material ZrTe2 Thin Film

ZrTe₂ is a candidate topological material from the layered two-dimensional transition-metal dichalcogenide family, and thus the material may show exotic electrical transport properties and may be promising for quantum device applications. In this work, we report the successful growth of layered ZrTe₂ thin film by pulsed-laser deposition and the experimental results of its magnetotransport properties. In the presence of a perpendicular magnetic field, the 60 nm thick ZrTe₂ film shows a large magnetoresistance of 3000% at 2 K and 9 T. A robust linear magnetoresistance is observed under an in-plane magnetic field, and negative magnetoresistance appears in the film when the magnetic field is parallel to the current direction. Furthermore, the Hall results reveal that the ZrTe₂ thin film has a high electron mobility of about 1.8 × 10⁴ cm² V^-1 s^-1 at 2 K. These findings provide insights into further investigations and potential applications of this layered topological material system.

Manifestation of Kinetic Inductance in Terahertz Plasmon Resonances in Thin-Film Cd3As2

Three-dimensional (3D) semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with their linear energy dispersion. In analogy to two-dimensional (2D) Dirac semimetals, such as graphene, Cd₃As₂ has shown ultrahigh mobility and large Fermi velocity and has been hypothesized to support plasmons at terahertz frequencies. In this work, we experimentally demonstrate synthesis of high-quality large-area Cd₃As₂ thin films through thermal evaporation as well as the experimental realization of plasmonic structures consisting of periodic arrays of Cd₃As₂ stripes. These arrays exhibit sharp resonances at terahertz frequencies with associated quality factors ( Q) as high as ∼3.7 (at 0.82 THz). Such spectrally narrow resonances can be understood on the basis of a long momentum scattering time, which in our films can approach ∼1 ps at room temperature. Moreover, we demonstrate an ultrafast tunable response through excitation of photoinduced carriers in optical pump/terahertz probe experiments. Our results evidence that the intrinsic 3D nature of Cd₃As₂ might provide for a very robust platform for terahertz plasmonic applications. Moreover, the long momentum scattering time as well as large kinetic inductance in Cd₃As₂ also holds enormous potential for the redesign of passive elements such as inductors and hence can have a profound impact in the field of RF integrated circuits.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8  ×  10¹⁵ cm^-3 to 4.3  ×  10¹⁸ cm^-3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase [Formula: see text] at electron concentration [Formula: see text] 2  ×  10¹⁸ cm^-3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Magnetic field-induced electronic phase transition in the Dirac semimetal state of black phosphorus under pressure

Different instabilities have been confirmed to exist in the three-dimensional (3D) electron gas when it is confined to the lowest Landau level in the extreme quantum limit. The recently discovered 3D topological semimetals offer a good platform to explore these phenomena due to the small sizes of their Fermi pockets, which means the quantum limit can be achieved at relatively low magnetic fields. In this work, we report the high-magnetic-field transport properties of the Dirac semimetal state in pressurized black phosphorus. Under applied hydrostatic pressure, the band structure of black phosphorus goes through an insulator-semimetal transition. In the high pressure topological semimetal phase, anomalous behaviors are observed on both magnetoresistance and Hall resistivity beyond the relatively low quantum limit field, which is demonstrated to indicate the emergence of an exotic electronic state hosting a density wave ordering. Our findings bring the first insight into the electronic interactions in black phosphorus under intense field.

Berry phase theory of planar Hall effect in topological insulators

The appearance of negative longitudinal magnetoresistance (LMR) in topological semimetals such as Weyl and Dirac semimetals is understood as an effect of chiral anomaly, whereas such an anomaly is not well-defined in topological insulators. Nevertheless, it has been shown recently in both theory and experiments that nontrivial Berry phase effects can give rise to negative LMR in topological insulators even in the absence of chiral anomaly. In this paper, we present a quasi-classical theory of another intriguing phenomenon in topological insulators - also ascribed to chiral anomaly in Weyl and Dirac semimetals- the so-called planar Hall effect (PHE). PHE implies the appearance of a transverse voltage in the plane of applied non-parallel electric and magnetic fields, in a configuration in which the conventional Hall effect vanishes. Starting from Boltzmann transport equations we derive the expressions for PHE and LMR in topological insulators in the bulk conduction limit, and show the important role played by orbital magnetic moment. Our theoretical results for magnetoconductance with non-parallel electric and magnetic fields predict detailed experimental signatures in topological insulators - specifically of planar Hall effect - that can be observed in experiments.

