The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.Comment: 15 page

Comment on "Exact results for survival probability in the multistate Landau-Zener model"

We correct the proof of Brundobler-Elser formula (BEF) provided in [2004 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907]. After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general $N$-level Landau-Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.Comment: 10 page

Excitonic pairing between nodal fermions

We study excitonic pairing in nodal fermion systems characterized by a vanishing quasiparticle density of states at the pointlike Fermi surface and a concomitant lack of screening for long-range interactions. By solving the gap equation for the excitonic order parameter, we obtain a critical value of the interaction strength for a variety of power-law interactions and densities of states. We compute the free energy and analyze possible phase transitions, thus shedding further light on the unusual pairing properties of this peculiar class of strongly correlated systems.Comment: 9 pages, 7 figures, minor revisions made, final versio

NJL interaction derived from QCD: vector and axial-vector mesons

In previous works effective non-local $SU(2)\times SU(2)$ NJL model was derived in the framework of the fundamental QCD. All the parameters of the model are expressed through QCD parameters: current light quark mass $m_0$ and average non-perturbative $\alpha_s$. The results for scalar and pseudo-scalar mesons are in satisfactory agreement to existing data. In the present work the same model without introduction of any additional parameters is applied for a description of masses and strong decay widths of $\rho$- and $a_1$-mesons. The results for both scalar and vector sectors agree with data with only one adjusted parameter $m_0$, with account of average $\alpha_s \simeq 0.415$, which is obtained in a previous work as well.Comment: 19 pages, 2 figures, 1 tabl

Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

HgTe quantum wells and surfaces of three-dimensional topological insulators support Dirac fermions with a single-valley band dispersion. In the presence of disorder they experience weak antilocalization, which has been observed in recent transport experiments. In this work we conduct a comparative theoretical study of the weak antilocalization in HgTe quantum wells and topological surface states. The difference between these two single-valley systems comes from a finite band gap (effective Dirac mass) in HgTe quantum wells in contrast to gapless (massless) surface states in topological insulators. The finite effective Dirac mass implies a broken internal symmetry, leading to suppression of the weak antilocalization in HgTe quantum wells at times larger than certain t_M, inversely proportional to the Dirac mass. This corresponds to the opening of a relaxation gap 1/t_M in the Cooperon diffusion mode which we obtain from the Bethe-Salpeter equation including relevant spin degrees of freedom. We demonstrate that the relaxation gap exhibits an interesting nonmonotonic dependence on both carrier density and band gap, vanishing at a certain combination of these parameters. The weak-antilocalization conductivity reflects this nonmonotonic behavior which is unique to HgTe QWs and absent for topological surface states. On the other hand, the topological surface states exhibit specific weak-antilocalization magnetoconductivity in a parallel magnetic field due to their exponential decay in the bulk.Comment: 14 pages, 10 figures, version as publishe

Carrier drift velocity and edge magnetoplasmons in graphene

We investigate electron dynamics at the graphene edge by studying the propagation of collective edge magnetoplasmon (EMP) excitations. By timing the travel of narrow wave-packets on picosecond time scales around exfoliated samples, we find chiral propagation with low attenuation at a velocity which is quantized on Hall plateaus. We extract the carrier drift contribution from the EMP propagation and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the characteristic length for Coulomb interaction at the edge and find it to be smaller than for soft, depletion edge systems.Comment: 5 pages, 3 figures of main text and 6 pages, 6 figures of supplemental materia

Nonlinear Resonance of Superconductor/Normal Metal Structures to Microwaves

We study the variation of the differential conductance $G=dj/dV$ of a normal metal wire in a Superconductor/Normal metal heterostructure with a cross geometry under external microwave radiation applied to the superconducting parts. Our theoretical treatment is based on the quasiclassical Green's functions technique in the diffusive limit. Two limiting cases are considered: first, the limit of a weak proximity effect and low microwave frequency, second, the limit of a short dimension (short normal wire) and small irradiation amplitude.Comment: 11 pages, 10 figure