 Cyclotron mass in a graphene cone

ID: cyclotron-mass-in-a-graphene-cone

A massless-cone description permits a nonzero cyclotron effective mass. For a circular constant-energy contour of area

S (E) = π E^{2} / (ℏ v_{F})^{2}

, the semiclassical definition gives

m_{c} = \frac{ℏ ^{2}}{2 π} \frac{d S}{d E} = \frac{∣ E _{F} ∣}{v _{F}^{2}} = \frac{ℏ π ∣ n ∣}{v _{F}} .

The vanishing mass parameter in a Dirac Hamiltonian and the finite cyclotron response away from neutrality are different statements. This makes the temperature dependence of Shubnikov-de Haas oscillations a useful test of the dispersion rather than a measurement of an Electron's vacuum rest mass.

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