Vanishing quantum oscillations in Dirac semimetal ZrTe5

One of the characteristics of topological materials is their nontrivial Berry phase. Experimental determination of this phase largely relies on a phase analysis of quantum oscillations. We study the angular dependence of the oscillations in a Dirac material [Formula: see text] and observe a striking spin-zero effect (i.e., vanishing oscillations accompanied with a phase inversion). This indicates that the Berry phase in [Formula: see text] remains nontrivial for arbitrary field direction, in contrast with previous reports. The Zeeman splitting is found to be proportional to the magnetic field based on the condition for the spin-zero effect in a Dirac band. Moreover, it is suggested that the Dirac band in [Formula: see text] is likely transformed into a line node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations.

Type I superconductivity in Dirac materials

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals while in the PdTe₂, superconductivity is clearly of the first kind. This is very rare in Dirac semi-metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic. Therefore the 'hybrid' Dirac-parabolic material is intermediate between the two extremes. A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D cone and used to determine anisotropic coherence lengths, the penetration depths and applied to recent extensive experiments. Magnetic properties of these superconductors are then studied in the parallel to the layers magnetic field on the basis of microscopically derived Ginzburg-Landau effective theory for the order parameter.

A possible candidate for triply degenerate point fermions in trigonal layered PtBi2

Triply degenerate point (TP) fermions in tungsten–carbide-type materials (e.g., MoP), which represent new topological states of quantum matter, have generated immense interest recently. However, the TPs in these materials are found to be far below the Fermi level, leading to the TP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically predict the existence of TP fermions with TP points close to the Fermi level in trigonal layered PtBi₂ by ab initio calculations, and experimentally verify the predicted band topology by magnetotransport measurements under high magnetic fields up to 40 T. Analyses of both the pronounced Shubnikov–de Haas and de Haas–van Alphen oscillations reveal the existence of six principal Fermi pockets. Our experimental results, together with those from ab initio calculations, reveal the interplay between transport behaviors and unique electronic structures, and support the existence of TP fermions in trigonal layered PtBi₂.

Triply degenerate point (TP) fermions have been reported in MoP but the TPs are far below the Fermi level. Here, Guo et al. predict and verify the possible existence of TP fermions in trigonal layered PtBi₂, where the TP points are close to the Fermi level.

Hot electron cooling in Dirac semimetal Cd3As2 due to polar optical phonons

A theory of hot electron cooling power due to polar optical phonons P _op is developed in 3D Dirac semimetal (3DDS) Cd₃As₂ taking account of hot phonon effect. Hot phonon distribution N _q and P _op are investigated as a function of electron temperature T _e, electron density n _e, and phonon relaxation time [Formula: see text]. It is found that P _op increases rapidly (slowly) with T _e at lower (higher) temperature regime. Whereas, P _op is weakly decreasing with increasing n _e. The results are compared with those for three-dimensional electron gas (3DEG) in Cd₃As₂ semiconductor. Hot phonon effect is found to reduce P _op considerably and it is stronger in 3DDS Cd₃As₂ than in Cd₃As₂ semiconductor. P _op is also compared with the hot electron cooling power due to acoustic phonons P _ac. We find that a crossover takes place from P _ac dominated cooling at low T _e to P _op dominated cooling at higher T _e. The temperature at which this crossover occurs shifts towards higher values with the increase of n _e. Also, hot electron energy relaxation time [Formula: see text] is discussed. It is suggested that [Formula: see text] can be tuned to achieve faster or slower energy loss for suitable applications of Cd₃As₂.

