In a presence of a magnetic field, the charge carriers of a Fermi sea group into Landau levels (LLs). At high enough magnetic field, the so called quantum limit is reached when the carriers are confined into the lowest Landau levels. In such limit electronic correlations are at work to generate new electronic states such as composite fermions and topological states in the fractional quantum Hall effect in two dimensional systems. In three dimensions this limit is still largely unexplored but exotic states of matter have been predicted to emerge. The exploration of this limit in semi-metal graphite started more than three decades ago. Renewed interest arose recently with magnetoresistance measurements that revealed unexpected transitions towards phases where transport anisotropies are consistent with the existence of chiral surface states [B. Fauque et al., Phys. Rev. Lett. 110, 266601 (2013) see also comment by J. Alicea in the journal club for condensed matter physics]. Exclusively studied with transport measurement so far the exact nature of those phases and the mechanism responsible for their appearance remain elusive.
|
Phase diagram of the quantum limit of graphite, extracted from ultrasound (colored circles) and magnetoresistance measurements (open symbols). We detect 4 transition lines: α, β, γ and δ signaled by a peak in the sound attenuation or by a discontinuity in the sound velocity (see figure below).
|
Inter-layer magnetoresistance of HOPG graphite at 4.2 K. Bottom panel: ultrasound properties (sound velocity in blue, ultrasound attenuation in orange) at 4.2 K in HOPG sample. What appears as broad and smooth features in the resistance appears as sharp transitions in the ultrasound properties.
|
We report for the first time a study of the elastic constant and ultrasound attenuation of graphite in magnetic fields up to 55 T. We show that this probe is more sensitive than magnetoresistance and allows drawing a more detailed phase diagram (see Figure). With the ultrasound technique we were able to provide the first thermodynamic evidence for the existence of a series of phase transitions in the quantum limit of graphite. Moreover, above the onset temperature, we detect a softening of the sound velocity, indicating that a Landau level crossing occurs in the vicinity of the phase transition. Finally by performing a thermodynamic analysis of the sound velocity anomaly, we conclude this electronic phase is likely to have a strong coupling to the lattice and uniaxial strains.
The role of the lattice in the formation of those states has so far been overlooked theoretically. These results have strong implications for our understanding of quantum limited electron fluids. See published article: Thermodynamic signatures of the field-induced states of graphite D. LeBoeuf, C. W. Rishau, G. Seyfarth, R. Küchler, M. Berdern, S. Wiedmann, W. Tabis, M. Frachet, K. Behnia, B. Fauqué Nat. Comm. 8 1337 (2017) |