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Electronic phase transition in graphene in a magnetic field

Graphene is comprised of a single layer of C atoms in a hexagonal lattice array.  The electronic state of graphene is of great interest because the electron energy increases linearly with momentum, just like for photons and neutrinos.  This is called a massless, Dirac dispersion.  The nature of the electronic state at zero energy (the “Dirac point”) in a strong magnetic field H is currently the subject of theoretical debate. The figure shows the resistance R0 at the Dirac point increasing abruptly by over 3 decades from 10 kΩ to 40.  Two competing theories describing the high-field insulating state are shown in the insets.   In the charge-density-wave (CDW) model (top inset), electrons preferentially occupy every other site (red circles).  In the “Kekule” model (lower inset), the bonds linking adjacent C atoms (blue ovals) shorten slightly in an alternating pattern reminiscent of benzene.  Which of these models (or future ones) is correct is being actively researched.
Resistance at the Dirac point
Figure 1 Plot of the resistance R0 at the Dirac point (red curve) vs. applied magnetic field H at temperature 0.3 K. The steep increase to 40 MΩ signals a phase transition to an insulating state at the critical field Hc. The sketches show the CDW (upper inset) and Kekule models (lower).