The thermodynamic critical field and specific heat of superconducting state in phosphorene under strain

• Published in: arXiv.org 2018-05
• Main Authors: Szewczyk, Kamila A, Kaczmarek, Adam Z, Drzazga, Ewa A
• Format: Article
• Language: English
• Subjects: BCS theory; Critical field (superconductivity); Critical temperature; Electrons; Mathematical analysis; Monolayers; Phonons; Phosphorene; Specific heat; Superconductivity; Thermodynamic properties
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1805.04284

In this work we present the thermodynamic properties of the superconducting state in phosphorene. In particular, we have examined the electron doped (\(n_{D}=1.3\times 10^{14} \rm{cm^{-2}}\)) and biaxially strained (4 %) monolayer of black phosphorous, which exhibits best thermodynamic stability and highest superconducting critical temperature (\(T_{c}\)) among all monolayer phosphorene structures. Due to the confirmed electron-phonon pairing mechanism and relatively high electron-phonon coupling constant in the studied material, we carried out the calculations in the framework of the Eliashberg formalism for a wide range of the Coulomb pseudopotential \(\mu^{\star}\in\langle 0.1, 0.3\rangle\). We have determined the thermodynamic critical field (\(H_{c}\)), and the specific heat difference (\(\Delta C\)) between superconducting (\(C^{S}\)) and normal state (\(C^{N}\)) as the functions of the temperature. In addition, we have calculated the dimensionless parameters \(R_{C}=\Delta C(T_{c})/C^{N}(T_{c})\) and \(R_{H}=T_{c}C^{N}(T_{c})/H^{2}_{c}(0)\), and also found their significant deviation from the expectations of the BCS theory. In particular, \(R_{C} \simeq \langle 2.724, 1.899\rangle\) and \(R_{H} \simeq \langle 0.133, 0.155\rangle\) for \(\mu^{\star}\in \langle 0.1, 0.3\rangle\).