Two new preprints

We are delighted to announce the simultaneous submission of two closely linked preprints to arXiv, representing a major joint effort between our group at Graz University of Technology and our collaborators at MIT’s Research Laboratory of Electronics.

The first, Ultrafast dynamics and light-induced superconductivity from first principles, develops a predictive ab initio framework for the nonequilibrium response of optically driven superconductors. The second, Fast Real-Axis Eliashberg Calculations: Full-bandwidth solutions beyond the constant density of states approximation, provides the critical methodological engine that makes the first possible. Together, these works open a new chapter in the first-principles description of conventional superconductors driven far from equilibrium.

The methodological foundation: solving Migdal-Eliashberg theory directly on the real-frequency axis

Nearly all experimentally accessible properties of a superconductor, such as tunneling spectra, optical conductivity, and quasiparticle lifetimes, are real-frequency quantities. Yet the Migdal-Eliashberg equations, the gold standard for ab initio strong-coupling superconductivity, are almost universally solved on the imaginary-frequency (Matsubara) axis and then analytically continued to real frequencies. Analytic continuation is an ill-conditioned inverse problem that amplifies numerical errors, blurs spectral features, and becomes increasingly unstable at low temperatures, precisely where the physics is most interesting.

In arXiv:2603.18199, we bypass this bottleneck entirely. We present a practical and efficient scheme to solve the finite-temperature Migdal-Eliashberg equations directly on the real-frequency axis, while retaining the full energy dependence of the electronic density of states. Most existing real-axis implementations sacrifice this in favour of a constant density of states approximation. A key algorithmic contribution is a reformulation of the integral kernel K(ω,ω’) that reduces the computational cost from the conventional O(N²) to O(N), enabling high-resolution solutions to converge in milliseconds (in the constant density of states case) to minutes (with the full variable density of states) on a standard laptop.

We demonstrate the importance of going beyond the constant density of states approximation on H₃S, the archetypal high-T_c hydride. H₃S hosts a prominent van Hove singularity near the Fermi level that induces strong particle-hole asymmetry. Our full-bandwidth real-axis solution yields a zero-temperature superconducting gap of 2Δ ≈ 60 meV, in close agreement with recent tunneling measurements, while the constant density of states approximation overshoots at 75 meV. The direct real-frequency solutions also display fine spectral structure inherited from α²F(ω) that is irretrievably lost in analytically continued results, and they remain numerically stable across the entire temperature range from millikelvin to above T_c.

The physics: ultrafast dynamics and photo-induced superconductivity from first principles

Armed with this fast real-axis solver, arXiv:2603.18182 constructs the first fully self-consistent, first-principles framework for the nonequilibrium response of conventional superconductors to ultrafast optical excitation. The approach couples a set of kinetic equations for the quasiparticle distribution f(E,t) and the phonon distribution n(ω,t), an extension of the Chang-Scalapino equations to the strong-coupling regime, solved self-consistently with the Migdal-Eliashberg equations on the real-frequency axis. All material-specific inputs, including the Eliashberg spectral function α²F(ω) and the phonon density of states, are computed from density functional (perturbation) theory. The optical response of the driven film is then obtained from the time-dependent complex conductivity via a Kubo formula, and the Maxwell equations are solved to yield the differential reflectance ΔR/R₀ and differential transmission −ΔT/T₀ for direct comparison with pump-probe experiments.

We validate the framework quantitatively on two conventional superconductors that could hardly be more different: Pb at ambient pressure, with its soft phonon spectrum and modest coupling, and LaH₁₀ at 165 GPa, where superconductivity is driven by stiff hydrogen vibrations and reaches T_c ≈ 250 K. For Pb, the temperature-dependent amplitude and recovery time of −ΔT/T₀ agree quantitatively with experiments. For LaH₁₀, the model captures the multi-timescale relaxation dynamics and the onset of a phonon bottleneck at higher fluences. This cross-material consistency across vastly different phonon energy scales and coupling strengths confirms the robustness of the approach.

Explaining and predicting photo-induced superconductivity

With validation in hand, we turn to the problem that has captivated the community for over a decade: photo-induced superconductivity. In the alkali-doped fulleride K₃C₆₀, mid-infrared pump pulses at 170 meV have been reported to induce signatures of superconductivity at temperatures far above the equilibrium T_c,0 ≈ 20 K, but the underlying mechanism has remained controversial.

Our calculations, using electron-phonon inputs computed with FHI-aims, reproduce a prominent peak in α²F(ω) at 170 meV, precisely the energy targeted by the pump in the experiments. Replicating the experimental conditions, we obtain a transient photo-induced gap Δ₀(t) > 0 at temperatures well above T_c,0, persisting briefly after the pump is switched off. This photo-induced state emerges entirely within the framework of conventional electron-phonon-mediated superconductivity. Resonant excitation of quasiparticles to energies matching the peak in α²F(ω) depletes the gap-edge population and enhances pairing, in close analogy to the long-known enhancement of superconductivity under microwave irradiation. The mechanism is therefore not exotic; it is a natural consequence of the phonon spectrum.

Crucially, this analysis reveals a general design principle. Materials with prominent high-frequency structure in α²F(ω) are candidate systems for photo-induced superconductivity. Guided by this insight, we identify calcium-intercalated graphite, CaC₆, as a promising new candidate and predict a photo-induced gap response comparable to that of K₃C₆₀ when pumped resonantly at its characteristic phonon frequency, a prediction that is directly testable with existing ultrafast spectroscopy equipment.

These two works are deeply intertwined. The fast real-axis Eliashberg solver is not merely a convenience for the nonequilibrium calculations; it is a necessity. Updating the full Migdal-Eliashberg solution at each time step of the kinetic equations would be prohibitive with traditional imaginary-axis methods that require analytic continuation. Our linear-scaling real-axis approach reduces this to a tractable computation, transforming a formally intractable problem into a practical tool for materials prediction.

We believe these results establish a new baseline for the theoretical study of driven superconductors, and we look forward to seeing how the community applies and extends this framework, particularly toward the long-standing goal of light-enhanced or even room-temperature superconductivity.

Check out the preprints at arXiv:2603.18182 and arXiv:2603.18199.