On the invariance of the 2d Hall conductivity for integer fillings

A system of independent electrons interacting with an arbitrary number of fixed point scatterers on the surface of an infinitely long cylinder is considered. It is shown that (at zero temperature) the equilibrium Byers-Yang Hall current takes the same value as for free electrons if the Fermi energy lies in an energy gap.     

Influence of exchange fields in hybrid pairing superconductors II. Selfconsistent ground states

A previously investigated model of a two band superconductor with hybrid pairing and molecular fields is enlarged by exchange interactions generating those fields. The fields are calculated selfconsistently in molecular field approximation at zero temperature. They turn out to stabilise the previously found new state of gapless superconductivity and non vanishing spin polarization for a wide range of exchange couplings, in particular for zero external field.Dedicated to B. Mühlschlegel on the occasion of his 60th birthdayWork performed within the research program of Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Example for the stability of band edges of extended states for the quantum Hall Hamiltonian on a finite cylinder

Levinson's theorem has been used to shown current compensation for the integer quantum Hall effect. We verify for a model of a finite number of point impurities implanted on a cylinder geometry, that the assumption for the applicability of the Levinson theorem is fulfilled.     

Comments on the equilibrium theory of the quantum hall effect

The relation between the thermal equilibrium Hall conductivity generated by minimal gauge transformation and the isolated Hall conductivity given by the Kubo formula is investigated. The contribution of the edge states and some general questions concerning the definition of the equilibrium Hall conductivity are discussed. It is shown that, in the case of an additive electron-impurity system, the two Hall conductivities coincide as long as the Fermi energy is situated in an energy gap.     

Influence of exchange fields in hybrid pairing superconductors,I: Ground states

Hybrid pairing superconductors with two bands of localized and delocalized states in the presence of uniform molecular fields and a finite displacement of the bands at the Fermi level are analyzed in mean field theory.At zero temperature, in addition to the usual BCS like ground state, agapless superconducting state withfinite spin polarization can be realized. The appearance of this state is somewhat analogous to the occurrence of the Fulde Ferrell state in a single band superconductor with an exchange field.We comment on the relevance of this model for heavy-fermion superconductors.Work performed within the research program of Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Immobilisation and characterisation of the demineralised, fully hydrated organic matrix of nacre - An atomic force microscopy study

Mimicry of the tough natural composite nacre in future bioengineering requires knowledge of the biomineralisation process. The insoluble organic matrix isolated from the shell of the gastropod Haliotis laevigata was characterised by protein chemistry, topographical and mechanical measurements. Demineralisation of nacre in dilute acetic acid or ethylenediaminetetraacetic acid revealed a set of soluble proteins and the insoluble matrix. The insoluble matrix contains a chitin core and firmly attached proteins, which could be removed by sodium dodecyl sulfate and glycerol indicating a hydrophobic interaction. Atomic force microscopy images of the native insoluble matrix showed a filamentous network with pores or holes, where the filaments showed globular attachments of different sizes, possibly the attached protein molecules. During direct observation of protein degradation imaged by atomic force microscopy the insoluble matrix gets smooth and flat indicating the removal of the attached proteins by proteases. We propose a model of protein coated chitin filaments for the insoluble matrix of nacre. Mechanical measurements by force mapping revealed a Young's modulus depending on the hydration state of the organic layers. The fully hydrated organic matrix has an elastic modulus below 1MPa comparable to some hydrogels.     

Linear response,persistent currents and related problems

Based on a general linear response approach we provide a systematic and unified survey of existing theories on persistent currents. The central notions in this context are equilibrium and dynamic persistent currents which are analyzed with respect to their similarities and differences in the canonical and grand canonical ensemble. We present criteria which relate the existence of persistent currents to the equipartition law and ergodicity for current correlators. We find that in additive Fermion systems at low temperatures both kinds of persistent currents coincide in the canonical ensemble whereas they differ in the grand canonical ensemble. Comparing different works on averaged persistent currents in diffusive mesoscopic rings within our framework and discussing several methods of calculating canonical currents with the help of grand canonical ensembles, we clarify some misunderstandings which have arisen in methodologically different approaches to the phenomenon of persistent currents. Finally, we relate the presence of dynamic persistent currents to the Hall conductivity on a finite cylinder and the center coordinate Kubo formula for the Hall conductivity.     

Comments on the widom Hall effect current formula

Recently Widom has derived a formula for the Hall current. The aim of the following comments is to clarify the relation between Widom's formula and the usual one.