A Clifford Algebra-based mathematical model for the determination of critical temperatures in superconductors
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ORIGINAL PAPER
A Clifford Algebra-based mathematical model for the determination of critical temperatures in superconductors Sudharsan Thiruvengadam1,2 • Matthew Murphy1
•
Karol Miller2
Received: 18 June 2019 / Accepted: 20 June 2020 Springer Nature Switzerland AG 2020
Abstract In recent years, numerous strides have been taken towards to discovery of superconducting lattices, exhibiting the Meissner–Ochsenfeld effect, at increasingly higher temperatures. In this work, we present a novel and generalised mathematical formulation, which maps the atomic and structural characteristics of superconducting lattice structures to their critical temperature. This formulation models many-agent systems by representing them as spatially distributed networks in R4;1 Conformal Geometric Algebraic space. Using these higher-dimensional mathematical representations, we present generalised relationships between the critical temperature and basic atomic information, including crystal unit cell data, for an arbitrary lattice structure. Case studies have been presented for Nd2Fe2Se2O3, LiFeAs, LaOFeAs, Sr2VO3FeAs, Sr2Mn2CuAs2O2 and Ba2YCu3O7. Keywords Conformal Geometric Algebra Superconductors Lattice Critical temperature
1 Introduction and motivation In recent years, numerous papers have been written advancing the state of the art of high temperature superconductors for applications in transportation, power distribution and electronics [1–7]. The discovery and subsequent application of hightemperature superconductors, near room temperature, is a highly desirable goal for both academia and industry [8]. The Meissner–Ochsenfeld effect is a temperature-dependent electromagnetic phenomenon, whereby the lattice structure experiences zero electrical resistance and & Sudharsan Thiruvengadam [email protected] 1
BlueStem Pty. Ltd., 128 Parry Avenue, Bull Creek, WA 6149, Australia
2
The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
123
Journal of Mathematical Chemistry
the lattice acts as a perfect diamagnet; magnetic flux is excluded from all but a thin penetration region near the surface [9]. The Meissner–Ochsenfeld effect occurs below the critical temperature (Tc ). It is understood that the Tc is related to the unit cell geometry and the electromagnetic field distributions of the lattice atoms [9–11]. Therefore, it is necessary for any generalised theoretical model for Tc prediction to incorporate both of these characteristics in a systematic and comprehensive manner. The aim of this work is to incorporate both geometry and the electromagnetic field distributions into a single generalised governing theoretical expression, that allows for arbitrary superconducting lattice structures to be related to Tc . Optimal doping configurations can be identified, by virtue of the detailed mapping of atomic properties and the geometric structure of the crystal lattice. Such doping configurations may lead to the increase of Tc for existing superconduct
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