Effective action approach to the Leggett's mode in two-band superconductors

We investigate a collective excitation (Leggett's mode) corresponding to small fluctuations of the relative phase of two condensates in two-band superconductor using the effective ``phase only'' action. We consider the possibility of observing Leggett's mode in MgB$_2$ superconductor and conclude that for the known at present values of the two-band model parameters for MgB$_2$ Leggett's mode arises above the two-particle threshold.Comment: 9 pages, RevTeX4; final version published in EPJ

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