Covalently Linked Porphyrins as One-Dimensional Conductors

We apply first-principles calculations to address the problem of the formation and characterization of covalently linked porphyrin-like structures. We show that upon pressure a rehybridization process takes place which leads to one-dimensional compounds resembling nanothreads, in which carbon atoms are all 4-fold coordinated. We also show that the resulting nanostructures have metallic character and possess remarkable mechanical properties. Moreover, in the case of porphyrin–metal complexes, we find that the covalently linked structures may be a platform for the stabilization of straight metallic wires

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.Comment: 4 pages, 4 figure

Fermions in an anisotropic random magnetic field

We study the localization of fermions in an anisotropic random magnetic field in two dimensions. It is assumed that the randomness in a particular direction is stronger than those in the other directions. We consider a network model of zero field contours, where there are two types of randomness - the random tunneling matrix element at the saddle points and unidirectional random variation of the number of fermionic states following zero field contours. After averaging over the random complex tunneling amplitude, the problem is mapped to an SU(2N) random exchange quantum spin chain in the $N \to 0$ limit. We suggest that the fermionic state becomes critical in an anisotropic fashion.Comment: 5 pages, replaced by revised version, accepted for publication in Europhysics Letter

Multifractality of wavefunctions at the quantum Hall transition revisited

We investigate numerically the statistics of wavefunction amplitudes $\psi({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|\psi|^2$ is log-normal, so that the multifractal spectrum $f(\alpha)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.Comment: 4 pages Late