Linear magnetoresistance caused by mobility fluctuations in n-doped Cd(3)As(2)

Ratio of 4:1 between ZnGeAs2and MnAs phases in a single composite and its impact on the structure-driven magnetoresistance

A strong influence of the lattice degree of freedom on magnetoresistance (MR) under high pressure underlies the conception of 'structure-driven' magnetoresistance (SDMR). In most magnetic or topological materials, the suppression of MR with increasing pressure is a general trend, while for some magnetic composites the MR enhances and even shows unusual behavior as a consequence of structural transition. Here we investigated the SDMR in the composite material based on the ZnGeAs2semiconductor matrix and MnAs magnetic inclusions in a phase ratio of 4:1. At ambient pressure, its magnetic and transport properties are governed by MnAs inclusions, i.e. it shows a Curie temperatureTC≈ 320 K and metallic-like conductivity. Under high pressure, the low-field room temperature MR undergoes multiple changes in the pressure range up to 7.2 GPa. The structural transition in the ZnGeAs2matrix has been found at ∼6 GPa, slightly lower than in the pure ZnGeAs2(6.2 GPa). The huge SDMR as high as 85% at 6.8 GPa and 2.5 kOe, which contains both positive and negative MR components, is accompanied by a pressure-induced metallic-like-to-semiconductor-like transition and the enhanced ferromagnetic order of MnAs inclusions. This observation offers a competing mechanism between the robust extrinsic ferromagnetism and high-pressure electronic properties of ZnGeAs2.

Cd2FeReO6: A High-TC Double Perovskite Oxide with Remarkable Tunneling Magnetoresistance

In this study, we successfully synthesized the double perovskite oxide Cd2FeReO6 by using a high-temperature and high-pressure method. The crystal structure was confirmed to belong to the P21/n space group, exhibiting approximately 68% ordering of Fe3+ and Re5+ ions at the perovskite B-site with the remaining regions showing antisite disorder. The measured Curie temperature of Cd2FeReO6 was 460 K, slightly lower than expected but still significantly above room temperature. Remarkably, Cd2FeReO6 displayed a remarkable low-field butterfly type tunneling magnetoresistance of -23% (-37% between the lowest and the largest values) at 5 K and 90 kOe, the highest among the A2FeReO6 (A = Ca, Sr, Pb, Ba) family. First-principles calculations provided insight into the origin of this observed magnetoresistance behavior, revealing Cd2FeReO6's half-metallic ferrimagnetic nature. This research extends our understanding of the double perovskite family and emphasizes its potential significance in the domains of spintronics and materials science. The exploration of differing magnetoresistance behaviors between Cd2FeReO6 and Ca2FeReO6, along with the influence of antisite disorder in Cd2FeReO6, opens intriguing avenues for further research.

Circular Photogalvanic Current in Ni-Doped Cd3As2 Films Epitaxied on GaAs(111)B Substrate

Magnetic element doped Cd₃As₂ Dirac semimetal has attracted great attention for revealing the novel quantum phenomena and infrared opto-electronic applications. In this work, the circular photogalvanic effect (CPGE) was investigated at various temperatures for the Ni-doped Cd₃As₂ films which were grown on GaAs(111)B substrate by molecular beam epitaxy. The CPGE current generation was found to originate from the structural symmetry breaking induced by the lattice strain and magnetic doping in the Ni-doped Cd₃As₂ films, similar to that in the undoped ones. However, the CPGE current generated in the Ni-doped Cd₃As₂ films was approximately two orders of magnitude smaller than that in the undoped one under the same experimental conditions and exhibited a complex temperature variation. While the CPGE current in the undoped film showed a general increase with rising temperature. The greatly reduced CPGE current generation efficiency and its complex variation with temperature in the Ni-doped Cd₃As₂ films was discussed to result from the efficient capture of photo-generated carriers by the deep-level magnetic impurity bands and enhanced momentum relaxation caused by additional strong impurity scattering when magnetic dopants were introduced.

