The anomalous Hall effect (AHE) arises from the interplay of spin-orbit interactions and ferromagnetic order and is a potentially useful probe of electron spin polarization, especially in nanoscale systems where direct measurement is not feasible. While AHE is rather well-understood in metallic ferromagnets, much less is known about the relevance of different physical mechanisms governing AHE in insulators. As ferromagnetic insulators, but not metals, lend themselves to gate-control of electron spin polarization, understanding AHE in the insulating state is valuable from the point of view of spintronic applications. Among the mechanisms proposed in the literature for AHE in insulators, the one related to a geometric (Berry) phase effect has been elusive in past studies. The recent discovery of quantized AHE in magnetically doped topological insulators - essentially a Berry phase effect - provides strong additional motivation to undertake more careful search for geometric phase effects in AHE in the magnetic semiconductors. Here we report our experiments on the temperature and magnetic field dependences of AHE in insulating, strongly-disordered two-dimensional Mn delta-doped semiconductor heterostructures in the hopping regime. In particular, it is shown that at sufficiently low temperatures, the mechanism of AHE related to the Berry phase is favoured.

We report the first experimental observation of superconductivity in Cd3As2 thin films without application of external pressure. Surface studies suggest that the observed transport characteristics are related to the polycrystalline continuous part of investigated films with homogeneous distribution of elements and the Cd-to-As ratio close to stoichiometric Cd3As2. The latter is also supported by Raman spectra of the studied films, which are similar to those of Cd3As2 single crystals. The formation of superconducting phase in films under study is confirmed by the characteristic behavior of temperature and magnetic field dependence of samples resistances, as well as by the presence of pronounced zero-resistance plateaux in dV /dI characteristics. The corresponding Hc−Tc plots reveal a clearly pronounced linear behavior within the intermediate temperature range, similar to that observed for bulk Cd3As2 and Bi2Se3 films under pressure, suggesting the possibility of nontrivial pairing in the films under investigation. We discuss a possible role of sample inhomogeneities and crystal strains in the observed phenomena.Weyl and Dirac semimetals (WSM and DSM) currently attract wide interest related to the existence of Dirac nodes in their electron spectrum and related nontrivial topological characteristics of both bulk and surface states [1][2][3]. A special attention is drawn to the Cd 3 As 2 compound, which proved to be air-stable, unlike some other DSM materials [4][5][6][7][8]. This compound is known and has been studied for quite a long time [9][10][11][12]. Nevertheless, it is still very popular since the Dirac nodes of this semimetal are protected by the crystal symmetry and the electron states exhibit interesting topological properties, such as spin-momentum locking. Due to the high symmetry, DSM materials can undergo transitions to other topological phases (e.g. WSM) as a result of breaking certain symmetries or applying some external factors.The existence of topologically protected electron states gives a new impetus to the problem of topological superconductivity (TSC) being discussed for a long time [13][14][15]. In particular, Refs. [16,17] provide a theoretical analysis of the possible types of SC pairing in the systems of Cd 3 As 2 type, including topologically nontrivial ones. Basically, the existence of nontrivial pairing potential (leading to the emergence of triplet Cooper pairs) should induce the formation of Majoranna modes at the surface of the crystal, which can be used in the faulttolerant quantum computing [14]. The SC phase emergence in Cd 3 As 2 was reported in Ref.[18], however, it was observed at pressures above the structural transition from the tetragonal to trigonal phase. While theoretical works suggest the stabilization of TSC phase upon such symmetry lowering [16,17], such transition also implies appearance of the gap at Dirac nodes, thus, suppressing the DSM phase. Additional indications of the SC phase in Cd 3 As 2 were also observed in the point-contact spectroscopy experiments and att...

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