Theory of the topological Anderson insulator

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian that can drive an ordinary band insulator into a topological insulator (having an inverted band gap). We calculate the location of the phase boundary at weak disorder and show that it corresponds to the crossing of a band edge rather than a mobility edge. Our mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling.Comment: 4 pages, 3 figures (updated figures, calculated DOS

Theory of the Topological Anderson Insulator

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic corrections / p 2 z to the Dirac Hamiltonian that can drive an ordinary band insulator into a topological insulator (having an inverted band gap). We calculate the location of the phase boundary at weak disorder and show that it corresponds to the crossing of a band edge rather than a mobility edge. Our mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling. DOI: 10.1103/PhysRevLett.103.196805 PACS numbers: 73.20.Fz, 03.65.Vf, 73.40.Lq, 73.43.Nq Topological insulators continue to surprise with unexpected physical phenomena [2] were confirmed by independent simulations The phenomenology of the TAI is similar to that of the quantum spin Hall (QSH) effect, which is well understood The crucial difference between the TAI and QSH phases is that the QSH phase extends down to zero disorder, while the TAI phase has a boundary at a minimal disorder strength. Put differently, the helical edge states in the QSH phase exist in spite of disorder, while in the TAI phase they exist because of disorder. Note that the familiar quantum Hall effect is like the QSH effect in this respect: The edge states in the quantum Hall effect exist already without disorder (although, unlike the QSH effect, they only form in a strong magnetic field). The computer simulations of Refs. [2,3] confront us, therefore, with a phenomenology without precedent: By what mechanism can disorder produce edge states with a quantized conductance? That is the question we answer in this Letter. We start from the low-energy effective Hamiltonian of a HgTe quantum well, which has the form [5] (1) This is a two-dimensional Dirac Hamiltonian (with momentum operator p ¼ Ài@r, Pauli matrices x , y , z , and a 2 Â 2 unit matrix 0 ), acting on a pair of spin-orbit coupled degrees of freedom from conduction and valence bands. The complex conjugate H Ã acts on the opposite spin. We assume time reversal symmetry (no magnetic field or magnetic impurities) and neglect any coupling between the two spin blocks H and H Ã [2], representative of a noninverted HgTe=CdTe quantum well The terms quadratic in momentum in Eq. We will now show that disorder can push the phase transition to positive values of m, which is the hallmark of a TAI. Qualitatively, the mechanism is as follows. Elastic scattering by a disorder potential causes states of definite momentum to decay exponentially as a function of PRL 103, 196805 (2009

Conditional embryonic lethality to improve the sterile insect technique in Ceratitis capitata (Diptera: Tephritidae)

<p>Abstract</p> <p>Background</p> <p>The sterile insect technique (SIT) is an environment-friendly method used in area-wide pest management of the Mediterranean fruit fly <it>Ceratitis capitata </it>(Wiedemann; Diptera: Tephritidae). Ionizing radiation used to generate reproductive sterility in the mass-reared populations before release leads to reduction of competitiveness.</p> <p>Results</p> <p>Here, we present a first alternative reproductive sterility system for medfly based on transgenic embryonic lethality. This system is dependent on newly isolated medfly promoter/enhancer elements of cellularization-specifically-expressed genes. These elements act differently in expression strength and their ability to drive lethal effector gene activation. Moreover, position effects strongly influence the efficiency of the system. Out of 60 combinations of driver and effector construct integrations, several lines resulted in larval and pupal lethality with one line showing complete embryonic lethality. This line was highly competitive to wildtype medfly in laboratory and field cage tests.</p> <p>Conclusion</p> <p>The high competitiveness of the transgenic lines and the achieved 100% embryonic lethality causing reproductive sterility without the need of irradiation can improve the efficacy of operational medfly SIT programs.</p

Kwant : a software package for quantum transport

International audienceKwant is a Python package for numerical quantum transport calculations. It aims to be a user-friendly, universal, and high-performance toolbox for the simulation of physical systems of any dimensionality and geometry that can be described by a tight-binding model. Kwant has been designed such that the natural concepts of the theory of quantum transport (lattices, symmetries, electrodes, orbital/spin/electron-hole degrees of freedom) are exposed in a simple and transparent way. Defining a new simulation setup is very similar to describing the corresponding mathematical model. Kwant offers direct support for calculations of transport properties (conductance, noise, scattering matrix), dispersion relations, modes, wave functions, various Green's functions, and out-of-equilibrium local quantities. Other computations involving tight-binding Hamiltonians can be implemented easily thanks to its extensible and modular nature

A general algorithm for computing bound states in infinite tight-binding systems

International audienceWe propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the approaches used to obtain propagating states and scattering matrices. We show that our algorithm is robust in presence of slowly decaying bound states where a diagonalization of a finite system would fail. It also allows to calculate the bound states that can be present in the middle of a continuous spectrum. We apply our technique to quantum billiards and the following topological materials: Majorana states in 1D superconducting nanowires, edge states in the 2D quantum spin Hall phase, and Fermi arcs in 3D Weyl semimetals

A general algorithm for computing bound states in infinite tight-binding systems

We propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the approaches used to obtain propagating states and scattering matrices. We show that our algorithm is robust in presence of slowly decaying bound states where a diagonalization of a finite system would fail. It also allows to calculate the bound states that can be present in the middle of a continuous spectrum. We apply our technique to quantum billiards and the following topological materials: Majorana states in 1D superconducting nanowires, edge states in the 2D quantum spin Hall phase, and Fermi arcs in 3D Weyl semimetals.QN/Akhmerov GroupQRD/Wimmer La