Disorder-Induced Magnetotransport Anomalies in Amorphous and Textured Co1-xSix Semimetal Thin Films

In recent times the chiral semimetal cobalt monosilicide (CoSi) has emerged as a prototypical, nearly ideal topological conductor hosting giant, topologically protected Fermi arcs. Exotic topological quantum properties have already been identified in CoSi bulk single crystals. However, CoSi is also known for being prone to intrinsic disorder and inhomogeneities, which, despite topological protection, risk jeopardizing its topological transport features. Alternatively, topology may be stabilized by disorder, suggesting the tantalizing possibility of an amorphous variant of a topological metal, yet to be discovered. In this respect, understanding how microstructure and stoichiometry affect magnetotransport properties is of pivotal importance, particularly in case of low-dimensional CoSi thin films and devices. Here we comprehensively investigate the magnetotransport and magnetic properties of ≈25 nm Co_1-xSi_x thin films grown on a MgO substrate with controlled film microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60). The resistivity of Co_1-xSi_x thin films is nearly insensitive to the film microstructure and displays a progressive evolution from metallic-like (dρ_xx/dT > 0) to semiconducting-like (dρ_xx/dT < 0) regimes of conduction upon increasing the silicon content. A variety of anomalies in the magnetotransport properties, comprising for instance signatures consistent with quantum localization and electron-electron interactions, anomalous Hall and Kondo effects, and the occurrence of magnetic exchange interactions, are attributable to the prominent influence of intrinsic structural and chemical disorder. Our systematic survey brings to attention the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in nanoscale thin films and devices.

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.

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.

Unconventional localization of electrons inside of a nematic electronic phase

Among iron-based superconductors, FeSe displays an anomalous electronic nematic state, strong electronic correlations, and orbitally dependent band shifts that can influence its superconducting pairing. Here, we report detailed magnetotransport studies of thin flakes of FeSe that reveal unconventional transport, in which the hole carriers remain highly mobile, whereas the mobility of the electron carriers is low, and weakly temperature dependent, inside the nematic phase. This suggests an unusual localization of negative charge carriers that may be caused by orbital-dependent enhanced correlations, scattering of spin fluctuations, and/or a topological electronic transition. As the superconductivity is suppressed by reducing the flake thickness, it suggests that the electron pockets participate actively in pairing. By doping, electron pockets expand, enabling high-Tc superconductivity.

The magnetotransport behavior inside the nematic phase of bulk FeSe reveals unusual multiband effects that cannot be reconciled with a simple two-band approximation proposed by surface-sensitive spectroscopic probes. In order to understand the role played by the multiband electronic structure and the degree of two-dimensionality, we have investigated the electronic properties of exfoliated flakes of FeSe by reducing their thickness. Based on magnetotransport and Hall resistivity measurements, we assess the mobility spectrum that suggests an unusual asymmetry between the mobilities of the electrons and holes, with the electron carriers becoming localized inside the nematic phase. Quantum oscillations in magnetic fields up to 38 T indicate the presence of a hole-like quasiparticle with a lighter effective mass and a quantum scattering time three times shorter, as compared with bulk FeSe. The observed localization of negative charge carriers by reducing dimensionality can be driven by orbitally dependent correlation effects, enhanced interband spin fluctuations, or a Lifshitz-like transition, which affect mainly the electron bands. The electronic localization leads to a fragile two-dimensional superconductivity in thin flakes of FeSe, in contrast to the two-dimensional high-Tc induced with electron doping via dosing or using a suitable interface.

Ultrafast Optical Probe of Coherent Acoustic Phonons in Dirac Semimetal Cd3As2 Film Epitaxied on GaAs(111)B Substrate

Coherent longitudinal acoustic phonon (CAP) generation in epitaxial Dirac semimetal Cd₃As₂ films with different thicknesses was investigated by a time-resolved reflectance technique. The short-lived weak CAP oscillations can be observed only in the thicker Cd₃As₂ films, and their central frequency of 0.039 THz has no dependence on sample thickness, but is nearly inversely proportional to the probe wavelength. For the 20 nm thin film, the observed long-lived CAP with a central frequency of 0.049 THz is generated in the GaAs(111)B substrate underneath. A sound velocity of 3800 m/s for the Cd₃As₂ film and 5360 m/s for the GaAs(111)B substrate is thus deduced. In addition, the opposite CAP amplitude and lifetime dependence on temperature further confirms the electronic and thermal stress origination of CAP generated in GaAs(111)B and Cd₃As₂ film, respectively, based on the propagating strain pulse model. The central frequency of CAP is found to be stable with increasing pumping fluence and temperature, which makes Cd₃As₂ a potential material for thermoelectric device applications.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Large Transverse and Longitudinal Magneto-Thermoelectric Effect in Polycrystalline Nodal-Line Semimetal Mg3 Bi2

