Comment on ``Analytic Structure of One-Dimensional Localization Theory: Re-Examining Mott's Law''

The low-frequency conductivity of a disordered Fermi gas in one spatial dimension is governed by the Mott-Berezinskii law $\sigma(\omega) \propto \omega^2 \ln \omega^2$. In a recent Letter [Phys. Rev. Lett. 84, 1760 (2000)] A. O. Gogolin claimed that this law is invalid, challenging our basic understanding of disordered systems and a massive amount of previous theoretical work. We point out two calculational errors in Gogolin's paper. Once we correct them, the Mott-Berezinskii formula is fully recovered. We also present numerical results supporting the Mott-Berezinskii formula but ruling out that of Gogolin.Comment: 1 page, 1 figure, RevTeX

Neutrality point of graphene with coplanar charged impurities

The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on $\alpha$, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when $\alpha$ is small, which is the case for graphene on a substrate with a high dielectric constant.Comment: (v3) 4 pages main paper, 2 pages supplementary info, no figure

Electronic response of graphene to linelike charge perturbations

The problem of electrostatic screening of a charged line by undoped or weakly doped graphene is treated beyond the linear-response theory. The induced electron density is found to be approximately doping independent, n(x)~(log x)^2/x^2, at intermediate distances x from the charged line. At larger x, twin p-n junctions may form if the external perturbation is repulsive for graphene charge carriers. The effect of such inhomogeneities on conductance and quantum capacitance of graphene is calculated. The results are relevant for transport properties of graphene grain boundaries and for local electrostatic control of graphene with ultrathin gates.Comment: Fixed typos and added reference

Feshbach resonance of heavy exciton-polaritons

We study interactions between polaritons formed by hybridization of excitons in a two-dimensional (2D) semiconductor with surface optical phonons or plasmons. These quasiparticles have a high effective mass and can bind into bipolaritons near a Feshbach-like scattering resonance. We analyze the phase diagram of a many-body condensate of heavy polaritons and bipolaritons and calculate their absorption and luminescence spectra, which can be measured experimentally.Comment: 11 pages, 7 figure

Late Gas accretion onto Primordial Minihalos: a Model for Leo T, Dark Galaxies and Extragalactic High-Velocity Clouds

In this letter we revisit the idea of reionization feedback on dwarf galaxy formation. We show that primordial minihalos with v_cir<20 km/s stop accreting gas after reionization, as it is usually assumed, but in virtue of their increasing concentration and the decreasing temperature of the intergalactic medium as redshift decreases below z=3, they have a late phase of gas accretion and possibly star formation. We expect that pre-reionization fossils that evolved on the outskirts of the Milky Way or in isolation show a bimodal star formation history with 12 Gyr old and <10 Gyr old population of stars. Leo T fits with this scenario. Another prediction of the model is the possible existence of a population of gas rich minihalos that never formed stars. More work is needed to understand whether a subset of compact high-velocity clouds can be identified as such objects or whether an undiscovered population exists in the voids between galaxies.Comment: 5 pages, 4 figures, accepted version MNRAS 392, L4

Exchange interaction in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is valid in several independent asymptotic regimes, including low electron density case, under the general condition of a strong spin-charge separation. Explicit formulas for the exchange constant are obtained for thin quantum rings and wires with realistic Coulomb interactions by calculating the pair-correlation function via a many-body instanton approach. A remarkably smooth interpolation between high and low electron density results is shown to be possible. These results are applicable to the case of one-dimensional wires of intermediate width as well. Our method can be easily generalized to other interaction laws, such as the inverse distance squared one of the Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the known exact results for the latter model and show that they are relevant for a realistic experimental setup in which the bare Coulomb interaction is screened by an edge of a two-dimensional electron gas.Comment: 12 pages, 5 figure