Thickness-Tunable Synthesis of Ultrathin Type-II Dirac Semimetal PtTe2 Single Crystals and Their Thickness-Dependent Electronic Properties

The recent discovery of topological semimetals has stimulated extensive research interest due to their unique electronic properties and novel transport properties related to a chiral anomaly. However, the studies to date are largely limited to bulk crystals and exfoliated flakes. Here, we report the controllable synthesis of ultrathin two-dimensional (2D) platinum telluride (PtTe₂) nanosheets with tunable thickness and investigate the thickness-dependent electronic properties. We show that PtTe₂ nanosheets can be readily grown, using a chemical vapor deposition approach, with a hexagonal or triangular geometry and a lateral dimension of up to 80 μm, and the thickness of the nanosheets can be systematically tailored from over 20 to 1.8 nm by reducing the growth temperature or increasing the flow rate of the carrier gas. X-ray-diffraction, transmission-electron microscopy, and electron-diffraction studies confirm that the resulting 2D nanosheets are high-quality single crystals. Raman spectroscopic studies show characteristics E_g and A_1g vibration modes at ∼109 and ∼155 cm^-1, with a systematic red shift with increasing nanosheet thickness. Electrical transport studies show the 2D PtTe₂ nanosheets display an excellent conductivity up to 2.5 × 10⁶ S m^-1 and show strong thickness-tunable electrical properties, with both the conductivity and its temperature dependence varying considerably with the thickness. Moreover, 2D PtTe₂ nanosheets show an extraordinary breakdown current density up to 5.7 × 10⁷ A/cm², the highest breakdown current density achieved in 2D metallic transition-metal dichalcogenides to date.

Evidence for a Dirac nodal-line semimetal in SrAs3

Dirac nodal-line semimetals with the linear bands crossing along a line or loop, represent a new topological state of matter. Here, by carrying out magnetotransport measurements and performing first-principle calculations, we demonstrate that such a state has been realized in high-quality single crystals of SrAs₃. We obtain the nontrivial π Berry phase by analysing the Shubnikov-de Haas quantum oscillations. We also observe a robust negative longitudinal magnetoresistance induced by the chiral anomaly. Accompanying first-principles calculations identifies that a single hole pocket enclosing the loop nodes is responsible for these observations.

π and 4π Josephson Effects Mediated by a Dirac Semimetal

Cd_{3}As_{2} is a three-dimensional topological Dirac semimetal with connected Fermi-arc surface states. It has been suggested that topological superconductivity can be achieved in the nontrivial surface states of topological materials by utilizing the superconductor proximity effect. Here we report observations of both π and 4π periodic supercurrents in aluminum-Cd_{3}As_{2}-aluminum Josephson junctions. The π period is manifested by both the magnetic-field dependence of the critical supercurrent and the appearance of half-integer Shapiro steps in the ac Josephson effect. Our macroscopic theory suggests that the π period arises from interference between the induced bulk superconductivity and the induced Fermi-arc surface superconductivity. The 4π period is manifested by the missing first Shapiro steps and is expected for topological superconductivity.

Topological nature of the node-arc semimetal PtSn4 probed by de Haas-van Alphen quantum oscillations

Dirac node arc semimetal state is a new topological quantum state which is proposed to exist in PtSn₄ (Wu et al 2016 Dirac node arcs in PtSn₄ Nat. Phys. 12 667-71). We present a systematic de Haas-van Alphen quantum oscillation study on this compound. Two intriguing oscillation branches, i.e. F ₁ and F ₂, are detected in the fast Fourier transformation spectra, both of which are characterized to possess tiny effective mass and ultrahigh quantum mobility. And the F ₂ branch exhibits an angle-dependent nontrivial Berry phase. The features are consistent with the existence of the node arc semimetal state and shed new light on its complicated Fermi surfaces and topological nature.

Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-Line Semimetals

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial π Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu_{3}PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.

