Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-dimensional metal; here disorder not only causes metal-insulator transition, as anticipated, but is fundamentally responsible for creating extended edge states. We determine the phase diagram of the topological Anderson insulator and outline its experimental consequences.

Three-dimensional topological insulators are characterized by the presence of a bandgap in their bulk and gapless Dirac fermions at their surfaces. New physical phenomena originating from the presence of the Dirac fermions are predicted to occur, and to be experimentally accessible via transport measurements in suitably designed electronic devices. Here we study transport through superconducting junctions fabricated on thin Bi2Se3 single crystals, equipped with a gate electrode. In the presence of perpendicular magnetic field B, sweeping the gate voltage enables us to observe the filling of the Dirac fermion Landau levels, whose character evolves continuously from electron- to hole-like. When B=0, a supercurrent appears, whose magnitude can be gate tuned, and is minimum at the charge neutrality point determined from the Landau level filling. Our results demonstrate how gated nano-electronic devices give control over normal and superconducting transport of Dirac fermions at an individual surface of a three-dimensional topological insulators.

Recent experiments have provided evidence that one-dimensional (1D) topological superconductivity can be realized experimentally by placing transition metal atoms that form a ferromagnetic chain on a superconducting substrate. We address some properties of this type of systems by using Slater-Koster tight-binding model to account for important features of the electronic structure of the transition transition metal chains on the superconducting substrate. We predict that topological superconductivity is nearly universal when ferromagnetic transition metal chains form straight lines on superconducting substrates and that it is possible for more complex chain structures. When the chain is weakly coupled to the substrate and is longer than superconducting coherence lengths, its proximity induced superconducting gap is ∼ ∆Eso/J where ∆ is the s-wave pair-potential on the chain, Eso is the spin-orbit splitting energy induced in the normal chain state bands by hybridization with the superconducting substrate, and J is the exchange-splitting of the ferromagnetic chain d-bands. Because of the topological character of the 1D superconducting state, Majorana end modes appear within the gaps of finite length chains. We find, in agreement with the experiment, that when the chain and substrate orbitals are strongly hybridized, Majorana end modes are substantially reduced in amplitude when separated from the chain end by less than the coherence length defined by the p-wave superconducting gap. We conclude that Pb is a particularly favorable substrate material for ferromagnetic chain topological superconductivity because it provides both strong s−wave pairing and strong Rashba spin-orbit coupling, but that there is an opportunity to optimize properties by varying the atomic composition and structure of the chain. Finally, we note that in the absence of disorder a new chain magnetic symmetry, one that is also present in the crystalline topological insulators, can stabilize multiple Majorana modes at the end of a single chain.

International audienceIn this work, we studied the effect of heterovalent Ca, Sr, Pb, and Ba substitution on the crystal structure, dielectric, local ferroelectric, and magnetic properties of the BiFeO3 multiferroic perovskite. Ceramic solid solutions with the general formula Bi0.7A0.3FeO3 (A is a doping element) were prepared and characterized by x-ray diffraction, dielectric, piezoresponse force microscopy (PFM), and magnetic measurements. It is shown that the crystal structure of the compounds is described within the space group R3c, permitting the spontaneous polarization, whose existence was confirmed by the PFM data. Magnetic properties of the solid solutions are determined by the ionic radius of the substituting element. Experimental results suggest that the increase in the radius of the A-site ion leads to the effective suppression of the spiral spin structure of BiFeO3, resulting in the appearance of net magnetization

The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal.