A high-magnetic-field-induced density-wave state in 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.

Possible charge ordering and anomalous transport in graphene/graphene quantum dot heterostructure

Observations of superconductivity and charge density waves (CDW) in graphene have been elusive thus far due to weak electron-phonon coupling (EPC) interactions. Here, we report a unique observation of anomalous transport and multiple charge ordering phases at high temperatures (T1∼213K,T2∼325K) in a 0D-2D van der Waals (vdW) heterostructure comprising of single layer graphene (SLG) and functionalized (amine) graphene quantum dots (GQD). The presence of functionalized GQD contributed to charge transfer with shifting of the Dirac point ∼ 0.05 eV above the Fermi level (ab initio   simulations) and carrier densityn∼-0.3×1012 cm-2confirming p-doping in SLG and two-fold increase in EPC interaction was achieved. Moreover, we elucidate the interplay between electron-electron and electron-phonon interactions to substantiate high temperature EPC driven charge ordering in the heterostructure through analyses of magnetotransport and weak anti-localization (WAL) framework. Our results provide impetus to investigate strongly correlated phenomena such as CDW and superconducting phase transitions in novel graphene based heterostructures.

Quantum-Hall physics and three dimensions

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivityσxyof a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivitiesσxyaccompanied by minima in the longitudinal resistivityρxx, can also be found in 3D materials. However, since typicallyρxxremains finite and a quantitative relation betweenσxyand the conductance quantume2/hcould not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the center stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.

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.

Unconventional Hall response in the quantum limit of HfTe5

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.

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.

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.

Emptying Dirac valleys in bismuth using high magnetic fields

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, B_empty, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across B_empty to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results but the Coulomb interaction may play a role in shaping the fine details.

Spear-anvil point-contact spectroscopy in pulsed magnetic fields

We describe a new design and experimental technique for point-contact spectroscopy in non-destructive pulsed magnetic fields up to 70 T. Point-contact spectroscopy uses a quasi-dc four-point measurement of the current and voltage across a spear-anvil point-contact. The contact resistance could be adjusted over three orders of magnitude by a built-in fine pitch threaded screw. The first measurements using this set-up were performed on both single-crystalline and exfoliated graphite samples in a 150 ms, pulse length 70 T coil at 4.2 K and reproduced the well known point-contact spectrum of graphite and showed evidence for a developing high field excitation above 35 T, the onset field of the charge-density wave instability in graphite.

Two phase transitions induced by a magnetic field in graphite

Different instabilities have been speculated for a three-dimensional electron gas confined to its lowest Landau level. The phase transition induced in graphite by a strong magnetic field, and believed to be a charge density wave, is the only experimentally established case of such instabilities. Studying the magnetoresistance in graphite for the first time up to 80 T, we find that the magnetic field induces two successive phase transitions, consisting of two distinct ordered states each restricted to a finite field window. In both states, an energy gap opens up in the out-of-plane conductivity and coexists with an unexpected in-plane metallicity for a fully gap bulk system. Such peculiar metallicity may arise as a consequence of edge-state transport expected to develop in the presence of a bulk gap.

Landau spectrum and twin boundaries of bismuth in the extreme quantum limit

The Landau spectrum of bismuth is complex and includes many angle-dependent lines in the extreme quantum limit. The adequacy of single-particle theory to describe this spectrum in detail has been an open issue. Here, we present a study of angle-resolved Nernst effect in bismuth, which maps the angle-resolved Landau spectrum for the entire solid angle up to 28 T. The experimental map is in good agreement with the results of a theoretical model with parabolic dispersion for holes and an extended Dirac Hamiltonian for electrons. The angular dependence of additional lines in the Landau spectrum allows us to uncover the mystery of their origin. They correspond to the lines expected for the hole Landau levels in a secondary crystal tilted by 108°, the angle between twinned crystals in bismuth. According to our results, the electron reservoirs of the two identical tilted crystals have different chemical potentials, and carriers across the twin boundary have different concentrations. An exceptional feature of this junction is that it separates two electron-hole compensated reservoirs. The link between this edge singularity and the states wrapping a three-dimensional electron gas in the quantum limit emerges as an outstanding open question.

Nernst response of the Landau tubes in graphite across the quantum limit

We report on a study of the Nernst effect in graphite extended up to 45 T. The Nernst response sharply peaks when a Landau tube is squeezed inside the thermally fuzzy Fermi surface and presents a temperature-independent fixed point when the tube flattens to a single ring. Beyond the quantum limit, the onset of the field-induced phase transition leads to a drastic drop in the Nernst response signaling the sudden vanishing of Landau tubes. The magnitude of this drop suggests the destruction of multiple Landau tubes possibly as a result of simultaneous nesting of the electron and hole pockets.

Phase diagram of bismuth in the extreme quantum limit

Elemental bismuth provides a rare opportunity to explore the fate of a three-dimensional gas of highly mobile electrons confined to their lowest Landau level. Coulomb interaction, neglected in the band picture, is expected to become significant in this extreme quantum limit, with poorly understood consequences. Here, we present a study of the angular-dependent Nernst effect in bismuth, which establishes the existence of ultraquantum field scales on top of its complex single-particle spectrum. Each time a Landau level crosses the Fermi level, the Nernst response sharply peaks. All such peaks are resolved by the experiment, and their complex angular dependence is in very good agreement with the theory. Beyond the quantum limit, we resolve additional Nernst peaks signaling a cascade of additional Landau sublevels caused by electron interaction.