Abstract
We use pseudo-quantum electrodynamics in order to describe the full electromagnetic interaction of the p electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the T→0 conductivity after a smooth zero-frequency limit is taken in Kubo’s formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous quantum valley Hall effect below an activation temperature of the order of 2 K. The transverse (Hall) valley conductivity is evaluated exactly and shown to coincide with the one in the usual quantum Hall effect. Finally, by considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P- and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect.Received 8 October 2013DOI:https://doi.org/10.1103/PhysRevX.5.011040This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society
Highlights
The experimental realization of graphene has opened the fascinating possibility of observing in a condensed matter system a number of interesting effects previously considered to occur exclusively in relativistic particle physics
By considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P- and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect
We evaluate the effects of pseudo-quantum electrodynamics (PQED) in the valley conductivity and show that, below an activation temperature TÃ, it exhibits a nonzero transverse component, which is quantized in the same way as in the usual quantum Hall effect (QHE)
Summary
The experimental realization of graphene has opened the fascinating possibility of observing in a condensed matter system a number of interesting effects previously considered to occur exclusively in relativistic particle physics. The experimental observation of the fractional QHE in ultraclean samples subject to a perpendicular magnetic field has closed the debate, undeniably demonstrating that the electronic interactions are important, at least for a certain energy (temperature) scale [15,16,17,18] Another intriguing transport property that has been investigated in graphene is the possibility of observing a quantized transverse (Hall) conductivity under unconventional circumstances. We evaluate the effects of PQED in the valley conductivity and show that, below an activation temperature TÃ, it exhibits a nonzero transverse component, which is quantized in the same way as in the usual QHE This effect is dynamically generated in graphene, when the full electromagnetic interaction is completely taken into account. G−μν1 − G−0;1μν 1⁄4 −e2Πμν; ð10Þ where G is the exact Aμ field Euclidean propagator and G0 is the free one, G0;μν p1ffiffiffiffiffi 2 p2
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