Non-linear transport in field-induced insulating states of graphite

Graphite exhibits multi-stage phase transitions in the quantum-limit states realized by magnetic fields applied along the c-axis. Despite extensive studies on this phenomenon, the origin remains a matter of debate to this day. We performed high-field magnetotransport measurements on single crystals of graphite, focusing on the non-linear conductivity in pulsed-magnetic fields of up to 75 T. The longitudinal magnetoresistance exhibits distinct non-linearity not only in the first but also in the second field-induced phases.

💡 Research Summary

In this work the authors investigate the nonlinear transport properties of Kish graphite subjected to ultra‑high magnetic fields applied along the crystallographic c‑axis, extending up to 75 tesla. Graphite, a semimetal with a layered structure, enters a quasi‑quantum‑limit regime already at modest fields (~7 T) where only the spin‑split lowest electron and hole Landau sub‑bands intersect the Fermi level. In this reduced‑dimensional state electron‑electron interactions become dominant, and a variety of many‑body instabilities have been proposed, including charge‑density‑wave (CDW), spin‑density‑wave (SDW), and excitonic condensate phases. Earlier experiments have identified a steep increase of the out‑of‑plane resistance around 30 T that sharpens at low temperature, signalling a field‑induced phase (often called Phase A) that terminates near 53 T. More recent studies have suggested additional phases (Phase B between 53 T and ~75 T and Phase C above 75 T), but their microscopic origin remains controversial.

The authors prepared high‑quality Kish graphite single crystals, attached contacts for measuring the c‑axis resistance (Rc), and performed pulsed‑field magnetotransport experiments at temperatures between 1.5 K and 4.2 K. Two pulsed‑magnet systems were employed: a 56 T magnet with a 36 ms pulse and a 75 T magnet with a 4 ms pulse. For the 56 T measurements they recorded full current–voltage (I–E) characteristics at several fixed magnetic fields; for the 75 T measurements, because of the very short pulse duration, they instead measured Rc as a function of applied current (0.2 mA and 0.5 mA).

The 56 T data reveal a clear double‑peak structure in Rc: a first peak at 34 T (the onset of Phase A) and a second peak at 53 T (the termination of Phase A and the beginning of Phase B). The peak amplitude grows as temperature is lowered, confirming the thermodynamic nature of the transition. I–E curves are linear at 24 T, but become increasingly super‑linear at higher fields. At 41.2 T a pronounced upward curvature appears at the highest electric fields, indicating the onset of non‑ohmic behavior. Similar super‑linear I–E traces are observed within Phase A at 45.5 T and 50 T, and also in Phase B at 56.3 T, albeit only at the lowest temperature (≈1.3 K). These observations demonstrate that nonlinear conduction is not confined to the first field‑induced phase but persists into the second phase.

In the 75 T experiments the authors could not obtain reliable I–E curves at the pulse maximum, but they compared Rc measured with two different currents. At 0.2 mA the double‑peak structure is clearly visible, whereas at 0.5 mA the peaks are strongly suppressed. This current‑dependent reduction of the resistance peaks is a hallmark of nonlinear transport: higher electric fields effectively “depin” the underlying ordered state, leading to an enhanced conductivity.

The authors discuss two principal interpretations. The first follows earlier work that attributes the nonlinearity to the sliding of a density‑wave condensate (CDW or SDW). In such a scenario a threshold electric field E0 separates the pinned (ohmic) regime from the sliding (non‑ohmic) regime. Theory predicts that E0 should increase as temperature falls below the transition temperature Tc(H) and should decrease as the magnetic field approaches the upper boundary of the density‑wave phase (≈53 T) because Tc(H) vanishes there. While the experimental data show an increase of E0 between 41.2 T and 45.5 T, they do not reveal the expected reduction near 50 T, casting doubt on a simple density‑wave sliding picture.

The second interpretation considers the possibility that Phase A (and perhaps Phase B) is an excitonic insulator. In an excitonic condensate the elementary carriers are charge‑neutral electron‑hole pairs; collective motion of such pairs would not generate a sliding current, so one would naively expect purely ohmic behavior. However, if a sufficiently strong electric field breaks the pairs, a sudden increase in free carriers could produce a super‑linear I–E characteristic. In this case the threshold field would be expected to grow monotonically with magnetic field, consistent with the observed trend of E0 increasing beyond 47 T. Recent studies on the prototypical excitonic material Ta₂NiSe₅, which remains ohmic up to very high fields, suggest that pair‑breaking nonlinearity is not universal, but the graphite data leave the question open.

Overall, the paper provides the first systematic evidence that nonlinear transport appears not only in the well‑studied Phase A but also in the higher‑field Phase B. The authors conclude that while the sliding‑density‑wave picture captures some aspects of the data, it cannot fully explain the observed field dependence of the threshold field. Conversely, an excitonic‑pair‑breaking scenario remains plausible but requires further experimental verification. They call for extended measurements at higher fields, finer temperature control, and possibly complementary probes (e.g., ultrasound, NMR) to discriminate between competing theories and to elucidate the nature of the multi‑stage field‑induced transitions in graphite.