# Ab Initio Theory of Superconductivity

**Superconductivity is an astonishing physical phenomenon that continues to perplex physicists. Unconventional high-T _{c} superconductivity (T_{c }≥ 100 K) discovered in copper-oxides thirty years ago still lacks a comprehensive explanation. Accurately explaining unconventional superconductivity is therefore one of the outstanding problems of condensed matter theory.**

The group of Peter Oppeneer develops analytic theory and computational approaches to provide a materials’ specific explanation of novel forms of superconductivity. In particular, we have developed the multiband, full-bandwidth anisotropic Eliashberg theory for selfconsistent calculations of unconventional and high-temperature superconductivity [1,2]. We solve the coupled anisotropic Eliashberg equations selfconsistently with input from first-principles calculations for the electron and phonon spectra and can treat both phonon and spin-fluctuations mediated superconductivity on equal footing [3]. To achieve this we have developed the Uppsala Superconductivity code (UppSC) capable of predicting *ab initio *high-temperature superconductivity as well as unconventional forms, such as multiband superconductivity, topological superconductivity, and both frequency even and odd superconductivity (see Fig. 1).

Our theoretical modeling and *selfconsistent* calculations enable deep insights into the fundamental origins and behavior of superconductivity and provide a step toward reaching its complete understanding. Our multiband, full-bandwidth anisotropic Eliashberg theory calculations for a monolayer FeSe on SrTiO_{3} highlight the importance of interfacial electron-phonon interaction that can explain the key experimental features and predict a T_{c} of ~60 K [2,4]. Our full-bandwidth calculations establish the importance of Cooper pairing of electrons away from the Fermi energy, so called *deep Fermi-sea Cooper pairing* [2].

**What the Uppsala Superconductivity (UppSC) code can do:**

This state-of-the-art code uses the *ab initio *calculated electronic and phononic (or spin-fluctuation) properties of a material and calculates the material's superconducting state in an *ab initio *manner by solving selfconsistently the coupled Eliashberg equations. The code is interfaced with DFT and DFPT calculations for electron-phonon systems. Some of the features of UppSC are:

- Treats full momentum and frequency dependence of electronic and bosonic self-energies
- Full bandwidth, momentum dependent, multi-band superconductivity
- Unconventional superconductivity, as simultaneous evaluation of frequency-even and odd superconductivity
- Unconventional, non s-wave symmetry of superconducting order
- Able to compute deep Fermi-sea Cooper pairing
- Adiabatic and nonadiabatic superconductivity
- Selfconsistent temperature dependent renormalization of quasiparticle bands
- Inclusion of Zeeman magnetic field and magnetic self-energy effects
- Numerical analytic continuation with three different methods
- Temperature, magnetic field and doping dependent solutions
- Evaluates experimental quantities like ARPES, STS and London penetration depth

**Contact**

Alex Aperis, Peter M. Oppeneer

**Funding**

Research Council (VR), Röntgen-Ångström Cluster.

**References**

- Aperis, Maldonado and Oppeneer,
*Ab initio theory of magnetic field induced odd-frequency superconductivity in MgB*Phys. Rev. B_{2}.**92**, 054516 (2015). - Aperis and Oppeneer,
*Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-T*Phys. Rev. B_{c}superconductivity in FeSe/SrTiO_{3}.**97**, 060501(R) (2018). - Bekaert, Aperis, Partoens, Oppeneer and Milosevic,
*Advanced first-principles theory of superconductivity including both lattice vibrations and spin fluctuations: The case of FeB*. Phys. Rev. B_{4}**97**, - Schrodi, Aperis, Oppeneer,
*Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO*Phys. Rev. B 98, 094509 (2018)._{3}, - Bekaert, Petrov, Aperis, Oppeneer and Milosevic,
*Hydrogen-induced high-temperature superconductivity in two-dimensional materials: Exemplary analysis of hydrogenated monolayer MgB*, arxiv (2019)._{2}