Topological semimetals provide new opportunities for exploring novel thermoelectric phenomena, owing to their exotic and nontrivial electronic structure topology around the Fermi surface. Herein, the discovery of large transverse and longitudinal magneto-thermoelectric (MTE) effects in Mg₃ Bi₂ is reported and predicted to be a type-II nodal-line semimetal in the absence of spin-orbit coupling (SOC). The maximum transverse power factor is 2182 μW m^-1 K^-2 at 13.5 K and 6 Tesla. The longitudinal power factor reaches up to 3043 μW m^-1 K^-2 , which is 20 times higher than that in a zero-strength magnetic field and is also comparable to state-of-the-art MTE materials. By compensating the Mg loss in Mg-rich conditions for tuning the carrier concentration close to intrinsic state, the sample fabricated in this study exhibits a large linear non-saturating magnetoresistance of 940% under a field of 14 Tesla. Using density functional calculations, the authors attribute the underlying mechanism to the parent linear-dispersed nodal-line electronic structure without SOC and the anisotropic Fermi surface shape with SOC, highlighting the essential role of high carrier mobility and open electron orbits in the moment space. This work offers a new avenue toward highly efficient MTE materials through defect engineering in polycrystalline topological semimetals.

Strain-induced circular photogalvanic current in Dirac semimetal Cd3As2 films epitaxied on a GaAs(111)B substrate

Dirac semimetal (DSM) Cd₃As₂ has drawn great attention for exploring the novel quantum phenomena and high-speed optoelectronic applications. The circular photogalvanic effect (CPGE) current, resulting from the optically-excited spin orientation transport, was theoretically predicted to vanish in an ideal Dirac system due to the symmetric photoexcitation about the Dirac point. Here, we reported the observation of the CPGE photocurrent in epitaxial Cd₃As₂ thin films grown on a GaAs(111)B substrate. The signature of the CPGE is confirmed by its sign reversal upon switching the helicity of optical radiation, as well as its dependence on the excitation incident angle and power. By comparison of the CPGE response between the films with different thicknesses, it is suggested that the observed CPGE results from the reduced structure symmetry and substantially modified electronic band structure of the Cd₃As₂ thin film that undergoes large epitaxial strain. Our experimental findings provide a valuable reference for the band engineering and exotic helicity-dependent photocurrent phenomena in DSMs towards their potential opto-spintronic device applications.

Polarization-dependent excitons and plasmon activity in nodal-line semimetal ZrSiS

The optical properties of the bulk ZrSiS nodal-line semimetal are theoretically studied within a many-body formalism. The G₀W₀ bands are similar to those calculated within the density functional theory, except near the Γ-point; in particular, no significant differences are found around the Fermi energy. On the other hand, the solution of the Bethe-Salpeter equation reveals significant excitonic activity, mostly as dark excitons which appear in a wide energy range. Bright excitons, in contrast, are less numerous, but their location and intensity depend greatly on the polarization of the incident electric field, as the absorption coefficient itself does. The binding energy of these excitons correlates well with their spatial distribution functions. In any case, good agreement with the available experimental data for absorption/reflection is achieved. Finally, the possible activation of plasma oscillations is investigated. Plasmons may be formed at low energies, but they are damped and decayed producing electron-hole pairs, more importantly for q along the Γ-M path.

