A new twist on graphene
Gauge fields have long been at the centre of fundamental theoretical developments in condensed-matter systems, providing a stepping stone towards exotic states of matter. In recent theory work, ETH physicists have shown that twisted graphene bilayers provide a natural platform to electrically create artificial gauge fields — thus establishing a playground to explore novel electronic phenomena.
The material world offers a rich display of quantum phenomena, from diverse forms of magnetism to broad varieties of superconductivity. And there is no end in sight. On a regular basis, we witness ever new surprises — just look at the trove of topological phases discovered over the past decade or so in various materials and engineered systems. Ensembles of interacting quantum particles seem to host a limitless number of unexpected phenomena. Nonetheless, systematically pushing the boundaries by predicting and realizing novel forms of quantum matter remains a challenge, for theorists and experimentalists alike. Hence the excitement when external pageAline Ramires, formerly working at the ETH Institute for Theoretical Studies, and Jose Lado, a postdoctoral researcher in the group of Professor Manfred Sigrist at the Institute for Theoretical Physics in the Department of Physics, recently predicted that graphene — a well-established quantum material — can be used in novel ways for exploring unconventional physics, which in turn might be harnessed in technological applications [1].
Engineering quantum matter with a twist
A great number of quantum many-body phenomena can be understood as the dynamics of particles, but some require a different perspective. Enter gauge fields. These have an important role in giving rise to interactions between particles. The simplest example is photons mediating electromagnetic interactions of charged particles, but gauge fields can also be generated artificially, through appropriate combinations of materials and external fields, and finding practical ways to do so is a major current goal in various areas of physics, from quantum optics to condensed-matter physics. The ability to tailor gauge fields holds the promise of opening up new avenues for exploring quantum many-body phenomena, in particular those where quantum particles interact strongly with one another.
Ramires and Lado turned their attention to graphene. Graphene is well established as a uniquely versatile material to realize exotic condensed-matter phenomena. A breakthrough discovery came last year in the form of ‘magic-angle graphene’, which consists of two layers of graphene that are rotated relative to one another. Such misaligned stacks exhibit superconductivity, among other noteworthy properties. In magic-angle graphene, the twist angle is around 1.1°. The ETH physicists considered in their calculations considerably smaller angles, only a fraction of a degree — in van-der-Waals heterostructures, such as bilayer graphene, the layers can be oriented at arbitrary angles, at least in principle.
In the 'tiny-angle' scenario, Ramires and Lado show, bilayer twisted graphene provides a natural platform to realize artificial gauge fields that can be controlled by an electric bias. The emergence of these gauge fields stems from a synergistic combination of the spatial modulations of the long-range pattern of the twisted structure (see figure) and an electrically controlled mass generation. As a result of that combination, the electrons experience an emergent gauge field that is not intrinsically present in graphene.
Fundamental and practical significance
In addition to their fundamental importance, gauge fields provide a stepping stone for unconventional states of matter, namely strongly correlated states, as gauge fields create a kind of localized levels known as Landau levels. The artificial gauge field predicted in the graphene platform also gives rise to its own pseudo-Landau levels. The most interesting feature is that, due to the modulated nature of the material, the emergent pseudo-Landau levels self-organize in a new structure, an emergent kagome lattice. Kagome lattices are structures of particular interest as they show high geometric frustration and therefore can host quantum states that display unconventional electronic and magnetic properties. This feature turns graphene into an exciting platform to explore the physics of frustrated systems, which have been predicted to give rise to interacting macroscopic quantum states known as quantum spin liquids.
Beyond artificial gauge fields
The ability to create gauge fields and tunable lattices in twisted graphene bilayers opens up new possibilities to explore exciting phenomena in solid-state devices. On the one hand, due to its electrical origin, the emergent gauge field could be modulated in time, potentially giving rise to controllable magnetic correlations, analogous to those recently realized in a cold-atom setup in the group of Professor Tilman Esslinger in the Institute for Quantum Electronics at ETH [2]. On the other hand, correlated states of pseudo-Landau levels might coexist with topological modes of the twisted bilayers, as recently shown by the group of Professor Klaus Ensslin in the Laboratory for Solid State Physics at ETH [3], yielding a paradigmatic material in which topological and correlated physics meet.
Poster child
The quest to realize unconventional physics in a solid-state system might have just experienced an unexpected twist with the work of Ramires and Lado. But their work also stands out on another, aesthetic front. The paper describing their findings has been published in October last year in Physical Review Letters [1], and an image related to the paper — depicting the band structure of biased tiny-angle twisted bilayer graphene in the pseudo Landau level regime — was chosen for the external pagecover of the issue in which it appeared. That image is now making a comeback as it features also as the April topical image of the 2019 calendar of the American Physical Society, bringing home to scientists around the world the elegance and beauty of this work.
References
[1] Ramires A, Lado JL. Electrically tunable gauge fields in tiny-angle twisted bilayer graphene. Phys. Rev. Lett. 121, 146801 (2018). external pagedoi: 10.1103/PhysRevLett.121.146801 external pagePreprint
[2] Görg F, Messer M, Sandholzer K, Jotzu G, Desbuquois R, Esslinger T. Enhancement and sign change of magnetic correlations in a driven quantum many-body system. Nature 553, 481 (2018). external pagedoi:10.1038/nature25135 external pageFree-to-read version
[3] Rickhaus P, Wallbank J, Slizovskiy S, Pisoni R, Overweg H, Lee Y, Eich M, Liu M-H, Watanabe K, Taniguchi T, Fal'ko V, Ihn T, Ensslin K. Transport through a network of topological channels in twisted bilayer graphene. Nano Letters 18, 6725 (2018). external pagedoi: 10.1021/acs.nanolett.8b02387 external pagePreprint