arXiv subjects

Clemens Schindler

Publications and source records attributed to Clemens Schindler.

7 recordsLinked to original sources

arXiv2023

On the Zariski topology on endomorphism monoids of omega-categorical structures

The endomorphism monoid of a model-theoretic structure carries two interesting topologies: on the one hand, the topology of pointwise convergence induced externally by the action of the endomorphisms on the domain via evaluation; on the other hand, the Zariski topology induced within the monoid by (non-)solutions to equations. For all concrete endomorphism monoids of $ω$-categorical structures on which the Zariski topology has been analysed thus far, the two topologies were shown to coincide, in turn yielding that the pointwise topology is the coarsest Hausdorff semigroup topology on those endomorphism monoids. We establish two systematic reasons for the two topologies to agree, formulated in terms of the model-complete core of the structure. Further, we give an example of an $ω$-categorical structure on whose endomorphism monoid the topology of pointwise convergence and the Zariski topology differ, answering a question of Elliott, Jonušas, Mitchell, Péresse and Pinsker.

math.LO↗

arXiv2023

The semigroup of increasing functions on the rational numbers has a unique Polish topology

The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions converges if and only if it is eventually constant at every argument. We develop new techniques to prove there is no other Polish topology turning this semigroup into a topological one, and show that previous techniques are insufficient for this matter.

math.RA↗

arXiv2020

Strong anisotropy of electron-phonon interaction in NbP probed by magnetoacoustic quantum oscillations

In this study, we report on the observation of de Haas-van Alphen-type quantum oscillations (QO) in the ultrasound velocity of NbP as well as `giant QO' in the ultrasound attenuation in pulsed magnetic fields. The difference of the QO amplitude for different acoustic modes reveals a strong anisotropy of the effective deformation potential, which we estimate to be as high as $9\,\mathrm{eV}$ for certain parts of the Fermi surface. Furthermore, the natural filtering of QO frequencies and the tracing of the individual Landau levels to the quantum limit allows for a more detailed investigation of the Fermi surface of NbP as was previously achieved by means of analyzing QO observed in magnetization or electrical resistivity.

cond-mat.other↗

arXiv2020

W*-Algebras as a complete axiomatisation of Von-Neumann algebras

By the Gelfand-Naimark theorem, any C*-algebra is isometrically isomorphic to a *-algebra of bounded operators on a Hilbert space which is closed with respect to the topology induced by the operator norm. Hence, the C*-algebras furnish an axiomatisation of the structure of those operator algebras. In fact, the axiomatisation is complete in the sense that the entire structural information considered on the closed *-algebra -- namely addition, scalar multiplication, adjunction and composition of operators as well as the operator norm -- is reflected in the C*-algebra. From this point of view, we treat Von-Neumann algebras, another class of operator algebras also defined as closed *-algebras, but with respect to another topology -- one possibility is the weak operator topology. The problem asking for an axiomatisation of Von-Neumann algebras was solved by S. Sakai who introduced so-called W*-algebras. They are C*-algebras which, considered as a Banach space, are isometrically isomorphic to the dual space of another Banach space called the predual. Sakai's theorem asserts that the W*-algebras provide an axiomatisation of Von-Neumann algebras. In this master's thesis, we give a proof of Sakai's theorem. In fact, we provide a stronger version of Sakai's theorem which shows that W*-algebras indeed form a complete axiomatisation analogous to the situation for C*-algebras. Additionally, we show uniqueness of the predual up to isometric isomorphism, simplifying Sakai's original proof by using our strengthened version of Sakai's theorem.

math.OA↗

arXiv2020

Effect of uniaxial stress on the electronic band structure of NbP

The Weyl semimetal NbP exhibits a very small Fermi surface consisting of two electron and two hole pockets, whose fourfold degeneracy in $k$ space is tied to the rotational symmetry of the underlying tetragonal crystal lattice. By applying uniaxial stress, the crystal symmetry can be reduced, which successively leads to a degeneracy lifting of the Fermi-surface pockets. This is reflected by a splitting of the Shubnikov-de Haas frequencies when the magnetic field is aligned along the $c$ axis of the tetragonal lattice. In this study, we present the measurement of Shubnikov-de Haas oscillations of single-crystalline NbP samples under uniaxial tension, combined with state-of-the-art calculations of the electronic band structure. Our results show qualitative agreement between calculated and experimentally determined Shubnikov-de Haas frequencies, demonstrating the robustness of the band-structure calculations upon introducing strain. Furthermore, we predict a significant shift of the Weyl points with increasing uniaxial tension, allowing for an effective tuning to the Fermi level at only 0.8% of strain along the $a$ axis.

cond-mat.mtrl-sci↗

arXiv2020

Anisotropic electrical and thermal magnetotransport in the magnetic semimetal GdPtBi

The half-Heusler rare-earth intermetallic GdPtBi has recently gained attention due to peculiar magnetotransport phenomena that have been associated with the possible existence of Weyl fermions, thought to arise from the crossings of spin-split conduction and valence bands. On the other hand, similar magnetotransport phenomena observed in other rare-earth intermetallics have often been attributed to the interaction of itinerant carriers with localized magnetic moments stemming from the $4f$-shell of the rare-earth element. In order to address the origin of the magnetotransport phenomena in GdPtBi, we performed a comprehensive study of the magnetization, electrical and thermal magnetoresistivity on two single-crystalline GdPtBi samples. In addition, we performed an analysis of the Fermi surface via Shubnikov-de Haas oscillations in one of the samples and compared the results to \emph{ab initio} band structure calculations. Our findings indicate that the electrical and thermal magnetotransport in GdPtBi cannot be solely explained by Weyl physics and is strongly influenced by the interaction of both itinerant charge carriers and phonons with localized magnetic Gd-ions and possibly also paramagnetic impurities.

cond-mat.mes-hall↗

arXiv2019

Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I

An axion insulator is a correlated topological phase, predicted to arise from the formation of a charge density wave in a Weyl semimetal. The accompanying sliding mode in the charge density wave phase, the phason, is an axion. It is expected to cause anomalous magneto-electric transport effects. However, this axionic charge density wave has so far eluded experimental detection. In this paper, we report the observation of a large, positive contribution to the magneto-conductance in the sliding mode of the charge density wave Weyl semimetal (TaSe4)2I for collinear electric and magnetic fields (E||B). The positive contribution to the magneto-conductance originates from the anomalous axionic contribution of the chiral anomaly to the phason current, and is locked to the parallel alignment of E and B. By rotating B, we show that the angular dependence of the magneto-conductance is consistent with the anomalous transport of an axionic charge density wave.

cond-mat.mes-hall↗