Magnetic field tuning of an excitonic insulator between the weak and strong coupling regimes in quantum limit graphite

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.

Crossover between strongly coupled and weakly coupled exciton superfluids

In fermionic systems, superconductivity and superfluidity occur through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, which is challenging in electronic systems. We studied graphene double layers separated by an atomically thin insulator. Under applied magnetic field, electrons and holes couple across the barrier to form bound magneto-excitons whose pairing strength can be continuously tuned by varying the effective layer separation. Using temperature-dependent Coulomb drag and counterflow current measurements, we were able to tune the magneto-exciton condensate through the entire phase diagram from weak to strong coupling. Our results establish magneto-exciton condensates in graphene as a model platform to study the crossover between two bosonic quantum condensate phases in a solid-state system.

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.

Non-saturating quantum magnetization in Weyl semimetal TaAs

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

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.

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.

Quantum limit transport and destruction of the Weyl nodes in TaAs

Weyl fermions are a recently discovered ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. Here we use magnetic fields up to 95 T to drive the Weyl semimetal TaAs far into its quantum limit, where only the purely chiral 0th Landau levels of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 T: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 T we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral Landau levels. Above 80 T we observe strong ultrasonic attenuation below 2 K, suggesting a mesoscopically textured state of matter. These results point the way to inducing new correlated states of matter in the quantum limit of Weyl semimetals.

Thermodynamic signatures of the field-induced states of graphite

When a magnetic field confines the carriers of a Fermi sea to their lowest Landau level, electron−electron interactions are expected to play a significant role in determining the electronic ground state. Graphite is known to host a sequence of magnetic field-induced states driven by such interactions. Three decades after their discovery, thermodynamic signatures of these instabilities are still elusive. Here we report the detection of these transitions with sound velocity measurements. The evolution of elastic constant anomalies with temperature and magnetic field allows to draw a detailed phase diagram which shows that the ground state evolves in a sequence of thermodynamic phase transitions. Our analysis indicates that the electron−electron interaction is not the sole driving force of these transitions and that lattice degrees of freedom play an important role.

Previous transport studies of graphite in strong magnetic fields have found a sequence of phase transitions with a still unresolved microscopic origin. Here the authors present ultrasound measurements enabling sharper resolution and demonstrating the thermodynamic nature of these transitions.

Charge Density Waves in Graphite: Towards the Magnetic Ultraquantum Limit

Graphite is a model system for the study of three-dimensional electrons and holes in the magnetic quantum limit, in which the charges are confined to the lowest Landau levels. We report magneto-transport measurements in pulsed magnetic fields up to 60 T, which resolve the collapse of two charge density wave states in two, electron and hole, Landau levels at 52.3 and 54.2 T, respectively. We report evidence for a commensurate charge density wave at 47.1 T in the electron Landau level, and discuss the likely nature of the density wave instabilities over the full field range. The theoretical modeling of our results predicts that the ultraquantum limit is entered above 73.5 T. This state is an insulator, and we discuss its correspondence to the "metallic" state reported earlier. We propose that this (interaction-induced) insulating phase supports surface states that carry no charge or spin within the planes, but does, however, support charge transport out of plane.