Solving simultaneously Dirac and Ricatti equations

We analyse the behaviour of the Dirac equation in $d=1+1$ with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-parameter families of solvable potentials. To illustrate the procedure in a simple but relevant context, we resort to a model which has proved useful in showing the phenomenon of fermion number fractionalization

Topological insulators for high performance terahertz to infrared applications

Topological insulators in the Bi2Se3 family have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Low frequency optical absorption due to the surface state is universally determined by the fine structure constant. When the thickness of these three dimensional topological insulators is reduced, they become quasi-two dimensional insulators with enhanced absorbance. The two dimensional insulators can be topologically trivial or non-trivial depending on the thickness, and we predict that the optical absorption is larger for topological non-trivial case compared with the trivial case. Since the three dimensional topological insulator surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high performance photo-detection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers, with a widely tunable band gap depending on the thickness

Quantum criticality between topological and band insulators in (3+1)(3+1)-dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semi-metallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semi-metallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semi-metallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases. Our results are also applicable to even number of flavors of Dirac fermions, and the band inversion transition in various non-topological narrow gap semiconductors.Comment: 16 pages, 14 figures; replaced with the version accepted by PR

Superconductivity in charge Kondo systems

We present a theory of superconductivity in charge Kondo systems, materials with resonant quantum valence fluctuations, in the regime where the transition temperature is comparable to the charge Kondo resonance. We find superconductivity induced by charge Kondo impurities, study how pairing of a superconducting host is enhanced due to charge Kondo centers and investigate the interplay between Kondo-scattering and inter-impurity Josephson coupling. We discuss the implications of our theory for Tl-doped PbTe, which has recently been identified as a candidate charge Kondo system.Comment: 4 pages, 4 figures; revised version; detailed discussion on the physics of Tl-doped PbTe adde

Topological Insulators with Inversion Symmetry

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the 2D quantum spin Hall phase and the 3D strong topological insulator these states are robust and are insensitive to weak disorder and interactions. In this paper we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z_2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials are strong topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.Comment: 16 pages, 7 figures; published versio

Topological Insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.Comment: 23 pages, 20 figures, Published versio

Band-Gap Nonlinearity in Lead Chalcogenide (PbQ, Q = Te, Se, S) Alloys

Narrow band-gap lead chalcogenides have been developed for several optical and electronic applications. However, band-gap energies of the ternary and quaternary alloys have received little attention compared with the parent binary phases. Here, we have fabricated single-phase ternary (PbTe)1−x(PbSe)x and quaternary (PbTe)0.9−y(PbSe)0.1(PbS)y and (PbTe)0.65−z(PbSe)0.35(PbS)z alloys and shown that although lattice parameters follow Vegard’s law as a function of composition, the bandgap energies exhibit a substantial bowing effect. The ternary (PbTe)1−x(PbSe)x system features a smaller bowing parameter predominantly due to the difference in electronegativity between Se and Te, whereas the larger bowing parameters in quaternary alloys are generated from a larger crystal lattice mismatch and larger miscibility gap. These findings can lead to further advances in tuning the band-gap and lattice parameters for optical and electronic applications of lead chalcogenides

Food-web structure in relation to environmental gradients and predator-prey ratios in tank-bromeliad ecosystems

Little is known of how linkage patterns between species change along environmental gradients. The small, spatially discrete food webs inhabiting tank-bromeliads provide an excellent opportunity to analyse patterns of community diversity and food-web topology (connectance, linkage density, nestedness) in relation to key environmental variables (habitat size, detrital resource, incident radiation) and predators: prey ratios. We sampled 365 bromeliads in a wide range of understorey environments in French Guiana and used gut contents of invertebrates to draw the corresponding 365 connectance webs. At the bromeliad scale, habitat size (water volume) determined the number of species that constitute food-web nodes, the proportion of predators, and food-web topology. The number of species as well as the proportion of predators within bromeliads declined from open to forested habitats, where the volume of water collected by bromeliads was generally lower because of rainfall interception by the canopy. A core group of microorganisms and generalist detritivores remained relatively constant across environments. This suggests that (i) a highly-connected core ensures food-web stability and key ecosystem functions across environments, and (ii) larger deviations in food-web structures can be expected following disturbance if detritivores share traits that determine responses to environmental changes. While linkage density and nestedness were lower in bromeliads in the forest than in open areas, experiments are needed to confirm a trend for lower food-web stability in the understorey of primary forests

Bumblebees exhibit the memory spacing effect

Associative learning is key to how bees recognize and return to rewarding floral resources. It thus plays a major role in pollinator floral constancy and plant gene flow. Honeybees are the primary model for pollinator associative learning, but bumblebees play an important ecological role in a wider range of habitats, and their associative learning abilities are less well understood. We assayed learning with the proboscis extension reflex (PER), using a novel method for restraining bees (capsules) designed to improve bumblebee learning. We present the first results demonstrating that bumblebees exhibit the memory spacing effect. They improve their associative learning of odor and nectar reward by exhibiting increased memory acquisition, a component of long-term memory formation, when the time interval between rewarding trials is increased. Bombus impatiens forager memory acquisition (average discrimination index values) improved by 129% and 65% at inter-trial intervals (ITI) of 5 and 3 min, respectively, as compared to an ITI of 1 min. Memory acquisition rate also increased with increasing ITI. Encapsulation significantly increases olfactory memory acquisition. Ten times more foragers exhibited at least one PER response during training in capsules as compared to traditional PER harnesses. Thus, a novel conditioning assay, encapsulation, enabled us to improve bumblebee-learning acquisition and demonstrate that spaced learning results in better memory consolidation. Such spaced learning likely plays a role in forming long-term memories of rewarding floral resources