From Low-Field Sondheimer Oscillations to High-Field Very Large and Linear Magnetoresistance in a SrTiO3-Based Two-Dimensional Electron Gas

Quantum materials harbor a cornucopia of exotic transport phenomena challenging our understanding of condensed matter. Among these, a giant, nonsaturating linear magnetoresistance (MR) has been reported in various systems, from Weyl semimetals to topological insulators. Its origin is often ascribed to unusual band structure effects, but it may also be caused by extrinsic sample disorder. Here, we report a very large linear MR in a SrTiO₃ two-dimensional electron gas and, by combining transport measurements with electron spectromicroscopy, show that it is caused by nanoscale inhomogeneities that are self-organized during sample growth. Our data also reveal semiclassical Sondheimer oscillations arising from interferences between helicoidal electron trajectories, from which we determine the 2DEG thickness. Our results bring insight into the origin of linear MR in quantum materials, expand the range of functionalities of oxide 2DEGs, and suggest exciting routes to explore the interaction of linear MR with features like Rashba spin-orbit coupling.

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.

Nontrivial Giant Linear Magnetoresistance in Nodal-Line Semimetal ZrGeSe 2D Layers

Linear magnetoresistance (LMR) is usually observed in topological quantum materials and plausibly connected with the topologically nontrivial surface state with Dirac-cone-like linear dispersion because the frequently encountered large Hall resistivity can be trivially mixed into the LMR via charge inhomogeneity. Herein, by applying an optimal gate voltage to nodal-line semimetal ZrGeSe two-dimensional (2D) layers with specific thicknesses, we observe a giant nonsaturated LMR of 8 × 10⁴% at 2 K and a magnetic field of 9 T. This giant LMR is accompanied by a very small Hall resistivity, which is inconsistent with the charge inhomogeneity mechanism. Our systematic results confirm that the giant LMR is maximized when the topological semimetal is in the "even-metal" regime and suppressed upon evolution to the normal "odd-metal" regime. The "even-to-odd" transition is universal regardless of the thicknesses of the crystals. A comparison with Abrikosov's quantum LMR theory indicates that the observed LMR cannot be trivial.

Anomalous magnetoresistance and magneto-thermal properties of the half-Heuslers,RPdSi (RY, Gd-Er)

Here, we present a detailed study on the magnetic, magneto-transport, and magneto-thermal properties of the equiatomic half-Heusler compounds with the general formula,RPdSi (R= Y and rare-earth, Gd-Er). These materials crystallize in two different superstructures of the TiNiSi-type orthorhombic unit cell with the space groupsPnmaandPmmn. Our magnetic and heat capacity measurements reveal the onset of an antiferromagnetic (AFM) ordering in the temperature range 3-16 K for all the local moments bearingRPdSi compounds, while the non-magnetic analog, YPdSi exhibits a Pauli-paramagnetic behaviour. The AFM state of these compounds can be tuned by magnetic field and temperature as demonstrated by the magnetic measurements below the Neel temperature (T_N). Most importantly, this tuning of the magnetic structure is well documented in the complex temperature and field dependence of magnetoresistance (MR) and magnetocaloric effect (MCE). Our study establishes a striking correlation of the commensurate/incommensurate AFM structure with that of positive/negative MR and MCE in this series of compounds. We emphasize that such a framework applies to a large number of AFM intermetallic systems.

Defect induced ferromagnetic ordering and room temperature negative magnetoresistance in MoTeP

The magneto-transport, magnetization and theoretical electronic-structure have been investigated on type-II Weyl semimetallic MoTeP. The ferromagnetic ordering is observed in the studied sample and it has been shown that the observed magnetic ordering is due to the defect states. It has also been demonstrated that the presence of ferromagnetic ordering in effect suppresses the magnetoresistance (MR) significantly. Interestingly, a change-over from positive to negative MR is observed at higher temperature which has been attributed to the dominance of spin scattering suppression.

Probing charge pumping and relaxation of the chiral anomaly in a Dirac semimetal

The linear band crossings of 3D Dirac and Weyl semimetals are characterized by a charge chirality, the parallel or antiparallel locking of electron spin to its momentum. These materials are believed to exhibit an E · B chiral magnetic effect that is associated with the near conservation of chiral charge. Here, we use magneto-terahertz spectroscopy to study epitaxial Cd3As2 films and extract their conductivities σ(ω) as a function of E · B. As field is applied, we observe a markedly sharp Drude response that rises out of the broader background. Its appearance is a definitive signature of a new transport channel and consistent with the chiral response, with its spectral weight a measure of the net chiral charge and width a measure of the scattering rate between chiral species. The field independence of the chiral relaxation establishes that it is set by the approximate conservation of the isospin that labels the crystalline point-group representations.

