Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects

We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of localization-delocalization quantum phase transition in the standard lattice models of disordered electron problem. Due to the local character of our theory, it can easily be combined with dynamical mean-field approaches to strongly correlated electrons, thus opening an attractive avenue for a genuine {\em non-perturbative} treatment of the interplay of strong interactions and strong disorder.Comment: 7 pages, 4 EPS figures, revised version to appear in Europhysics Letter

Magnetic Field Suppression of the Conducting Phase in Two Dimensions

The anomalous conducting phase that has been shown to exist in zero field in dilute two-dimensional electron systems in silicon MOSFETs is driven into a strongly insulating state by a magnetic field of about 20 kOe applied parallel to the plane. The data suggest that in the limit of T -> 0 the conducting phase is suppressed by an arbitrarily weak magnetic field. We call attention to striking similarities to magnetic field-induced superconductor-insulator transitions

Optical conductivity of the half-filled Hubbard chain

We combine well-controlled analytical and numerical methods to determine the optical conductivity of the one-dimensional Mott-Hubbard insulator at zero temperature. A dynamical density-matrix renormalization group method provides the entire absorption spectrum for all but very small coupling strengths. In this limit we calculate the conductivity analytically using exact field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another weak feature becomes visible around the middle of the absorption band.Comment: 4 pages with 3 eps figures, published version (changes in text and references

Carbon nitrides: synthesis and characterization of a new class of functional materials

Carbon nitride compounds with high N[thin space (1/6-em)]:[thin space (1/6-em)]C ratios and graphitic to polymeric structures are being investigated as potential next-generation materials for incorporation in devices for energy conversion and storage as well as for optoelectronic and catalysis applications. The materials are built from C- and N-containing heterocycles with heptazine or triazine rings linked via sp2-bonded N atoms (N(C)3 units) or –NH– groups. The electronic, chemical and optical functionalities are determined by the nature of the local to extended structures as well as the chemical composition of the materials. Because of their typically amorphous to nanocrystalline nature and variable composition, significant challenges remain to fully assess and calibrate the structure–functionality relationships among carbon nitride materials. It is also important to devise a useful and consistent approach to naming the different classes of carbon nitride compounds that accurately describes their chemical and structural characteristics related to their functional performance. Here we evaluate the current state of understanding to highlight key issues in these areas and point out new directions in their development as advanced technological materials.Our work on carbon nitride materials has been supported by the EPSRC (EP/L017091/1) and the EU Graphene Flagship grant agreement No. 696656 - GrapheneCore1. Additional support to advance the science and technology of these materials was also received from the UCL Enterprise Fund and the Materials Innovation Impact Acceleration funding enabled by the UK EPSRC