Impact of domain disorder on optoelectronic properties of layered semimetal MoTe2

We address the impact of crystal phase disorder on the generation of helicity-dependent photocurrents in layered MoTe2, which is one of the van der Waals materials to realize the topological type-II Weyl semimetal phase. Using scanning photocurrent microscopy, we spatially probe the phase transition and its hysteresis between the centrosymmetric, monoclinic 1T’ phase to the symmetry-broken, orthorhombic Td phase as a function of temperature. We find a highly disordered photocurrent response in the intermediate temperature regime. Moreover, we demonstrate that helicity-dependent and ultrafast photocurrents in MoTe2 arise most likely from a local breaking of the electronic symmetries. Our results highlight the prospects of local domain morphologies and ultrafast relaxation dynamics on the optoelectronic properties of low-dimensional van der Waals circuits.

The Topology of the Configuration Space of a Mathematical Model for Cycloalkenes

As a mathematical model for cycloalkenes, we consider equilateral polygons whose interior angles are the same except for those of the both ends of the specified edge. We study the configuration space of such polygons. It is known that for some case, the space is homeomorphic to a sphere. The purpose of this chapter is threefold: First, using the h-cobordism theorem, we prove that the above homeomorphism is in fact a diffeomorphism. Second, we study the best possible condition for the space to be a sphere. At present, only a sphere appears as a topological type of the space. Then our third purpose is to show the case when a closed surface of positive genus appears as a topological type.

Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal Td-WTe2

Layered van der Waals semimetallic Td-WTe2, exhibiting intriguing properties which include non-saturating extreme positive magnetoresistance (MR) and tunable chiral anomaly, has emerged as a model topological type-II Weyl semimetal system. Here, ∼45 nm thick mechanically exfoliated flakes of Td-WTe2 are studied via atomic force microscopy, Raman spectroscopy, low-T/high-μ0H magnetotransport measurements and optical reflectivity. The contribution of anisotropy of the Fermi liquid state to the origin of the large positive transverse MR⊥ and the signature of chiral anomaly of the type-II Weyl Fermions are reported. The samples are found to be stable in air and no oxidation or degradation of the electronic properties is observed. A transverse MR⊥∼1200 % and an average carrier mobility of 5000 cm2V−1s−1 at T=5K for an applied perpendicular field μ0H⊥=7T are established. The system follows a Fermi liquid model for T≤50K and the anisotropy of the Fermi surface is concluded to be at the origin of the observed positive MR. Optical reflectivity measurements confirm the anisotropy of the electronic behaviour. The relative orientation of the crystal axes and of the applied electric and magnetic fields is proven to determine the observed chiral anomaly in the in-plane magnetotransport. The observed chiral anomaly in the WTe2 flakes is found to persist up to T=120K, a temperature at least four times higher than the ones reported to date.

Topological type of discriminants of some special families

We will describe the topological type of the discriminant curve of the morphism $$(\ell , f)$$ ( ℓ , f ) , where $$\ell $$ ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.

Semicontinuity of Gauss maps and the Schottky problem

We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application we obtain that in the case of theta divisors this degree answers the Schottky problem. Our proof computes the degree of Gauss maps by specialization of Lagrangian cycles on the cotangent bundle. We also get similar results for the intersection cohomology of varieties with a finite morphism to an abelian variety; it follows that many components of Andreotti–Mayer loci, including the Schottky locus, are part of the stratification of the moduli space of ppav’s defined by the topological type of the theta divisor.

A Refined Lines/Regions and Lines/Lines Topological Relations Model Based on Whole-Whole Objects Intersection Components

Refined topological relations play an important role in spatial database quality control. Currently, there is no unified and reasonable method to represent refined line/region and line/line topological relations in two-dimensional (2D) space. In addition, the existing independent line/region and line/line models have some drawbacks such as incomplete type discrimination and too many topological invariants. In this paper, a refined line/region and line/line topological relations are represented uniformly by the sequence, dimension, and topological type of the intersection components. To make the relevant definitions conform to the traditional cognitions in 2D Euclidean space, the (simple) spatial object is defined based on manifold topology, and the spatial intersection components are defined based on the whole-whole object intersection set. Then the topological invariant of node degree is introduced, and the adjacent point kinds (e.g., “Null”, “On”, “In”, and “Out”) are defined to distinguish the intersection component types. Excluding impossible and symmetrical types, 29 types of intersection-lines (including 21 between lines/regions and 8 between lines/lines), and 6 types of intersection-points (including 2 between lines/regions and 4 between lines/lines) are classified. On this basis, a node degree-based whole-whole object intersection sets (N-WWIS) model for refined line/region and line/line topological relations is presented, and it can be combined with the Euler number-based whole object intersection and difference (E-WID) model (coarse level) to form a hierarchical representation method of topological relations. Furthermore, a prototype system based on the N-WWIS model for automatic topological integrity checking is developed and some evaluation experiments are conducted with OpenStreetMap (OSM) data is presented based on the classification of intersection components. The experimental results show that the N-WWIS model will enable the geographic information systems (GIS) community to develop automated topological conflict checking and dealing tools for spatial data updates and quality control.