Room-Temperature Spin Transport in Cd3As2

As the need for ever greater transistor density increases, the commensurate decrease in device size approaches the atomic limit, leading to increased energy loss and leakage currents, reducing energy efficiencies. Alternative state variables, such as electronic spin rather than electronic charge, have the potential to enable more energy-efficient and higher performance devices. These spintronic devices require materials capable of efficiently harnessing the electron spin. Here we show robust spin transport in Cd₃As₂ films up to room temperature. We demonstrate a nonlocal spin valve switch from this material, as well as inverse spin Hall effect measurements yielding spin Hall angles as high as θ_SH = 1.5 and spin diffusion lengths of 10-40 μm. Long spin-coherence lengths with efficient charge-to-spin conversion rates and coherent spin transport up to room temperature, as we show here in Cd₃As₂, are enabling steps toward realizing actual spintronic devices.

Topologically driven linear magnetoresistance in helimagnetic FeP

The helimagnet FeP is part of a family of binary pnictide materials with the MnP-type structure, which share a nonsymmorphic crystal symmetry that preserves generic band structure characteristics through changes in elemental composition. It shows many similarities, including in its magnetic order, to isostructural CrAs and MnP, two compounds that are driven to superconductivity under applied pressure. Here we present a series of high magnetic field experiments on high-quality single crystals of FeP, showing that the resistance not only increases without saturation by up to several hundred times its zero-field value by 35 T, but that it also exhibits an anomalously linear field dependence over the entire range when the field is aligned precisely along the crystallographic c-axis. A close comparison of quantum oscillation frequencies to electronic structure calculations links this orientation to a semi-Dirac point in the band structure, which disperses linearly in a single direction in the plane perpendicular to field, a symmetry-protected feature of this entire material family. We show that the two striking features of magnetoresistance-large amplitude and linear field dependence-arise separately in this system, with the latter likely due to a combination of ordered magnetism and topological band structure.

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.

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.

Large linear magnetoresistance caused by disorder in WTe2-δthin film

Weyl semimetal WTe2has attracted considerable attention owing to its extremely large, unsaturated and quadratic magnetoresistance. Here, we study the magnetotransport properties of WTe2-δthin film, which shows an unsaturated and linear magnetoresistance of up to ∼1650%. A more complex and accurate method, known as the maximum entropy mobility spectrum, is used to analyze the mobility and density of carriers. The results show that linear magnetoresistance can be explained by the classical disorder model because the slope of linear magnetoresistance and the crossover field are proportional to the mobility and inverse mobility, respectively. Furthermore, the validity of the maximum entropy mobility spectrum is validated by the Shubnikov-de Haas oscillations. Moreover, at low temperature, we determined that the unsaturated and near-quadratic magnetoresistance in the WTe1.93thin film can be explained by charge compensation. Note that the electron-hole compensation is broken in the WTe1.42thin film, which indicates that the carrier scattering induced by the disorder may suppress the charge compensation in the WTe2sample with defects/dopants. To summarize, the discovery of disorder-induced linear magnetoresistance allows us to explain different magnetoresistance behaviors of WTe2.

Large longitudinal magnetoresistance of multivalley systems

The longitudinal magnetoresistance (MR) is assumed to be hardly realized as the Lorentz force does not work on electrons when the magnetic field is parallel to the current. However, in some cases, longitudinal MR becomes large, which exceeds the transverse MR. To solve this problem, we have investigated the longitudinal MR considering multivalley contributions based on the classical MR theory. We have showed that the large longitudinal MR is caused by off-diagonal components of a mobility tensor. Our theoretical results agree with the experiments of large longitudinal MR in IV-VI semiconductors, especially in PbTe, for a wide range of temperatures, except for linear MR at low temperatures.

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.

