Emptying Dirac valleys in bismuth using high magnetic fields

Electronic instability in pressured black phosphorus under strong magnetic field

In this paper, we have systematically studied the electronic instability of pressured black phosphorous (BP) under strong magnetic field. We first present an effective model Hamiltonian for pressured BP near theLifshitzpoint. Then we show that when the magnetic field exceeds a critical value, the nodal-line semimetal (NLSM) state of BP with a small band overlap re-enters the semiconductive phase by re-opening a small gap. This results in a narrow-bandgap semiconductor with a partially flat valence band edge. Moreover, we demonstrate that above this critical magnetic field, two possible instabilities, i.e. charge density wave phase and excitonic insulator (EI) phase, are predicted as the ground state for high and low doping concentrations, respectively. By comparing our results with the experiment (Sunet al2018Sci. Bull.631539), we suggest that the field-induced instability observed experimentally corresponds to an EI. Furthermore, we propose that the semimetallic BP under pressure with small band overlaps may provide a good platform to study the magneto-exciton insulators. Our findings bring the first insight into the electronic instability of topological NLSM in the quantum limit.

Metamagnetic multiband Hall effect in Ising antiferromagnet ErGa2

Frustrated rare-earth-based intermetallics provide a promising platform for emergent magnetotransport properties through exchange coupling between conduction electrons and localized rare-earth magnetic moments. Metamagnetism, the abrupt change of magnetization under an external magnetic field, is a signature of first-order magnetic phase transitions; recently, metamagnetic transitions in frustrated rare earth intermetallics have attracted interest for their accompanying nontrivial spin structures (e.g., skyrmions) and associated nonlinear and topological Hall effects (THE). Here, we present metamagnetism-induced Hall anomalies in single-crystalline ErGa2, which recalls features arising from the THE but wherein the strong Ising-type anisotropy of Er moments prohibits noncoplanar spin structures. We show that the observed anomalies are neither due to anomalous Hall effect nor THE; instead, can be accounted for via 4f-5d interactions which produce a band-dependent mobility modulation. This leads to a pronounced multiband Hall response across the magnetization process-a metamagnetic multiband Hall effect that resembles a topological-Hall-like response but without nontrivial origins. The present findings may be of general relevance in itinerant metamagnetic systems regardless of coplanar/noncoplanar nature of spins and are important for the accurate identification of Hall signals due to emergent magnetic fields.

Quantum-classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering quantum effects under a magnetic field, such as the Landau quantization and quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum-classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of the thermal Green's function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.

Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe5

The quantum limit (QL) of an electron liquid, realised at strong magnetic fields, has long been proposed to host a wealth of strongly correlated states of matter. Electronic states in the QL are, for example, quasi-one dimensional (1D), which implies perfectly nested Fermi surfaces prone to instabilities. Whereas the QL typically requires unreachably strong magnetic fields, the topological semimetal ZrTe5 has been shown to reach the QL at fields of only a few Tesla. Here, we characterize the QL of ZrTe5 at fields up to 64 T by a combination of electrical-transport and ultrasound measurements. We find that the Zeeman effect in ZrTe5 enables an efficient tuning of the 1D Landau band structure with magnetic field. This results in a Lifshitz transition to a 1D Weyl regime in which perfect charge neutrality can be achieved. Since no instability-driven phase transitions destabilise the 1D electron liquid for the investigated field strengths and temperatures, our analysis establishes ZrTe5 as a thoroughly understood platform for potentially inducing more exotic interaction-driven phases at lower temperatures.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

The topology of the surface states of a bismuth crystal remains an ongoing debate. Here, the authors observe surface electric conductivity with a magnetic field parallel to the two-dimensional boundary between the three-dimensional bismuth crystal and vacuum, but this effect is absent in antimony crystals indicating a link between band symmetry and boundary conductance.

Spin-valley locking and bulk quantum Hall effect in a noncentrosymmetric Dirac semimetal BaMnSb2

Spin-valley locking in monolayer transition metal dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a Dirac semimetal BaMnSb2. This is revealed by comprehensive studies using first principles calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy measurements. Moreover, this material also exhibits a stacked quantum Hall effect (QHE). The spin-valley degeneracy extracted from the QHE is close to 2. This result, together with the Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we also observed a plateau in the z-axis resistance, suggestive of a two-dimensional chiral surface state present in the quantum Hall state. These findings establish BaMnSb2 as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states.

Wide Critical Fluctuations of the Field-Induced Phase Transition in Graphite

In the immediate vicinity of the critical temperature (T_{c}) of a phase transition, there are fluctuations of the order parameter that reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperature window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to a high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20%) reduction in the amplitude of the magnetic field (from 33 to 27 T) leads to a threefold decrease of T_{c} and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T_{c}. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the 3DXY universality class as in the case of the ^{4}He superfluid transition.

Critical point for Bose-Einstein condensation of excitons in graphite

An exciton is an electron-hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose-Einstein condensation of excitons. At this critical field, hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.

