Magnetic field induced (thermodynamic) phase transitions in graphite

One of the most common and reliable indicators of a phase transition into a new state of matter is anomalies (e.g. discontinuities or singularities) in thermodynamic properties such as specific heat capacity. This is how the superfluid phases of helium 4 and helium 3 were both discovered. Further transport experiments were required to show that the new states of matter were actually superfluids. This point was highlighted at the end of my last post.

In 2014, I wrote about the puzzling magnetoresistance of graphite and some experiments that were interpreted as evidence of a metal-insulator transition when the electrons are in the lowest Landau level of the graphene layers. This interpretation was partly motivated by theoretical predictions of charge density wave (CDW) transitions in this regime. I expressed some caution and skepticism about this interpretation, highlighting problems in other systems where magnetoresistance anomalies were given such interpretations.  I suggested that thermodynamic measurements should be performed.

In 2015, I highlighted similar issues, suggesting there is no metal-insulator transition in extremely large magnetoresistance materials, contrary to claims in luxury journals. Within two months my claim was shown to be correct.

I was delighted to recently learn from Benoit Fauque that he and his collaborators have now performed measurements of the specific heat of graphite in high magnetic fields.

Wide critical fluctuations of the field-induced phase transition in graphite 

Christophe Marcenat, Thierry Klein, David LeBoeuf, Alexandre Jaoui, Gabriel Seyfarth, Jozef Kačmarčík, Yoshimitsu Kohama, Hervé Cercellier, Hervé Aubin, Kamran Behnia, Benoît Fauqué

The figure below shows the ratio of the specific heat to temperature versus temperature for different values of the magnetic field. In an elemental metal, this would be the temperature and field-independent and equal to the specific heat coefficient gamma. The temperature dependence and peak at a particular temperature are reminiscent of the behaviour for a BCS superconductor or quasi-one-dimensional CDW transition.

I want to highlight a couple of nice things about this data and the analysis in the paper. First, the value of the specific heat coefficient at small fields is several orders of magnitude smaller than in an elemental metal (due to the low density and effective mass of charge carriers) and has a value consistent with band structure calculations. I presume that measuring such small values is a significant experimental achievement. 

Secondly, the linear increase in gamma with the magnetic field and the rate of increase are also consistent with band structure. These agreements increase confidence in the reliability of the measurements and their identification with electronic contributions to the specific heat. For context, the field of strongly correlated electron materials is littered with dubious identifications. An example concerns claims of spinons in an organic charge-transfer salt.

Most importantly the data above suggests that there is a thermodynamic phase transition and that the transition temperature increases with the magnetic field. The corresponding phase diagram can be compared to that suggested by the magnetoresistance measurements from 2014. This is done in the figure below.

The fact that the transition temperature deduced from the specific heat is tracking the anomalies in the earlier magnetoresistance measurements suggests the identification of the latter with a metal-insulator transition back in 2014 was correct. I am happy to be have been proven wrong! That's good science!