A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we consider a variation of the model, which represents a superconductor with longer ranged kinetic energy and pairing amplitudes, as is likely to occur in more realistic systems. It possesses a richer zero temperature phase diagram and has several quantum phase transitions. From an exact solution of the model these phases can be classified according to the number of Majorana zero modes of an open chain: 0, 1, or 2 at each end. The model posseses a multicritical point where phases with 0, 1, and 2 Majorana end modes meet. The number of Majorana modes at each end of the chain is identical to the topological winding number of the Anderson's pseudospin vector that describes the BCS Hamiltonian. The topological classification of the phases requires a unitary time-reversal symmetry to be present. When this symmetry is broken, only the number of Majorana end modes modulo 2 can be used to distinguish two phases. In one of the regimes, the wave functions of the two phase shifted Majorana zero modes decays exponentially in space but in an oscillatory manner. The wavelength of oscillation is identical to the asymptotic connected spin-spin correlation of the XY -model in a transverse field to which our model is dual.

We propose a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs). We show that, by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrate that such a topological superconductivity is stabilized by moderate electron-electron interactions. The proposed setup avoids the application of a magnetic field or local voltage gates, and requires weaker interactions compared with nonhelical nanowires.

Microbiologically influenced corrosion (MC) of steel has been attributed to the activity of biofilms that include anaerobic microorganisms such as iron-respiring bacteria, yet the mechanisms by which these organisms influence corrosion have been unclear. To study this process, we generated mutants of the iron-respiring bacterium Shewanella oneidensis strain MR-1 that were defective in biofilm formation and/or iron reduction. Electrochemical impedance spectroscopy was used to determine changes in the corrosion rate and corrosion potential as a function of time for these mutants in comparison to the wild type. Counter to prevailing theories of MC, our results indicate that biofilms comprising iron-respiring bacteria may reduce rather than accelerate the corrosion rate of steel. Corrosion inhibition appears to be due to reduction of ferric ions to ferrous ions and increased consumption of oxygen, both of which are direct consequences of microbial respiration.Microbes perform oxidation and reduction reactions that profoundly affect the stability of minerals in the environment, with consequences ranging from the promotion of acid mine drainage (19) to the bioremediation of organically polluted groundwater (7). In industrial settings, perhaps the most familiar metal transformation is the rusting of iron and steel, and microbes are thought to play an important role in this process (1). Microbiologically influenced corrosion (MC) can be a serious industrial problem and affects diverse processes ranging from water distribution in cast iron mains and sewers to transport of natural gas in steel pipelines. It has been estimated that for the United States oil industry alone, MC causes hundreds of millions of dollars in damage to the production, transport, and storage of oil every year (3). Yet the mechanistic basis of MC, despite its importance, has remained unclear.A prevailing theory of MC holds that biofilms promote corrosion by inducing the formation of corrosion cells. This is thought to occur as a consequence of aerobic respiratory activity within biofilms that leads to the establishment of local cathodic and anodic regions on the steel surface, which promotes electron flow (6). Recent evidence, however, suggests that aerobically respiring bacteria may protect steel from corrosion over the long term (5), which raises questions regarding the extent to which aerobic respiration contributes to MC. Other explanations for MC include corrosion promotion by anaerobes such as sulfate-reducing and iron-reducing bacteria. Current theories maintain that sulfate reducers promote corrosion by consuming hydrogen and inducing ferrous sulfide formation and that iron reducers promote corrosion by reductively dissolving the protective ferric oxide coating that forms on the steel surface (6, 17). Biofilm communities that develop on the surfaces of corroding materials in natural environments are heterogeneous, and therefore there is significant uncertainty concerning how these communities affect corrosion in any given environment.Our goal...

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