Capacitive detection of magnetostriction, dielectric constant, and magneto-caloric effects in pulsed magnetic fields

We report on the development of a capacitance measuring system that allows measurements of capacitance in pulsed magnetic fields up to 61 T. By using this system, magnetic-field responses of various physical quantities, such as magnetostriction, magnetic-field-induced change in complex dielectric constant, and magneto-caloric effect, can be investigated in pulsed-magnetic-field conditions. Here, we examine the validity of our system for investigations of these magnetic-field-induced phenomena in pulse magnets. For the magnetostriction measurement, magnetostriction of a specimen can be measured through a change in the capacitance between two aligned electrodes glued on the specimen and a dilatometer. We demonstrate a precise detection of valley polarization in semimetallic bismuth through a magnetostriction signal with a resolution better than 10^-6 of the relative length change. For the magnetic-field-induced change in complex dielectric constant, we successfully observed clear dielectric anomalies accompanied by magnetic/magnetoelectric phase transitions in multiferroic Pb(TiO)Cu₄(PO₄)₄. For the measurement of magneto-caloric effect, a magnetic-field-induced change in sample temperature was verified for Gd₃Ga₅O₁₂ with a capacitance thermometer made of a non-magnetic ferroelectric compound KTa_1-xNb_xO₃ (x = 0.02) whose capacitance is nearly field-independent. These results show that our capacitance measuring system is a promising tool to study various magnetic-field-induced phenomena, which have been difficult to detect in pulsed magnetic fields.

Investigation of growth characteristics and semimetal-semiconductor transition of polycrystalline bis-muth thin films

The preferred orientation growth characteristics and surface roughness of polycrystalline bis-muth (Bi) thin films fabricated on glass substrates using the molecular beam epitaxy method were investigated at temperatures ranging from 18 to 150°C. The crystallization and morphology were analyzed in detail and the polycrystalline metal film structure-zone model (SZM) was modified to fit the polycrystalline Bi thin film. The boundary temperature between Zone T and Zone II in the SZM shifted to higher temperatures with the increase in film thickness or the decrease of growth rate. Furthermore, the effect of the thickness and surface roughness on the transport properties was investigated, especially for Bi thin films in Zone II. A two-transport channels model was adopted to reveal the influence of the film thickness on the competition between the metallic surface states and the semiconducting bulk states, which is consistent with the results of Bi single-crystal films. Therefore, the polycrystalline Bi thin films are expected to replace the single-crystal films in the application of spintronic devices.

Thermodynamic evidence of magnetic-field-induced complete valley polarization in bismuth

We investigated the fundamental physical properties in the ultra-quantum limit state of bismuth through measurements of magnetoresistance, magnetization, magnetostriction, and ultrasound attenuation in magnetic fields up to 60T. For magnetic fields applied along the bisectrix direction of a single crystal, a drastic sign reversal in magnetostriction was observed at approximately 39T, which could be ascribed to the complete valley polarization in the electron Fermi pockets. The application of magnetic fields along the binary direction presented an anomalous feature at approximately 50T only in the magnetoresistance. The emergence of a field-induced splitting of a valley was proposed as a possible origin of this anomaly.

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.

Corrections to the magnetoresistance formula for semimetals with Dirac electrons: the Boltzmann equation approach validated by the Kubo formula

The magnetoresistance (MR) in semimetals with Dirac (or Weyl) electrons and free holes is investigated on the basis of the Boltzmann theory. The MR is modified from the conventional results with free electrons and holes in a very complex way due to the correction of the Dirac dispersion. The obtained formula explicitly includes the magnetic field dependence, which is very useful for the analysis of experimental results. In order to verify the validity of our results, the results obtained by the Boltzmann approach are compared with those by the Kubo theory. It is revealed that, by taking into account the field dependence of carrier density, the MR obtained by the Boltzmann theory almost perfectly agrees with that based on the Kubo theory even in the high-field region (in the quantum limit) except for the quantum oscillations. It is also shown that the MR in semimetals increases linearly with respect to the field in the quantum limit due to the drastic change of the carrier density, which is a significant characteristic of semimetals.

Magnetoresistance and valley degree of freedom in bulk bismuth

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Realization of a Valley Superlattice

In a number of widely studied materials, such as Si, AlAs, Bi, graphene, MoS_{2}, and many transition metal dichalcogenide monolayers, electrons acquire an additional, spinlike degree of freedom at the degenerate conduction band minima, also known as "valleys." External symmetry-breaking fields such as mechanical strain, or electric or magnetic fields, can tune the valley polarization of these materials, making them suitable candidates for "valleytronics." Here we study a quantum well of AlAs, where the two-dimensional electrons reside in two energetically degenerate valleys. By fabricating a strain-inducing grating on the sample surface, we engineer a spatial modulation of the electron population in different valleys, i.e., a "valley superlattice" in the quantum well plane. Our results establish a novel manipulation technique of the valley degree of freedom, paving the way to realizing a valley-selective layered structure in multivalley materials, with potential application in valleytronics.