Band structure of the P, D, and G surfaces

Abstract

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.

Structural, magnetic and magnetocaloric properties of La0.8Gd0.2Fe11.4Si1.6

“…It is known that c 1 is positive and minimum at T C for both firstand second-order transitions. On the other hand, c 2 (T) crosses zero at T C in the case of second-order transition, while it crosses zero at temperatures above T C in the case of first-order transition [4]. From the figure, it is clear that the transition in La 0.8 Gd 0.2 Fe 11.4 Si 1.6 is of second order.…”

“…These plots show a maximum near the T C with the value of 7.9 J/kg K for 50 kOe. The entropy change observed in the case of LaFe 11.4 Si 1.6 for a field of 50 kOe is 20 J/kg K [4].…”

“…Fujita et al [4] have reported that La(Fe,Si) 13 compounds crystallize in NaFe 13 -type structure and exhibit metamagnetic transition, which is due to the discontinuous splitting of the 3d band. It is also reported that giant MCE observed in some of these compounds is a result of the first-order magnetic transition at the Curie temperature (T C ).…”

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

“…The process is probably severe and breaks with natural limits set by the uncertainty principle, but it has been demonstrated that the attractive geometric potential is valid and important to some curved systems [21][22][23]. On actual grounds, the curved surface with certain thickness is the real existence.…”

“…(11). It is easy to decompose into the surface dynamics (22) and the normal dynamics (23) by repeating the above adopted procedure. The surface integral (26) plays the role of a boundary condition, which vanishes, and that the Schrödinger equation (11) is stipulated only by the volume integral (25).…”