A theory of the strain-dependent critical field in Nb₃Sn, based on anharmonic phonon generation

Abstract

We propose a theory to explain the strain dependence of the critical properties in A15 superconductors. Starting from the strong-coupling formula for the critical temperature, and assuming that the strain sensitivity stems mostly from the electron-phonon α 2 F function, we link the strain dependence of the critical properties to a widening of α 2 F . This widening is attributed to the nonlinear generation of phonons, which takes place in the anharmonic deformation potential induced by the strain. Based on the theory of sum-and difference-frequency wave generation in nonlinear media, we obtain an explicit connection between the widening of α 2 F and the anharmonic energy. The resulting model is fit to experimental datasets for Nb 3 Sn, and the anharmonic energy extracted from the fits is compared with first-principles calculations.

GLAG theory for superconducting property variations with A15 composition in Nb3Sn wires

“…(1), (5) and (6). The result of the strong-coupling correction to H c 2 approximately equals to the calculated value 19 of 1.17 at T c  = 17.8 K. The calculated EP interaction parameter λ ep at the stoichiometry 25 at% Sn is slightly lower than the generally accepted value of 1.8 27 . However, at larger derivation from the stoichiometry, the calculated λ ep differs relatively larger from the value of 1.8.

Figure 3EP correction parameters, the Debye temperature θ D and energy gap Δ(0), versus tin content.

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Fundamental origin of the large impact of strain on superconducting Nb3Sn

“…For strain in the [110] direction, the change in H c2 is for 77% attributable to a change in the electronic properties. These findings are in contrast to other analyses in which mostly an a priori assumption was made that changes in the phonon spectrum [28,[45][46][47][48][49], or changes in the electron DOS [50][51][52], are the dominant cause for the large strain sensitivity of Nb 3 Sn. We also note that an assumption that changes in the phonon spectrum dominate the effects of strain, is in conflict with the experimental evidence that ρ n changes substantially with strain [33,36]: ρ n is at temperatures below 18K mainly determined by defect scattering and not by the phonons.…”

Estimate of density-of-states changes with strain in A15 Nb 3 Sn superconductors

“…Several attempts at determining a generic parameterization for the critical properties (the critical temperature T c , the upper critical field l 0 H c2 , and the critical current density J c ) have been made in the past decades, which involves the empirical characterization and interpretation of uniaxial strain dependence [7][8][9], the microscopic modeling based on the strain-induced modifications in the electron-phonon spectrum [10][11][12], the electron density of states (DOS) [13,14] or both [15], and the models with a semi-empirical construction which balances the need for well-founded formalisms for the important features of the strain effects and practical engineering application to multifilamentary composite Nb 3 Sn wire measurements implementation [16][17][18]. Because of the failure to make explicit an underlying microscopic mechanisms, the description of the strain sensitivity in superconducting Nb 3 Sn offered by empirical/semi-empirical modeling and analytics exhibits its limitations in achieving the comprehensive characterizations [14,16].…”

“…The role of strain-induced anharmonicity on the phonon spectrum as a source of the strain effects in A15 Nb 3 Sn strands has been recognized and emphasized in the literatures [10][11][12], where the strain dependence of the critical temperature T c is focused on. Since the strain effects on the critical current density J c in the Nb-Sn system arise from the field-temperature phase boundary shifts and strain-dependent changes of the flux line to lattice interactions, the improved understanding of the strain sensitivity in superconducting Nb 3 Sn calls for an endeavor to determine the DOS at the Fermi surface N(E F ) as function of strain, which will help contribute to future studies on the microscopic-based strain description of the temperature-dependent upper critical field l 0 H c2 (T) [16].…”

“…The inherent mechanism of the phenomenon that the superconducting properties of A15 Nb 3 Sn are highly strain sensitive is not fully elucidated, with the aim of clarifying whether the strain sensitivity originates from the electronic modifications, the quantitative interpretation of the measured resistivity data of materials under the coupled effects of uniaxial compressive strain states, temperature and various magnetic fields will give a insight into the features in the electron DOS behavior of strained Nb 3 Sn superconductors [19]. Although various models have been introduced for the reversible depression in the critical superconducting properties of Nb 3 Sn superconductors due to strain [7][8][9][10][11][12][13][14][15], the quantitative analysis of the electron DOS of Nb 3 Sn as function of strain is further required to obtain a better physical picture.…”