# 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 multichannel, 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 multichannel superconductivity, i.e., mediated by phonons, spin-fluctuations and charge fluctuations that are treated 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, multichannel pairing 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]. For bulk FeSe our selfconsistent calculations show that spin-fluctuations are the main driver of the observed unconventional superconductivity with a T_{c} ~ 8 K [5].

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

This state-of-the-art code uses the *ab initio *calculated electronic and phononic (or spin / charge fluctuation) properties of a material and calculates the material's superconducting state in an *ab initio *manner by solving selfconsistently the coupled Eliashberg equations (for recent results, see the references below). 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
- Multichannel superconductivity, treating phonons, and spin / charge fluctuations
- 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}. - Schrodi, Aperis and Oppeneer,
*Eliashberg theory for spin-fluctuations mediated superconductivity: Application to bulk and monolayer FeSe*. Phys. Rev. B**102**014502 (2020). - Bekaert, Petrov, Aperis, Oppeneer and Milosevic,
*Hydrogen-induced high-temperature superconductivity in two-dimensional materials: Exemplary analysis of hydrogenated monolayer MgB*. Phys. Rev. Lett._{2}**123**, 077001 (2019). - Schrodi, Oppeneer and Aperis,
*Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation.*Phys. Rev. B**102**, - Schrodi, Aperis and Oppeneer,
*Prominent Cooper Pairing Away From the Fermi Level and its Spectroscopic Signature in Twisted Bilayer Graphene*. Phys. Rev. Res. – Rapid Commun.**2**, 012066 (2020). - Aperis, Morooka and Oppeneer,
*Influence of electron-phonon coupling strength on signatures of even and odd-frequency superconductivity*. Ann. Phys.**417,**168095 (2020). - Schrodi, Aperis and Oppeneer,
*Improved performance of Matsubara space calculations – A case study within Eliashberg theory of superconductivity*. Phys. Rev. B**99**, *Schrodi, Aperis and Oppeneer, Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO*Phys. Rev. B_{3}.**98**,*Zhou, Semenok, Xie, Huang, Duan, Aperis et al., High-Pressure Synthesis of Magnetic Neodymium Polyhydrides.*JACS**142**,