What is it about?
Superconductivity is an intriguing phenomenon in condensed matter physics. In a superconductor, electrons flow without any resistance, allowing for perpetual electrical currents. At low temperatures, these electrons pair up in a particular manner forming what are called Cooper pairs. In 2018, researchers first observed superconducting and other insulating correlated phases in twisted bilayer graphene. Since then, extensive experimental and theoretical efforts have been made to further understand this system and other moiré and non-moiré graphene-based structures. Currently, superconductivity seems to be ubiquitous to graphene multilayers as it has been observed experimentally in several twisted systems as well as their non-twisted counterpart. Normally, electrons repel each other because they share the same charge. However, in a superconducting state, they end up forming bound states. In most superconductors, this attraction is mediated by the interaction between electrons and atomic lattice vibrations (phonons). These materials are known as conventional superconductors, while in unconventional superconductors the emergence of superconductivity can be attributed to other correlation effects. According to this work, this could be the case of graphene multilayers in which the electron-electron interactions are capable of mediating superconductivity with critical temperatures in good agreement with the experiments. We develop a theoretical framework based on the Kohn-Luttinger mechanism and apply it to different graphene moiré systems. We analyze the contribution of pure electron-electron interactions, electron-phonon interactions, and Umklapp processes to the strength of the superconducting phases in these moiré systems. Furthermore, we identify that the distinctive features of the electron wave functions in magic-angle twisted bilayer graphene magnify the role played by Umklapp processes, which results in a considerable enhancement of the critical temperature in comparison to other twisted systems.
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Why is it important?
Although superconductivity is now a common feature in different graphene multilayers, its characteristics vary markedly among them. These differences complicate the formulation of a generic microscopic theory, yet they also offer invaluable insights into the phenomena that need to be addressed by such a theory. Identifying the underlying mechanism driving superconductivity in graphene multilayers is essential for understanding the plethora of correlated phases seen in experiments.
Perspectives
A successful theory of superconductivity in graphene multilayers should reproduce as many experimental observations as possible in all stacks, within a unified framework with the least number of parameters with no well-known magnitude. Our superconductivity-from-repulsion, Kohn-Luttinger-like, RPA mechanism fulfills these criteria, yielding critical temperatures in agreement with experiments in twisted bilayer, twisted trilayer, rhombohedral trilayer, Bernal bilayer (with and without WSe2) and twisted double bilayer graphene. More importantly, it reproduces reasonably well the global trend observed in graphene stacks in which the critical temperature varies along three orders of magnitude. The results presented here, together with previous work, put forward the KL-RPA mechanism as a realistic theory of superconductivity in multilayers of graphene.
Alejandro Jimeno-Pozo
IMDEA Nanociencia
This is one of my favorite articles in my career. It is important to mention that theoretical estimates of critical temperatures (Tc) in superconductors typically have a strong dependence on the choice of parameters used in the calculations. Interestingly, by using the same set of parameters in the corresponding multilayers, we have been able to predict general trends for the Tc in twisted and non-twisted graphene multilayers within three orders of magnitude. Our calculations describe semi-quantitatively systems where the superconducting properties vary over a large range. This fact suggests that the interactions studied here play a significant role in the superconductivity of these materials. Additionally, we also predict the existence of superconductivity in helical twisted trilayer graphene and in different samples of twisted double bilayer graphene.
Dr Pierre Anthony Pantaleon
IMDEA Nanoscience
My collaborators have elegantly addressed the physics implications of this outcome. I would like to talk about the theoretical formulation of the Umklapp process. At a mean-field level, portraying the interaction within a Moire system necessitates elevating the charge density operator to a vector form. This transformation enables the concise representation of various physical quantities, including the Hartree and Fock potentials. Notably, the susceptibility, embodying the electron-hole bubble, emerges as the outer product of this vector. We are convinced that significant untapped potential lies within this formulation, awaiting further exploration.
Min Long
Read the Original
This page is a summary of: Evolution of superconductivity in twisted graphene multilayers, Proceedings of the National Academy of Sciences, July 2024, Proceedings of the National Academy of Sciences,
DOI: 10.1073/pnas.2405259121.
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Resources
Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene
Twisted bilayer graphene has a rich phase diagram, including superconductivity. Recently, an unexpected discovery has been the observation of superconductivity in non-twisted graphene bilayers and trilayers. In this Perspective, we give an overview of the search for uncommon phases in non-twisted graphene systems. We first contextualize these recent results within earlier work in the field, before examining the new experimental findings. Finally, we analyse the numerous theoretical models that study the underlying physical processes in these systems.
Superconductivity from electronic interactions and spin-orbit enhancement in bilayer and trilayer graphene
We discuss a Kohn-Luttinger-like mechanism for superconductivity in Bernal bilayer graphene and rhombohedral trilayer graphene. Working within the continuum model description without free parameters, we find that the screened long-range Coulomb interaction alone gives rise to superconductivity with critical temperatures that agree with experiments. We observe that the order parameter changes sign between valleys, which implies that both materials are valley-singlet, spin-triplet superconductors. Adding Ising spin-orbit coupling leads to a significant enhancement in the critical temperature, also in line with experiment, and the superconducting order parameter shows locking between the spin and valley degrees of freedom.
Band structure and superconductivity in twisted trilayer graphene
We study the symmetries of twisted trilayer graphene's band structure under various extrinsic perturbations, and analyze the role of long-range electron-electron interactions near the first magic angle. The electronic structure is modified by these interactions in a similar way to twisted bilayer graphene. We analyze electron pairing due to long-wavelength charge fluctuations, which are coupled among themselves via the Coulomb interaction and additionally mediated by longitudinal acoustic phonons. We find superconducting phases with either spin-singlet/valley-triplet or spin-triplet/valley-singlet symmetry, with critical temperatures up to a few Kelvin for realistic choices of parameters.
Contributors
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