Controllable p-n junctions in three-dimensional Dirac semimetal Cd3As2 nanowires

We demonstrate a controllable p-n junction in a three-dimensional Dirac semimetal (DSM) Cd₃As₂ nanowire with two recessed bottom gates. The device exhibits four different conductance regimes with gate voltages, the unipolar (n-n and p-p) and bipolar (n-p and n-p) regimes, where p-n junctions are formed. The conductance in the p-n junction regimes decreases drastically when a magnetic field is applied perpendicular to the nanowire. In these regimes, the device shows quantum dot behavior, whereas the device exhibits conductance plateaus in the n-n regime at high magnetic fields. Our experiment shows that the ambipolar tunability of DSM nanowires can enable the realization of quantum devices based on quantum dots and electron optics.

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.

Quantized surface transport in topological Dirac semimetal films

Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin film samples, where bulk dimensionality, Fermi energy, and band topology are systematically controlled. We reveal essential involvement of bulk states in the quantized surface transport and the resultant quantum Hall degeneracy depending on the bulk occupation. Our demonstration of surface transport controlled in film samples also paves a way for engineering Fermi-arc-mediated transport in topological semimetals.

Superior Magnetoresistance Performance of Hybrid Graphene Foam/Metal Sulfide Nanocrystal Devices

Interfaces between metals and semiconducting materials can inevitably influence the magnetotransport properties, which are crucial for technological applications ranging from magnetic sensing to storage devices. By taking advantage of this, a metallic graphene foam is integrated with semiconducting copper-based metal sulfide nanocrystals, i.e., Cu₂ZnSnS₄ (copper-zinc-tin-sulfur) without direct chemical bonding and structural damage, which creates numerous nanoboundaries that can be basically used to tune the magnetotransport properties. Herein, the magnetoresistance of a graphene foam is enhanced from nearly 90 to 130% at room temperature and under the application of 5 T magnetic field strength due to the addition of Cu₂ZnSnS₄ nanocrystals in high densities. We believe that the enhancement of magnetoresistance in hybrid graphene foam/Cu₂ZnSnS₄ nanocrystals is due to the evolution of the mobility fluctuation mechanism, triggered by the formation of nanoboundaries. Incorporating Cu₂ZnSnS₄ nanocrystals into a graphene foam not only provides an effective way to further enhance the magnitude of magnetoresistance but also opens a suitable window to achieve efficient and highly functional magnetic sensors with a large, linear, and controllable response.

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.

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.

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.

High Hole Mobility and Nonsaturating Giant Magnetoresistance in the New 2D Metal NaCu4Se4 Synthesized by a Unique Pathway

The new compound NaCu₄Se₄ forms by the reaction of CuO and Cu in a molten sodium polyselenide flux, with the existence of CuO being unexpectedly critical to its synthesis. It adopts a layered hexagonal structure (space group P6₃/ mmc with cell parameters a = 3.9931(6) Å and c = 25.167(5) Å), consisting of infinite two-dimensional [Cu₄Se₄]^- slabs separated by Na⁺ cations. X-ray photoelectron spectroscopy suggests that NaCu₄Se₄ is mixed-valent with the formula (Na⁺)(Cu⁺)₄(Se^2-)(Se^-)(Se₂)^2-. NaCu₄Se₄ is a p-type metal with a carrier density of ∼10²¹ cm^-3 and a high hole mobility of ∼808 cm² V^-1 s^-1 at 2 K based on electronic transport measurements. First-principles calculations suggest the density of states around the Fermi level are composed of Cu-d and Se-p orbitals. At 2 K, a very large transverse magnetoresistance of ∼1400% was observed, with a nonsaturating, linear dependence on field up to 9 T. Our results indicate that the use of metal oxide chemical precursors can open reaction paths to new low-dimensional compounds.

Nonsaturating large magnetoresistance in semimetals

The rapidly expanding class of quantum materials known as topological semimetals (TSMs) displays unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far, many possible sources of extraordinarily large nonsaturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to available theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle ([Formula: see text]), along with magnetoresistance in four different nonmagnetic semimetals with high mobilities, NbP, TaP, NbSb₂, and TaSb₂, all of which exhibit nonsaturating large magnetoresistance (MR). We find that the distinctly different temperature dependences, [Formula: see text], and the values of [Formula: see text] in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP are uncompensated semimetals with linear dispersion, in which the nonsaturating magnetoresistance arises due to guiding center motion, while NbSb₂ and TaSb₂ are compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous nonsaturating large magnetoresistance in TSMs.

