2025 Simons Collaboration on New Frontiers in Superconductivity Annual Meeting

The Simons Collaboration on New Frontiers in Superconductivity (https://www.simonssuperconductivity.org/) met for their first annual meeting at the Simons Foundation in New York on Thursday, November 6th, and Friday, November 7th, 2025. In addition to talks and poster presentations from the Simons Collaboration participants, the meeting hosted two distinguished external speakers: Steven Kivelson from Stanford University and Stevan Nadj-Perge from the California Institute of Technology.
The meeting on Thursday, November 6th, started with the opening talk from collaboration director Bogdan Andrei Bernevig (Princeton University), “Progress report on superconductivity.” External speaker Steven Kivelson (Stanford University) followed with a talk titled “The physics of the superconducting T c in the cuprates.” After lunch, principal investigator Nikolai Prokofiev (University of Massachusetts, Amherst) gave a talk titled “Solution of the Coulomb pseudopotential problem.” Collaboration principal investigator Miguel Marques (Ruhr University Bochum) presented “Machine-learning accelerated search for new superconductors.” Nick Bultinck (Ghent University) gave the final talk of the day, titled “Recent results with applications to twisted WSe2, bilayer nickelates, and cuprates.”

Friday, November 7th, started with a talk by collaboration co-director Andrey Chubukov (University of Minnesota), titled “Breakdown of the Migdal–Eliashberg theory.” External speaker Stevan Nadj-Perge (California Institute of Technology) presented the talk “Resolving spectral gaps and many-body resonances in superconducting twisted trilayer graphene.” The final talk was given by co-director Päivi Törmä (Aalto University), “Quantum geometry and superconductivity: From model systems to real materials.”

The meeting focused on front-line developments in the theory of superconductivity relevant for the goals of the collaboration. The topics included new methods to describe strong correlations and unconventional superconductivity, the role of quantum geometry and topology in superconductivity, machine learning predictions of new superconductors, as well as two-dimensional and moiré materials with new degrees of freedom that affect superconductivity. The meeting goal was to define future research directions in these areas and overall was productive and successful.

Andrei Bernevig
Princeton University

Progress Report on Superconductivity

Andrei Bernevig will report progress on (1) an analytical understanding of electron phonon superconductivity, its bounds, and its potential for increasing Tc, and (2) our group’s new efforts on machine learning material and superconducting material discovery.
 

Nick Bultinck
Ghent University

Recent Results with Applications to Twisted Wse2, Bilayer Nickelates and Cuprates
View Slides (PDF)

Nick Bultinck will report on (1) a new type of multi-Q order in twisted WSe2, (2) evidence for strongly correlated superconductivity in bilayer nickelates, and (3) a connection between spin stripes, potential disorder, and a theory for strange metals.
 

Andrey Chubukov
University of Minnesota

Breakdown of the Migdal-Eliashberg Theory

Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option — a collapse to a polaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling, at which a polaron state develops. We show that at small density, this happens well before the dressed phonon softens.

This is particularly true in 3D systems, where the critical coupling for polaron formation scales with the density. We present analytical reasoning for this behavior based on exact diagrammatic treatment of the on-site Holstein model for the spin polarized case and argue that polaron formation is unrelated to the physics close to Fermi-surface. Closer to half-filling, MET extends to strong coupling, and the leading instability is towards a CDW order, while polarons develop from an CDW-ordered state.

Collaboration with N. Prokofiev
 

Steven Kivelson
Stanford University

The Physics of the Superconducting Tc in the Cuprates

Steven Kivelson will discuss some of the physical principles that govern superconducting transition temperatures, Tc, in the cuprates. Superconductivity is a quintessential intermediate coupling phenomenon, so generically the maximum Tc occurs at a point at which the physics is crossing over from one regime to another. Kivelson will particularly highlight the role of of pairing (i.e., the superconducting gap scale) and phase ordering (i.e., the superfluid stiffness) in determining Tc in different regions of the cuprate phase diagram.

As part of this, Kivelson will attempt to disentangle which measured quantities reflect the properties of a putative disorder-free “ideal” cuprate, and which are consequences of the unavoidable disorder associated with the fact that (most of) the cuprates are alloys — rather than stoichiometric materials. Two interesting consequences of this are analysis that he will discuss are:

(1) There is direct evidence against any significant contribution to the pairing interaction from nearly-quantum-critical fluctuations of any sort.

(2) For a range of interplane coupling, a bilayer consisting of an overdoped and an underdoped copper-oxide plane can have a higher Tc than any corresponding symmetric bilayer system, reflecting physics that has, perhaps, already been established in trilayer cuprates.
 

