How the screened Coulomb interaction induces superconductivity in twisted bilayer graphene

Twistology could be the study of unexpected changes or developments in stories or situations, from coups d’état to the fatherhood of Darth Vader. In condensed matter physics there is something similar, although the preferred name is twistronics (from twist and electronics). It is understood as the study of how the angle (the twist) between layers of two-dimensional materials can change their electrical properties. Materials such as twisted bilayer graphene (TBG) have been shown to have vastly different electronic behaviour, ranging from non-conductive to superconductive, that depends sensitively on the angle between the layers.

Moiré pattern arising from the superposition of two graphene lattices twisted 4°. Source: Wikimedia Commons

The development of superconducting devices was greatly stimulated after the acceptance of the basic theory of superconductivity proposed in 1957 by John Bardeen, Leon Cooper, and Robert Schrieffer. The authors of the BCS theory, as it is known, received the Nobel Prize for their work in 1972. The basic idea is that the electron waves in the superconducting state no longer act independently, as in Bloch’s model. Instead, they are paired together at the so-called critical temperature so that their wave functions act as one unit as they interact with the crystal lattice. Moreover, all of the electron pairs move together in one collective motion, so that if any single electron is scattered by the lattice it is pulled back into the flow by its partner, and if any pair of electrons is somehow scattered off track, it is pulled back into the collective flow by all the other pairs. Since there is no scattering or inelastic collisions, there is no resistance, and the material becomes a superconductor.

The pairing interaction responsible for superconductivity in TBG has been intensively studied. Among other possible pairing mechanisms, the effect of phonons, the proximity of the chemical potential to a van Hove singularity in the density of states and excitations of insulating phases, and the role of electronic screening have been considered.

Now, Tommaso Cea and Francisco Guinea study 1 how the screened Coulomb interaction induces pairing in TBG. The researchers obtain critical temperatures of magnitude 1 to 10 K and provide estimates and trends in agreement with the experimental measurements.

The long-range Coulomb interaction, projected onto the central bands of TBG, is described by an energy scale in the range of 20 to 100 meV. As a result, this interaction modifies significantly the shape and width of the bands of TBG near the so-called first magic angle. The authors focus on low-energy excitations in TBG, including particle–hole excitations, plasmons, and acoustic phonons, analysing the way in which these excitations lead to superconductivity, by means of well-tested diagrammatic techniques.

The scientists find that the screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron–hole pairs. Importantly, scattering processes involving large momentum transfers play a crucial role in the formation of Cooper pairs.

This is another important theoretical contribution to understand superconductivity in general, and particularly in TBG.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may be copied verbatim or almost verbatim from the referenced research papers.

References

  1. Tommaso Cea & Francisco Guinea (2021) PNAS doi: 10.1073/pnas.2107874118

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