Estimating the Single-Element Concentration of Intercalated Insulators for the Emergence of Superconductivity

Abstract

To predict whether a compound will superconduct and to predict its transition temperature T c prior to measurement have always been desires of the materials science community. Matthias was first to report the necessary conditions for the occurrence of superconductivity in elements, compounds, and alloys in terms of density (valence electrons per atom). This current report is motivated by somewhat similar empirical observations concerning the importance of valence electrons per unit cell; more specifically, dopant valence electrons per unit cell within intercalated insulators. In this article, though not exhaustive, a representative list of 40 superconductors will be used to show that the onset of superconductivity (insulator–superconductor boundary) within intercalated insulators can easily be modeled, almost exactly, by the ideal gas law equation. Given this observation, in contrast to Matthias, interactions are semiclassically accounted for to ultimately determine the single-element onset concentration needed to bring about superconductivity within many intercalated insulators known to date. The 13 compounds which were previously intercalated and will be discussed include inorganics, TiSe2, C60, YBa2Cu3O6, IrTe2, Bi2Se3, MoS2, ZrNCl, HfNCl, BP (black phosphorus), HoTe3, and Y2Te5, and organics, C22H14 and C14H10. In essence, the overall objective of this report is to offer a slightly different viewpoint on superconductivity, led by empirical observations, which seemingly leads to predictable experimental outcomes. If newly discovered materials further validate this approach to intercalated superconductors, with minor refinements, a route to purposefully designing superconductors may be accessible through onset conditions outlined in this article.

Intercalate Superconductivity and van der Waals Equation

“…This yields from eq 1 an onset transition temperature of 0.96 K, which is close to the measured value T c-onset = 1 K. Similarly, most transition temperatures calculated from the ideal gas law equation were lower than those from experimentally measured T c-onset . 10 This was perhaps due to a misunderstanding of the pressure variable P which was fixed to 1 atm (i.e., the lab pressure during experiment). If pressure is not held constant, but instead calculated, an interesting feature emerges from the data.…”

“…A more recent study on the emergence of superconductivity from intercalated compounds, specifically at the insulator–superconductor boundary of those intercalated by a single element, revealed the boundary closely follows the ideal gas law relation, as shown in eq 1 . 10 Where P and V unit are the pressure (1 atm) and unit cell volume, respectively. The variables x onset , N val , K β , and T c-onset are the minimum intercalant concentration required for superconductivity to emerge such that T c ≠ 0 at constant pressure, the number of valence electrons of the intercalant (including s and d electrons for transition metals), Boltzmann constant, and the experimentally measured transition temperature at x onset , respectively.…”

“… 11 Now it is shown to empirically embody the behavior of intercalant valence electrons at the insulator–superconductor boundary, while aiding in the prediction of the onset of superconductivity, as well. 10 …”

“…Although the ideal gas law relation is a close approximation for onset conditions, it is not exact. 10 Therefore, the aim of this report is to apply the extended ideal gas law equation (van der Waals equation) to superconducting intercalated compounds to gain insight on the reason for the apparent deviation from eq 1 . Special attention is placed on the pressure parameter “ P ” to reveal the attractive interactions among superconducting intercalant valence electrons.…”

“…These were chosen as representatives from the list of 40 intercalated compounds whose onset conditions were previously shown to be easily modeled by the ideal gas law equation. 10 Although the proposed argument in upcoming sections holds for all 40 compounds, only Cu x TiSe 2 and YBa 2 Cu 3 O 6+ x will be discussed in this article. This is because they appear quite different from each other at first glance.…”