Debye lunch lecture - Riccardo Reho (CMI)

DFT for Superconductors: theory and implementation in the SIESTA code

Abstract: Superconductivity is one of the most captivating quantum phenomena, offering a potential solution for the increasing societal demand of sustainable energy resources. Superconducting density functional theory (SCDFT) [1] is a theoretical framework that combines density functional theory (DFT) [2, 3] with the Bogoliubov—de Gennes (BdG) formalism [4]. SCDFT allows for a general form of the pairing interaction and, hence, can describe normal/superconductor interfaces and unconventional superconductors, in addition to conventional ones [5]. In this talk, we present SIESTA—BdG [5], an implementation of the semi-phenomenological SCDFT approach of Suvasini et al. [6, 7] in the SIESTA method [8]. We demonstrate the accuracy and efficiency of our implementation in predicting physically relevant quantities (superconducting charge density, band structure, superconducting gap, density of states) for conventional (Pb, Nb), and unconventional (FeSe) superconductors. Moreover, we apply this method to a semiconductor—superconductor (SM—SC) hybrid devices composed of PbTe and Pb. These devices have been proposed as promising platforms for detecting and analyzing Majorana zero modes [9]. We focus on the interfacial properties, discussing the conditions required for the emergence of Majorana Zero modes. Lastly, we show how the SIESTA-BdG forms the basis for modelling quantum transport in superconducting devices.

References

1. Oliveira, L. N., Gross, E. K. U. & Kohn, W. Density-Functional Theory for Superconductors. Physical Review Letters 60, 2430–2433. issn: 0031-9007 (2022) (June 1988).

2. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Physical review 136, B864 (1964).

3. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Physical review 140, A1133 (1965).

4. Bogoljubov, N., Tolmachov, V. V. & Širkov, D. A new method in the theoryof superconductivity. Fortschritte der physik 6, 605–682 (1958).

5. R. Reho, N. Wittemeier, A. H. Kole, P. Ordejón, and Z. Zanolli. Density functional bogoliubov-de gennes theory for superconductors implemented in the siesta code. Phys. Rev. B, 110:134505, Oct 2024

6. Suvasini, M. & Gyorffy, B. A Multiple Scattering Method for Solving Bogoliubov-de Gennes Equations of Superconductivity. Physica C: Superconductivity 195, 109–126. issn: 09214534. (2022) (May 1992).

7. Suvasini, M. B., Temmerman, W. M. & Gyorffy, B. L. Computational aspects of density-functional theories of superconductors. Phys. Rev. B 48, 1202–1210 (2 July 1993).

8. Soler, J. M. et al. The SIESTA Method for Ab Initio Order- N Materials Simulation. Journal of Physics: Condensed Matter 14, 2745–2779. issn:0953-8984, 1361-648X. (2021) (Mar. 2002).

9. R. Reho, A. R. Botello-Méndez,  and Z. Zanolli. First–principles investigation of Proximity-Induced Superconductivity in PbTe/Pb hybrid devices, in preparation (2024)