Shockley model description of surface states in topological insulators

We show that the surface states in topological insulators can be understood based on a well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case corresponding to the sequence of layers connected via the amplitudes, which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the complex function t(k,p) defines the properties of the surface states. The surface states exist for the in-plane momenta p, where the winding number of the function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the winding number defines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. The projection of the vortex line on the two-dimensional momentum p space encircles the domain where the surface states exist. We illustrate how our approach works for a well-known TI model on a diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. The phase transition occurs when the vortex lines reconnect from spiral to circular form. We discuss the Shockley model description of Bi_2Se_3 and the applicability of the continuous approximation for the description of the topological edge states. We conclude that the tight-binding model gives a better description of the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII added, Refs. [33]-[35] added; Corresponds to the published versio

Advanced-power-reactor design concepts and performance characteristics

Five reactor cooling concepts which allow continued reactor operation following a single rupture of the coolant system are presented for application with the APR. These concepts incorporate convective cooling, double containment, or heat pipes to ensure operation after a coolant line rupture. Based on an evaluation of several control system concepts, a molybdenum clad, beryllium oxide sliding reflector located outside the pressure vessel is recommended

Pleural mesothelioma and lung cancer risks in relation to occupational history and asbestos lung burden.

BACKGROUND: We have conducted a population-based study of pleural mesothelioma patients with occupational histories and measured asbestos lung burdens in occupationally exposed workers and in the general population. The relationship between lung burden and risk, particularly at environmental exposure levels, will enable future mesothelioma rates in people born after 1965 who never installed asbestos to be predicted from their asbestos lung burdens. METHODS: Following personal interview asbestos fibres longer than 5 µm were counted by transmission electron microscopy in lung samples obtained from 133 patients with mesothelioma and 262 patients with lung cancer. ORs for mesothelioma were converted to lifetime risks. RESULTS: Lifetime mesothelioma risk is approximately 0.02% per 1000 amphibole fibres per gram of dry lung tissue over a more than 100-fold range, from 1 to 4 in the most heavily exposed building workers to less than 1 in 500 in most of the population. The asbestos fibres counted were amosite (75%), crocidolite (18%), other amphiboles (5%) and chrysotile (2%). CONCLUSIONS: The approximate linearity of the dose-response together with lung burden measurements in younger people will provide reasonably reliable predictions of future mesothelioma rates in those born since 1965 whose risks cannot yet be seen in national rates. Burdens in those born more recently will indicate the continuing occupational and environmental hazards under current asbestos control regulations. Our results confirm the major contribution of amosite to UK mesothelioma incidence and the substantial contribution of non-occupational exposure, particularly in women

Focussing quantum states

Does the size of atoms present a lower limit to the size of electronic structures that can be fabricated in solids? This limit can be overcome by using devices that exploit quantum mechanical scattering of electron waves at atoms arranged in focussing geometries on selected surfaces. Calculations reveal that features smaller than a hydrogen atom can be obtained. These structures are potentially useful for device applications and offer a route to the fabrication of ultrafine and well defined tips for scanning tunneling microscopy.Comment: 4 pages, 4 figure