An edge index for the Quantum Spin-Hall effect

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.Comment: 4 pages, 3 figure

Simultaneous quantization of edge and bulk Hall conductivity

The edge Hall conductivity is shown to be an integer multiple of $e^2/h$ which is almost surely independent of the choice of the disordered configuration. Its equality to the bulk Hall conductivity given by the Kubo-Chern formula follows from K-theoretic arguments. This leads to quantization of the Hall conductance for any redistribution of the current in the sample. It is argued that in experiments at most a few percent of the total current can be carried by edge states.Comment: 6 pages Latex, 1 figur

Spontaneous edge currents for the Dirac equation in two space dimensions

Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques.Comment: 10 pages; final versio

Scattering theory for lattice operators in dimension d≥3d\geq 3

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension $d\geq 3$ the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in presence of embedded eigenvalues and threshold singularities.Comment: Minor errors and misprints corrected; new result on absense of embedded eigenvalues for potential scattering; to appear in RM

Anomalous Drude Model

A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long tail and even a non-vanishing first moment. The collision averaged motion is either regular diffusive or L\'evy-flight like. The anomalous diffusion coefficients show complex scaling laws. The conductivity can be calculated in the diffusive regime. The model is of interest for the phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter

Interacting fermions in self-similar potentials

We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.Comment: 18 pages, 10 EPS figure

Investigation of quantum transport by means of O(N) real-space methods

Quantum transport for different systems is investigated by developing the Kubo formula on a basis of orthogonal polynomials. Results on quantum Hall systems are presented with particular attention to metal insulator transitions and new universalities. Other potential applications of the present method for RKKY mesoscopic interaction and insight for large scale computational problems, are given.Comment: 7 pages, 8 figure

Z_2 Invariants of topological insulators as geometric obstructions

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones

Characterization of Rhodamine-123 as a Tracer Dye for Use In In vitro Drug Transport Assays

Fluorescent tracer dyes represent an important class of sub-cellular probes and allow the examination of cellular processes in real-time with minimal impact upon these processes. Such tracer dyes are becoming increasingly used for the examination of membrane transport processes, as they are easy-to-use, cost effective probe substrates for a number of membrane protein transporters. Rhodamine 123, a member of the rhodamine family of flurone dyes, has been used to examine membrane transport by the ABCB1 gene product, MDR1. MDR1 is viewed as the archetypal drug transport protein, and is able to efflux a large number of clinically relevant drugs. In addition, ectopic activity of MDR1 has been associated with the development of multiple drug resistance phenotype, which results in a poor patient response to therapeutic intervention. It is thus important to be able to examine the potential for novel compounds to be MDR1 substrates. Given the increasing use rhodamine 123 as a tracer dye for MDR1, a full characterisation of its spectral properties in a range of in vitro assay-relevant media is warranted. Herein, we determine λmax for excitation and emission or rhodamine 123 and its metabolite rhodamine 110 in commonly used solvents and extraction buffers, demonstrating that fluorescence is highly dependent on the chemical environment: Optimal parameters are 1% (v/v) methanol in HBSS, with λex = 505 nm, λem = 525 nm. We characterise the uptake of rhodamine 123 into cells, via both passive and active processes, and demonstrate that this occurs primarily through OATP1A2-mediated facilitated transport at concentrations below 2 µM, and via micelle-mediated passive diffusion above this. Finally, we quantify the intracellular sequestration and metabolism of rhodamine 123, demonstrating that these are both cell line-dependent factors that may influence the interpretation of transport assays

Classification of Inhibitors of Hepatic Organic Anion Transporting Polypeptides (OATPs): Influence of Protein Expression on Drug–Drug Interactions

ABSTRACT: The hepatic organic anion transporting poly-peptides (OATPs) influence the pharmacokinetics of several drug classes and are involved in many clinical drug−drug interactions. Predicting potential interactions with OATPs is, therefore, of value. Here, we developed in vitro and in silico models for identification and prediction of specific and general inhibitors of OATP1B1, OATP1B3, and OATP2B1. The maximal transport activity (MTA) of each OATP in human liver was predicted from transport kinetics and protein quantification. We then used MTA to predict the effects of a subset of inhibitors on atorvastatin uptake in vivo. Using a data set of 225 drug-like compounds, 91 OATP inhibitors were identified. In silico models indicated that lipophilicity and polar surface area are key molecular features of OATP inhibition. MTA predictions identified OATP1B1 and OATP1B3 as major determinants of atorvastatin uptake in vivo. The relative contributions to overall hepatic uptake varied with isoform specificities of the inhibitors