Strong magnetic field induces at least two phase transitions in graphite beyond the quantum limit where many-body effects are expected. We report on a study using a state-of-the-art nondestructive magnet allowing to attain 90.5 T at 1.4 K, which reveals a new field-induced phase and evidence that the insulating state destroyed at 75 T is an excitonic condensate of electron-hole pairs. By monitoring the angle dependence of in-plane and out-of-plane magnetoresistance, we distinguish between the role of cyclotron and Zeeman energies in driving various phase transitions. We find that, with the notable exception of the transition field separating the two insulating states, the threshold magnetic field for all other transitions display an exact cosine angular dependence. Remarkably, the threshold field for the destruction of the second insulator (phase B) is temperature-independent with no detectable Landau-level crossing nearby. We conclude that the field-induced insulator starts as a weak-coupling spin-density-wave, but ends as a strong-coupling excitonic insulator of spin-polarized electron-hole pairs.

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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.

We report a study of fermiology, electrical anisotropy, and Fermi liquid properties in the layered ternary boride MoAlB, which could be peeled into two-dimensional (2D) metal borides (MBenes). By studying the quantum oscillations in comprehensive methods of magnetization, magnetothermoelectric power, and torque with the first-principle calculations, we reveal three types of bands in this system, including two 2D-like electronic bands and one complex three-dimensional-like hole band. Meanwhile, a large out-of-plane electrical anisotropy (ρbb /ρaa ∼ 1100 and ρbb /ρcc ∼ 500, at 2 K) was observed, which is similar to those of the typical anisotropic semimetals but lower than those of some semiconductors (up to 105). After calculating the Kadowaki–Woods ratio (KWR = A/γ 2), we observed that the ratio of the in-plane A a,c /γ 2 is closer to the universal trend, whereas the out-of-plane A b /γ 2 severely deviates from the universality. This demonstrates a 2D Fermi liquid behavior. In addition, MoAlB cannot be unified using the modified KWR formula like other layered systems (Sr2RuO4 and MoOCl2). This unique feature necessitates further exploration of the Fermi liquid property of this layered molybdenum compound.