Phase transition studies of Na3Bi system under uniaxial strain

We investigated the electronic properties and phase transitions of Na₃Bi in four structural phases (space groups P6₃/mmc, P [Formula: see text] c1, Fm [Formula: see text] m and Cmcm) under constant-volume uniaxial strain using the first-principles method. For P6₃/mmc and P [Formula: see text] c1-Na₃Bi, an important phase transition from a topological Dirac semimetal (TDS) to a topological insulator appears under compression strain around 4.5%. The insulating gap increases with the increasing compressive strain and up to around 0.1 eV at a strain of 10%. However, both P6₃/mmc and P [Formula: see text] c1-Na₃Bi still keep the properties of a TDS within a tensile strain of 0-10%, although the Dirac points move away from the Γ point along Γ-A in reciprocal space as the tensile strain increases. The Na₃Bi with space group Fm [Formula: see text] m is identified as a topological semimetal with the inverted bands between Na-3s and Bi-6p and a parabolic dispersion in the vicinity of Γ point. Interestingly, for Fm [Formula: see text] m-Na₃Bi, both compression and tensile strain lead to a TDS which is identified by calculating surface Fermi arcs and topological invariants at time-reversal planes (k _z   =  0 and k _z   =  π/c) in reciprocal space. Additionally, we confirmed the high pressure phase Cmcm-Na₃Bi is an ordinary insulator with a gap of about 0.62 eV. It is noteworthy that its gap almost keeps constant around 0.60 eV within a compression strain of 0-10%. In contrast, a remarkable phase transition from an insulator to a metal phase appears under tensile strain. Moreover, this phase transition is highly sensitive to tensile strain and takes place only at a strain 1.0%. These strain-induced electronic structures and phase transitions of the Na₃Bi system in various phases are important due to their possible applications under high pressure in future electronic devices.

Quantum Dots Formed in Three-dimensional Dirac Semimetal Cd3As2 Nanowires

We demonstrate quantum dot (QD) formation in three-dimensional Dirac semimetal Cd₃As₂ nanowires using two electrostatically tuned p-n junctions with a gate and magnetic fields. The linear conductance measured as a function of gate voltage under high magnetic fields is strongly suppressed at the Dirac point close to zero conductance, showing strong conductance oscillations. Remarkably, in this regime, the Cd₃As₂ nanowire device exhibits Coulomb diamond features, indicating that a clean single QD forms in the Dirac semimetal nanowire. Our results show that a p-type QD can be formed between two n-type leads underneath metal contacts in the nanowire by applying gate voltages under strong magnetic fields. Analysis of the quantum confinement in the gapless band structure confirms that p-n junctions formed between the p-type QD and two neighboring n-type leads under high magnetic fields behave as resistive tunnel barriers due to cyclotron motion, resulting in the suppression of Klein tunneling. The p-type QD with magnetic field-induced confinement shows a single hole filling. Our results will open up a route to quantum devices such as QDs or quantum point contacts based on Dirac and Weyl semimetals.

Structural characterisation of high-mobility Cd3As2 films crystallised on SrTiO3

Cd₃As₂ has long been known as a high-mobility semiconductor. The recent finding of a topological semimetal state in this compound has demanded growth of epitaxial films with high crystallinity and controlled thickness. Here we report the structural characterisation of Cd₃As₂ films grown on SrTiO₃ substrates by solid-phase epitaxy at high temperatures up to 600 °C by employing optimised capping layers and substrates. The As triangular lattice is epitaxially stacked on the Ti square lattice of the (001) SrTiO₃ substrate, producing (112)-oriented Cd₃As₂ films exhibiting high crystallinity with a rocking-curve width of 0.02° and a high electron mobility exceeding 30,000 cm²/Vs. The systematic characterisation of films annealed at various temperatures allowed us to identify two-step crystallisation processes in which out-of-plane and subsequently in-plane directions occur with increasing annealing temperature. Our findings on the high-temperature crystallisation process of Cd₃As₂ enable a unique approach for fabricating high-quality Cd₃As₂ films and elucidating quantum transport by back gating through the SrTiO₃ substrate.

Quantum Hall states observed in thin films of Dirac semimetal Cd3As2

A well known semiconductor Cd₃As₂ has reentered the spotlight due to its unique electronic structure and quantum transport phenomena as a topological Dirac semimetal. For elucidating and controlling its topological quantum state, high-quality Cd₃As₂ thin films have been highly desired. Here we report the development of an elaborate growth technique of high-crystallinity and high-mobility Cd₃As₂ films with controlled thicknesses and the observation of quantum Hall effect dependent on the film thickness. With decreasing the film thickness to 10 nm, the quantum Hall states exhibit variations such as a change in the spin degeneracy reflecting the Dirac dispersion with a large Fermi velocity. Details of the electronic structure including subband splitting and gap opening are identified from the quantum transport depending on the confinement thickness, suggesting the presence of a two-dimensional topological insulating phase. The demonstration of quantum Hall states in our high-quality Cd₃As₂ films paves a road to study quantum transport and device application in topological Dirac semimetal and its derivative phases.