Unconventional Integer Quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by 2+1 dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity $\sigma_{xy} = - (2 e^2/h)(2n+1)$ with $n=0,1,...$, that notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the $n=0$ Landau level and was discovered in recent experiments on ultrathin graphite films.Comment: 4 pages, RevTeX4, 2 EPS figures; version accepted for publication in Physical Review Letter

Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps

By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for the interpretation of recent experiments are discussed.Comment: 13 pages, 7 figures. v2: analysis for ribbons with armchair edges added, to appear in Phys. Rev.

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity in low dimensional systems

A phase diagram for a 2D metal with variable carrier density has been studied using the modulus-phase representation for the order parameter in a fully microscopic treatment. This amounts to splitting the degrees of freedom into neutral fermion and charged boson degrees of freedom. Although true long range order is forbidden in two dimensions, long range order for the neutral fermions is possible since this does not violate any continuous symmetry. The phase fluctuations associated with the charged degrees of freedom destroy long range order in the full system as expected. The presence of the neutral order parameter gives rise to new features in the superconducting condensate formation in low dimensional systems. The resulting phase diagram contains a new phase which lies above the superconducting (here Berezinskii-Kosterlitz-Thouless) phase and below the normal (Fermi-liquid) phase. We identify this phase with the pseudogap phase observed in underdoped high-$T_{c}$ superconducting compounds above their critical temperature. We also find that the phase diagram persists even in the presence of weak 3-dimensionalisation.Comment: 4 pages, LaTeX; invited paper presented at New^3SC-1, Baton Rouge, USA, 1998. To be published in Int.J.Mod.Phys.

BRST quantization of quasi-symplectic manifolds and beyond

We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is applied to describe the geometry underlying these brackets as well as to develop a deformation quantization procedure in this particular case. This can be viewed as an extension of the Fedosov deformation quantization to a wide class of \textit{irregular} Poisson structures. In a more general case, the factorizable Poisson brackets are shown to be closely connected with the notion of $n$-algebroid. A simple description is suggested for the geometry underlying the factorizable Poisson brackets basing on construction of an odd Poisson algebra bundle equipped with an abelian connection. It is shown that the zero-curvature condition for this connection generates all the structure relations for the $n$-algebroid as well as a generalization of the Yang-Baxter equation for the symplectic structure.Comment: Journal version, references and comments added, style improve

Phase Fluctuations and Pseudogap Properties: Influence of Nonmagnetic Impurities

The presence of nonmagnetic impurities in a 2D ``bad metal'' depresses the superconducting Berezinskii-Kosterlitz-Thouless transition temperature, while leaving the pairing energy scale unchanged. Thus the region of the pseudogap non-superconducting phase, where the modulus of the order parameter is non-zero but its phase is random, and which opens at the pairing temperature is substantially bigger than for the clean system. This supports the premise that fluctuations in the phase of the order parameter can in principle describe the pseudogap phenomena in high-$T_c$ materials over a rather wide range of temperatures and carrier densities. The temperature dependence of the bare superfluid density is also discussed.Comment: 11 pages, LaTeX, 1 EPS figure; final version to appear in Low.Temp.Phy

Deformation quantization of linear dissipative systems

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding Poisson tensor is allowed to explicitly depend on time. Starting from this pseudo-Hamiltonian formulation we develop a consistent deformation quantization procedure involving a non-stationary star-product $*_t$ and an ``extended'' operator of time derivative $D_t=\partial_t+...$, differentiating the $\ast_t$-product. As in the usual case, the $\ast_t$-algebra of physical observables is shown to admit an essentially unique (time dependent) trace functional $\mathrm{Tr}_t$. Using these ingredients we construct a complete and fully consistent quantum-mechanical description for any linear dynamical system with or without dissipation. The general quantization method is exemplified by the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte

Transport of Dirac quasiparticles in graphene: Hall and optical conductivities

The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle and Nernst signal also exhibit rather unusual behavior, in particular when there is an excitonic gap in the spectrum of the Dirac quasiparticle excitations.Comment: 25 pages, RevTeX4, 8 EPS figures; final version published in PR