Electronic bands of twisted graphene layers

The recent discovery of insulating behavior and superconductivity in twisted graphene bilayers[1, 2] has attracted a great deal of attention among the contributors to the cond-mat archive, as over 60 entries have been posted in the period March-October 2018 (see also a previous entry in this journal club[3]). There are many reasons for this impact: new broken symmetry phases in a two dimensional system, unconventional superconductivity, and novel features in the electronic bands, among others. The focus of this commentary is on interesting contributions to the latter issue, the unconventional electronic bands of twisted graphene layers. As it is argued below, these bands show features not encountered before in condensed matter physics. The articles listed above have clarified significantly the mysteries of these bands, although a number of problems remain open. Space considerations prevent a detailed analysis of the many insights into other topics, such as superconductivity itself. Many interesting papers have also been posted in the cond-mat repository recently. The electronic structure of twisted bilayers was considered shortly after research on graphene began[4]. This seminal paper provides the minimal model for this structure. The basic idea follows the approach which leads from atomistic to tight binding and to continuum