Broken-symmetry ν=0\nu=0 quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $\nu=0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp}$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp}$. The critical value of $E_{\perp}$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp,{\rm cr}}=E_{\perp}^{\rm off}+a B$, where $E_{\perp}^{\rm off}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones).Comment: 20 pages, 9 multi-panel figures; final published version with a more detailed comparison of the results with the experimental dat

Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.Comment: 22 pages, 5 figures; Final version published in the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matte

Large N dynamics in QED in a magnetic field

The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of 1/N expansion. The existence of a threshold value N_{thr}, dividing the theories with essentially different dynamics, is established. For the number of flavors N << N_{thr}, the dynamical mass is very sensitive to the value of the coupling constant \alpha_b, related to the magnetic scale \mu = |eB|. For N of order N_{thr} or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with cutoff of order |eB| and the dimensional coupling constant G \sim 1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially \alpha_b independent (the dynamics with an infrared stable fixed point). The value of N_{thr} separates a weak coupling dynamics (with \tilde{\alpha}_b \equiv N\alpha_b << 1) from a strong coupling one (with \tilde{\alpha}_b \gtrsim 1) and is of order 1/\alpha_b.Comment: 4 pages, REVTe

Magnetic field driven metal-insulator phase transition in planar systems

A theory of the magnetic field driven (semi-)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativistic like) dispersion relation for low energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential and temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the "offset" magnetic field $B_c$, determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite.Comment: 22 pages, REVTeX, 16 figures. The version corresponding to that published in Phys.Rev.

Effect of Coulomb interactions on the physical observables of graphene

We give an update of the situation concerning the effect of electron-electron interactions on the physics of a neutral graphene system at low energies. We revise old renormalization group results and the use of 1/N expansion to address questions of the possible opening of a low-energy gap, and the magnitude of the graphene fine structure constant. We emphasize the role of Fermi velocity as the only free parameter determining the transport and electronic properties of the graphene system and revise its renormalization by Coulomb interactions in the light of recent experimental evidence.Comment: Proceedings of the Nobel Symposium on graphene 2010, to appear as a special issue in Physica Script

Magnetic Catalysis: A Review

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.Comment: 37 pages, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee. Version 2: references adde

Edge states in quantum Hall effect in graphene (Review Article)

We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum of graphene with zigzag and armchair edges.We find that in the case of a half-plane or a ribbon with a zigzag edges, there are gapless edge states only when a spin gap dominates over a Dirac mass gap. In the case of a half-plane with an armchair edge, the existence of the gapless edge states depends on the specific type of Dirac mass gaps. The implications of these results for the dynamics in the quantum Hall effect in graphene are discussed