Shockley model description of surface states in topological insulators

We show that the surface states in topological insulators can be understood based on a well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case corresponding to the sequence of layers connected via the amplitudes, which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the complex function t(k,p) defines the properties of the surface states. The surface states exist for the in-plane momenta p, where the winding number of the function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the winding number defines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. The projection of the vortex line on the two-dimensional momentum p space encircles the domain where the surface states exist. We illustrate how our approach works for a well-known TI model on a diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. The phase transition occurs when the vortex lines reconnect from spiral to circular form. We discuss the Shockley model description of Bi_2Se_3 and the applicability of the continuous approximation for the description of the topological edge states. We conclude that the tight-binding model gives a better description of the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII added, Refs. [33]-[35] added; Corresponds to the published versio

Interlayer tunneling spectroscopy of graphite at high magnetic field oriented parallel to the layers

Interlayer tunneling in graphite mesa-type structures is studied at a strong in-plane magnetic field $H$ up to 55 T and low temperature $T=1.4$ K. The tunneling spectrum $dI/dV$ vs. $V$ has a pronounced peak at a finite voltage $V_0$. The peak position $V_0$ increases linearly with $H$. To explain the experiment, we develop a theoretical model of graphite in the crossed electric $E$ and magnetic $H$ fields. When the fields satisfy the resonant condition $E=vH$, where $v$ is the velocity of the two-dimensional Dirac electrons in graphene, the wave functions delocalize and give rise to the peak in the tunneling spectrum observed in the experiment.Comment: 6 pages, 6 figures; corresponds to the published version in Eur. Phys. J. Special Topics, Proceedings of the IMPACT conference 2012, http://lptms.u-psud.fr/impact2012

Occurrence of Calcium Oscillations in Human Spermatozoa Is Based on Spatial Signaling Enzymes Distribution

In human spermatozoa, calcium dynamics control most of fertilization events. Progesterone, present in the female reproductive system, can trigger several types of calcium responses, such as low-frequency oscillations. Here we aimed to identify the mechanisms of progesterone-induced calcium signaling in human spermatozoa. Progesterone-induced activation of fluorophore-loaded spermatozoa was studied by fluorescent microscopy. Two computational models were developed to describe the spermatozoa calcium responses: a homogeneous one based on a system of ordinary differential equations and a three-dimensional one with added space dimensions and diffusion for the cytosolic species. In response to progesterone, three types of calcium responses were observed in human spermatozoa: a single transient rise of calcium concentration in cytosol, a steady elevation, or low-frequency oscillations. The homogenous model provided qualitative description of the oscillatory and the single spike responses, while the three-dimensional model captured the calcium peak shape and the frequency of calcium oscillations. The model analysis demonstrated that an increase in the calcium diffusion coefficient resulted in the disappearance of the calcium oscillations. Additionally, in silico analysis suggested that the spatial distribution of calcium signaling enzymes governs the appearance of calcium oscillations in progesterone-activated human spermatozoa

The First Case of Cytauxzoon spp. in Russia: The Parasite Conquers Eurasia

Over the last two decades, Cytauxzoon spp. has been conquering Eurasia, although this fact has only been brought to light through recent more intensive research after the discovery of C. manul in Pallas’ cat. In Europe, Cytauxzoon was detected mainly in southern countries and later in central Europe. This pathogen has now been found in Russia for the first time (50 km from Moscow), this being the most northern sighting in Eurasia. A captive serval (Leptailurus serval) was found to be infected. Hematological analysis showed a crucial decrease in the number of leukocytes and erythrocytes, as well as in hemoglobin concentration. Genetic analysis confirmed the presence of Cytauxzoon spp. in serval blood at the beginning of the disease period. The identical pathogen was found in one bobcat at the same breeding center. Two other haplotypes of Cytauxzoon spp. were obtained from domestic cats at the same location, identical to the samples from Italy. One new haplotype, which was sequenced for the first time, was found in 7/7 investigated Amur wildcats (100%). The high occurrence and diversity of these pathogens suggest that they are present in free-ranging domestic cats and wild felids in Russia, and may be considered a potential threat to the endangered species. Current research shows that the genetic diversity of this pathogen may be even higher than it was suggested previously. Further genetic research is necessary to describe the diversity and phylogeny of this pathogen in Eurasia

Misdiagnosis of diabetic foot ulcer in patients with undiagnosed skin malignancies

A growing number of studies report dermal malignancies mimicking diabetic foot ulcers (DFUs). We reviewed clinical cases reporting malignant tumours misdiagnosed to be DFU aiming to identify factors contributing to misdiagnosis. We systematically searched in PubMed for clinical cases reporting on misdiagnosis of DFU in patients with cancer. A chi-square analysis was conducted to show the link between the incidence of initial DFU misdiagnosis and patient age, gender and wound duration. Lesions misdiagnosed to be DFU were subsequently diagnosed as melanoma (68% of the cases), Kaposi's sarcoma (14%), squamous cell carcinoma (11%), mantle cell lymphoma, and diffuse B-cell lymphoma (both by 4%). Older age (≥65 years) was associated with a significantly increased risk of malignancy masked as DFU (OR: 2.452; 95% CI: 1.132 to 5.312; P value = .019). The risk of such suspicion in older patients (age ≥ 65 years) was 145% higher than in younger patients (age < 65 years). Clinicians should maintain a high level of awareness towards potentially malignant foot lesions in elderly patients with diabetes (age ≥ 65)