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.

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.

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.

Gate-tuned quantum Hall states in Dirac semimetal (Cd1-x Zn x )3As2

The recent discovery of topological Dirac semimetals (DSMs) has provoked intense curiosity not only regarding Weyl physics in solids but also about topological phase transitions originating from DSMs. One specific area of interest is controlling the dimensionality to realize two-dimensional quantum phases such as quantum Hall and quantum spin Hall states. For investigating these phases, the Fermi level is a key controlling parameter. From this perspective, we report the carrier density control of quantum Hall states realized in thin films of DSM Cd₃As₂. Chemical doping of Zn combined with electrostatic gating has enabled us to tune the carrier density both over a wide range and continuously, even across the charge neutrality point. Comprehensive analyses of gate-tuned quantum transport have revealed Landau-level formation from linearly dispersed sub-bands and its contribution to the quantum Hall states. Our findings also pave the way for investigating the low-energy physics near the Dirac points of DSMs.

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.

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.

Observation of the Quantum Hall Effect in Confined Films of the Three-Dimensional Dirac Semimetal Cd_{3}As_{2}

The magnetotransport properties of epitaxial films of Cd_{3}As_{2}, a paradigm three-dimensional Dirac semimetal, are investigated. We show that an energy gap opens in the bulk electronic states of sufficiently thin films and, at low temperatures, carriers residing in surface states dominate the electrical transport. The carriers in these states are sufficiently mobile to give rise to a quantized Hall effect. The sharp quantization demonstrates surface transport that is virtually free of parasitic bulk conduction and paves the way for novel quantum transport studies in this class of topological materials. Our results also demonstrate that heterostructuring approaches can be used to study and engineer quantum states in topological semimetals.

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.

Anomalous cyclotron mass dependence on the magnetic field and Berry's phase in (Cd1-x-y Zn x Mn y )3As2 solid solutions

Shubnikov-de Haas (SdH) effect and magnetoresistance measurements of single crystals of diluted II-V magnetic semiconductors (Cd_1-x-y Zn _x Mn _y )₃As₂ (x  +  y  =  0.4, y  =  0.04 and 0.08) are investigated in the temperature range T  =  4.2 ÷ 300 K and in transverse magnetic field B  =  0 ÷ 25 T. The values of the cyclotron mass m _c, the effective g-factor g*, and the Dingle temperature T _D are defined. In one of the samples (y  =  0.04) a strong dependence of the cyclotron mass on the magnetic field m _c(B)  =  m _c(0)  +  αB is observed. The value of a phase shift close to β  =  0.5 indicates the presence of Berry phase and 3D Dirac fermions in a single crystals of (Cd_1-x-y Zn _x Mn _y )₃As₂ in one of the samples (y  =  0.08).

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd_{3}As_{2}, or Na_{3}Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

A magnetic topological semimetal Sr1-yMn1-zSb2 (y, z < 0.1)

Weyl (WSMs) evolve from Dirac semimetals in the presence of broken time-reversal symmetry (TRS) or space-inversion symmetry. The WSM phases in TaAs-class materials and photonic crystals are due to the loss of space-inversion symmetry. For TRS-breaking WSMs, despite numerous theoretical and experimental efforts, few examples have been reported. In this Article, we report a new type of magnetic semimetal Sr_1-yMn_1-zSb₂ (y, z < 0.1) with nearly massless relativistic fermion behaviour (m^∗ =  0.04 - 0.05m₀, where m₀ is the free-electron mass). This material exhibits a ferromagnetic order for 304 K  <  T  <  565 K, but a canted antiferromagnetic order with a ferromagnetic component for T  <  304 K. The combination of relativistic fermion behaviour and ferromagnetism in Sr_1-yMn_1-zSb₂ offers a rare opportunity to investigate the interplay between relativistic fermions and spontaneous TRS breaking.