Ab Initio Theory of Superconductivity

Superconductivity is an astonishing physical phenomenon that continues to perplex physicists. Unconventional high-Tc superconductivity (T≥ 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).

Superconductivity phase diagram
Fig. 1. Ab initio calculated multi-band, frequency even and odd superconductivity of MgB2Calculated selfconsistent magnetic field (H) – temperature (T) phase diagrams of frequency-even (panel A) and frequency-odd superconductivity (panel B). Panel C: calculated magnetic field dependence of the even-frequency, spin singlet superconducting (ESS) gap and of the odd-frequency, spin triplet (OST) superconducting gap at the two bands of MgB2, at 4.2 K [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 SrTiO3 highlight the importance of interfacial electron-phonon interaction that can explain the key experimental features and predict a Tc 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 Tc ~ 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


Alex Aperis, Peter M. Oppeneer


Research Council (VR), Röntgen-Ångström Cluster.


  1. Aperis, Maldonado and Oppeneer, Ab initio theory of magnetic field induced odd-frequency superconductivity in MgB2Phys. Rev. B 92, 054516 (2015).
  2. Aperis and Oppeneer, Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-Tc superconductivity in FeSe/SrTiO3Phys. Rev. B 97, 060501(R) (2018).
  3. Bekaert, Aperis, Partoens, Oppeneer and Milosevic, Advanced first-principles theory of superconductivity including both lattice vibrations and spin fluctuations: The case of FeB4. Phys. Rev. B 97, 014503 (2018).
  4. Schrodi, Aperis, Oppeneer, Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO3Phys. Rev. B 98, 094509 (2018).
  5. Schrodi, Aperis and Oppeneer, Eliashberg theory for spin-fluctuations mediated superconductivity: Application to bulk and monolayer FeSe. Phys. Rev. B 102 014502 (2020).
  6. Bekaert, Petrov, Aperis, Oppeneer and Milosevic, Hydrogen-induced high-temperature superconductivity in two-dimensional materials: Exemplary analysis of hydrogenated monolayer MgB2. Phys. Rev. Lett. 123, 077001 (2019).
  7. Schrodi, Oppeneer and Aperis, Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation. Phys. Rev. B 102, 024503 (2020).
  8.  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).
  9. Aperis, Morooka and Oppeneer, Influence of electron-phonon coupling strength on signatures of even and odd-frequency superconductivity. Ann. Phys. 417, 168095 (2020).
  10. Schrodi, Aperis and Oppeneer, Improved performance of Matsubara space calculations – A case study within Eliashberg theory of superconductivity. Phys. Rev. B 99, 184508 (2019).
  11. Schrodi, Aperis and Oppeneer, Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO3. Phys. Rev. B 98, 094509 (2018).
  12. Zhou, Semenok, Xie, Huang, Duan, Aperis et al., High-Pressure Synthesis of Magnetic Neodymium Polyhydrides. JACS 142, 2803–2811 (2020).
Last modified: 2022-01-03