Miguel Marques
Research Center Future Energy Materials and Systems of the Ruhr University Bochum

Machine-Learning Accelerated Search for New Superconductors

The quest for high-temperature superconductors remains a central challenge in materials science. Machine learning (ML) offers a powerful new paradigm to accelerate this discovery process. This talk will present our ML-accelerated search for novel conventional superconductors with high critical temperatures (Tc). Our efforts span both ambient and high-pressure conditions, where we predict new stable superconducting phases. We also discuss our search for new compounds that share key structural or electronic properties with the high-Tc ceramic superconductors. This dual approach leverages ML to explore vast chemical spaces, overcoming traditional computational bottlenecks. Our work highlights the potential of AI to revolutionize the discovery of next-generation superconducting materials.
 

Stevan Nadj-Perge
Caltech

Resolving Spectral Gaps and Many-Body Resonances in Superconducting Twisted Trilayer Graphene
View Slides (PDF)

Magic-angle twisted trilayer graphene (MATTG) exhibits a plethora of strongly correlated electronic phases that spontaneously break its underlying symmetries. Despite great experimental efforts, the microscopic nature of these phases and their relationship to emerging superconductivity in this system are still elusive. In this talk, Stevan Nadj-Perge will present our latest results on scanning tunneling microscopy experiments that focus on tracking the formation of correlated phases preceding superconductivity in MATTG. Surprisingly, in a certain range of filling factors within the superconducting dome, we discover the existence of two well-resolved gaps pinned at the Fermi level. While the outer gap, previously associated with the pseudogap phase, persists at high temperatures and magnetic fields, the newly revealed inner gap is more fragile in line with superconductivity MATTG transport experiments. Nadj-Perge will discuss several additional measurements that further corroborate the superconducting nature of the inner gap and strongly suggest that the outer gap originates from the splitting of the many-body Kondo-like resonance due to the breaking of the valley symmetry. Our results suggest an intricate hierarchy of correlated phases in MATTG.
 

Nikolay Prokofiev
University of Massachusetts, Amherst

Solution of the Coulomb Pseudopotential Problem

More than a century after the discovery of superconductivity, the role of Coulomb interaction VC in this phenomenon remained unsolved. The majority of ab initio calculations of conventional superconductors are based on semi-phenomenological replacement of VC effects with the repulsive pseudopotential µ* and exchange-correlation ansatz for the three-point vertex function. Using a variational diagrammatic Monte Carlo method for the uniform electron gas, we obtained precise values of the pseudopotential and the vertex function for typical electron densities found in materials. We find that the solution for the “bare” pseudopotential is significantly larger than phenomenological inputs (almost by a factor of 3), offering a different parameterization of µ* in materials. With this new input, we computed superconducting Tc for simple metals without empirical tuning of parameters, resolved long-standing discrepancies between the theory and experiment, and uncovered a pressure-induced quantum phase transition in Al above 60 GPa and proximity to quantum criticality in Mg and Na below 10 K. Our work establishes a controlled ab initio framework for electron-phonon superconductivity beyond the weak electron correlations limit, paving the way for reliable Tc calculations and design of novel superconducting materials.
 

Päivi Törmä
Aalto University

Quantum Geometry and Superconductivity: From Model Systems to Real Materials

We have found that superconductivity and superfluidity are connected to quantum geometry [1,2]: the superfluid weight in a multiband system is proportional to the minimal quantum metric of the band. The quantum metric is connected to the Berry curvature, which relates superconductivity to the topological properties of the band. Using this theory, we have shown that superconductivity is possible also in a flat band where individual electrons would not move.

In this talk, Päivi Törmä will briefly introduce these concepts and then discuss our efforts within the Simons Collaboration to bring them from model systems, where they have been primarily considered, towards real materials where they may help in understanding superconductivity and achieving it at higher temperatures. To this end, Törmä will discuss the effect of disorder, superfluid weight of twisted bilayer graphene, quantum geometry effects in rhombohedral graphene superconductivity, and calculation of superfluid weight for more complex materials.

[1] S. Peotta, P. Törmä, Nature Commun. 6, 8944 (2015); K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B.A. Bernevig, P. Törmä, Phys. Rev. B 106 , 014518 (2022). [2] P Törmä, Phys. Rev. Lett. 131, 240001 (2023); P. Törmä, S. Peotta, B.A. Bernevig, Nat. Rev. Phys. 4, 528 (2022); J. Yu, B.A. Bernevig, R. Queiroz, E. Rossi, P. Törmä, B.-J. Yang, arXiv:2501.00098, to appear in npj Quantum Materials (2025)