Understanding, Engineering, and Probing Correlated Many-Body Physics in Superlattices of Graphene and Beyond

Project Information

SuperCorr

Grant agreement ID: 101040651

DOI

10.3030/101040651

EC signature date 30 March 2022

Start date 1 June 2022

End date 31 May 2027

Funded under

• European Research Council (ERC)

Total cost

€ 1 346 126,00

EU contribution

€ 1 346 126,00

Coordinated by

UNIVERSITY OF STUTTGART
Germany

Periodic Reporting for period 1 - SuperCorr (Understanding, Engineering, and Probing Correlated Many-Body Physics in Superlattices of Graphene and Beyond)

Reporting period: 2022-06-01 to 2024-11-30

Summary of the context and overall objectives of the project

Exploring the plethora of solid-state systems to realize exotic many-body phases is not only motivated by fundamental questions but also by potential quantum-technological applications. In both cases, the central challenges are to control the system to engineer a phase of interest, to develop the theoretical understanding of the microscopic physics, and to be able to probe it. SuperCorr addresses these challenges in the context of artificial superlattice systems created by stacking and twisting van der Waals materials or by arranging adatoms on surfaces of materials, pushing these emerging fields in several new directions. To this end, we use a broad combination of analytical and numerical techniques of condensed matter physics and machine learning approaches, while staying in close contact with experiment. SuperCorr explores possible superconducting mechanisms/states compatible with experiment and develops ways of probing them, studies the impact of topologically obstructed bands on the correlated physics, the potential of spin-orbit-coupling in moiré systems, the shortcomings and opportunities provided by inhomogeneities, as well as machine-learning-aided data analysis. Each of these research directions has the potential to open new avenues for designing and studying novel many-body states in correlated superlattices.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

R1: We showed how convolutional neural networks can be used to extract highly non-trivial microscopic physics from scanning tunneling microscopy data in graphene moiré systems (Nature Communications 14, 5012), using nematic order in twisted double-bilayer graphene as an example.

R2: In an experimental collaboration, the presence of the superconducting diode effect at zero external magnetic field in a twisted graphene moiré system was demonstrated (Nature Physics 18, 1221-1227). On the theory side, we extended our understanding of this effect by developing a theory (Physical Review Letters 132, 046003) based on a back-action mechanism that can explain, for the first time, the extremely large diode effect efficiency observed. We further showed that the superconducting diode effect does not even require finite magnetization and can also be stabilized by altermagnets (Phys. Rev. B 110, 024503), introducing the “altermagnetic diode effect”.

R3: We proposed the first graphene moiré superlattice setup where the strength of spin orbit coupling can be tuned in situ (Phys. Rev. Lett. 130, 066001). We demonstrated that this can lead to “Möbius Fermi surfaces” with semi-classical trajectories that require two full revolutions to be closed, and with consequences for quantum oscillations and superconducting instabilities (Phys. Rev. B 109, 035159).

R4: We have developed two possible explanations for recent tunneling experiments in the superconducting state in twisted bi- and trilayer graphene: In one explanation (Nature Communications 15, 1713), thermal fluctuations are taken into account which naturally lead to interesting “vestigial” pairing states, yielding spectral functions that are consistent with experiment. In a second explanation (Nature Communications 14, 7134), we ask the question whether similar spectral functions can also be obtained in a mean-field picture and identify a novel purely interband pairing state. In a related work (arXiv:2308.00748) we have proposed a model involving “quadratic Dirac cones” yielding highly non-trivial renormalization-group flows.

R5: Inspired by recent experiments demonstrating the creation of atomically sharp moiré interfaces between oxides with different Bravais lattices and finite twist, we developed the, to the best of our knowledge, first systematic band theory for these novel systems (Phys. Rev. B 110, 125143). We present case studies illustrating the huge potential for band engineering and show that there are novel forms of “geometric magic angles”.

R6: We have further extended our understanding of the correlated physics in Chern bands as they are realized in moiré graphene: (a) in Chern-two bands, we showed that CDW phases are competing with a tetrahedral magnet at half-integer filling and uncovered an exotic emergent symmetry (SciPost Phys. 14, 040); (b) we found a novel guiding principle, which we dub the “three-rule”, for ideal Chern bands with strong repulsion (arXiv:2406.09505); (c) we studied the correlated insulators and competing superconductors in the Chern bands of twisted WSe2 (arXiv:2407.02393).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

R1: The proposed multi-channel machine-learning architecture is very general and can be applied to a variety of different forms of order and physics questions in moiré superlattices and beyond. We expect that combined machine learning, theoretical physics, and experimental work of this from will play an important role in condensed matter physics in the years to come.

R2: The superconducting diode effect is not only fundamentally interesting, since it pushes the boundaries of our microscopic understanding of superconductivity, but also potentially of practical relevance as it constitutes a superconducting analogue of the ubiquitous semiconducting diode. In that regard, the extremely large diode effect efficiency and the presence of the effect in moiré graphene without external magnetic field are particularly appealing. Our theoretical analysis provides strong constraints on the microscopic physics and, thus, guidance for future experiments. Furthermore, by showing that also altermagnets can stabilize a diode effect, we connect superconducting diodes with another very active, yet hitherto unrelated, field of altermagnetism.

R3: Having, for the first time, an external knob to tune the spin-orbit coupling is expected to be an important step forward in the field of graphene moiré superlattices since in many experiments it is not clear what the role is of nearby TMD layers. Furthermore, we demonstrate a hallmark signature of our proposed exotic form of “Möbius fermi surfaces” that can be observed experimentally.

R4: The nature and pairing mechanism of the superconducting state in twisted graphene layers are an important part of the central mysteries of the field. In that regard, recent tunneling experiments came as a surprise. However, our two possible pairing states are not only able to explain the observed phenomenology but also constitute novel forms of pairing, already interesting from a purely theoretical point of few in their own right.

R5: Due to the experimental advances in the creation of moiré interfaces of oxides, it is to be expected that there will be many groups studying these systems in the near future. In that context, our work will likely provide an important theoretical foundation. We hope that the proposed novel form of geometric magic angles can be demonstrated experimentally in the future.

R6: The predicted gapped phase at half-integer filling of (a) has now been observed experimentally. In our work (b), we already showed how the “three-rule” principle can be combined with perturbation theory to capture correlated metallic, superconducting behavior as well as fractional Chern insulators. We expect it to become the starting point of many follow-up works studying short-range interactions in Chern bands. Finally, (c) provides crucial insights into the correlated physics (insulators and superconductors) in twisted WSe2, which we expect to take center stage among the van der Waals moiré systems in the next few years.

Some of the exotic pairing states that have been studied in SuperCorr.