Condensed Matter Theory

Abstract:

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales, may signal collapse to globule, or necklace states, respectively. In the presence of added salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length. It is also found that the onset of conformational instability is a reentrant phenomenon as a function of polyelectrolyte length for the unscreened case, and the Debye length or salt concentration for the screened case. This may be relevant in understanding the experimentally observed reentrant condensation of DNA.

Abstract:

We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are generalisations of the network model introduced previously in the context of the integer quantum Hall plateau transition. We show that the generalisations required can be re-expressed as corresponding to the introduction of absorption and amplification into either the original network model, or the variants of it that represent disordered superconductors. In addition, we demonstrate that by imposing appropriate constraints on disorder, a lattice version of the Dirac equation with a random vector potential can be obtained, as well as new types of critical behaviour. These models represent a convenient starting point for analytic discussions and computational studies, and we investigate in detail a two-dimensional example without time-reversal invariance. It exhibits both localised and critical phases, and band-centre singularities in the critical phase approach more closely in small systems the expected asymptotic form than in other known realisations of the symmetry class.

Abstract:

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential, within the framework of a classical non-linear sigma model. We discuss the behaviour of the system using a heuristic picture for the competition between exchange and screening, and test our conclusions with extensive numerical simulations. We obtain a phase diagram for the system as a function of disorder strength and deviation of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration. In the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at weak disorder and small deviation from integer filling to a spin glass at stronger disorder or large charge deviation. We characterise the spin glass phase in terms of its magnetic and charge response, as well as its ac conductivity.