Disorder in Twisted Bilayer Graphene

We develop a theory for a qualitatively new type of disorder in condensed matter systems arising from local twist-angle fluctuations in two strongly coupled van der Waals monolayers twisted with respect to each other to create a flat band moir\'e superlattice. The new paradigm of 'twist angle disorder' arises from the currently ongoing intense research activity in the physics of twisted bilayer graphene. In experimental samples of pristine twisted bilayer graphene, which are nominally free of impurities and defects, the main source of disorder is believed to arise from the unavoidable and uncontrollable non-uniformity of the twist angle across the sample. To address this new physics of twist-angle disorder, we develop a real-space, microscopic model of twisted bilayer graphene where the angle enters as a free parameter. In particular, we focus on the size of single-particle energy gaps separating the miniband from the rest of the spectrum, the Van Hove peaks, the renormalized Dirac cone velocity near charge neutrality, and the minibandwidth. We find that the energy gaps and minibandwidth are strongly affected by disorder while the renormalized velocity remains virtually unchanged. We discuss the implications of our results for the ongoing experiments on twisted bilayer graphene. Our theory is readily generalized to future studies of twist angle disorder effects on all electronic properties of moir\'e superlattices created by twisting two coupled van der Waals materials with respect to each other.Comment: 17 pages, 13 figures (published version

More Than 1,001 Problems with Protein Domain Databases: Transmembrane Regions, Signal Peptides and the Issue of Sequence Homology

Large-scale genome sequencing gained general importance for life science because functional annotation of otherwise experimentally uncharacterized sequences is made possible by the theory of biomolecular sequence homology. Historically, the paradigm of similarity of protein sequences implying common structure, function and ancestry was generalized based on studies of globular domains. Having the same fold imposes strict conditions over the packing in the hydrophobic core requiring similarity of hydrophobic patterns. The implications of sequence similarity among non-globular protein segments have not been studied to the same extent; nevertheless, homology considerations are silently extended for them. This appears especially detrimental in the case of transmembrane helices (TMs) and signal peptides (SPs) where sequence similarity is necessarily a consequence of physical requirements rather than common ancestry. Thus, matching of SPs/TMs creates the illusion of matching hydrophobic cores. Therefore, inclusion of SPs/TMs into domain models can give rise to wrong annotations. More than 1001 domains among the 10,340 models of Pfam release 23 and 18 domains of SMART version 6 (out of 809) contain SP/TM regions. As expected, fragment-mode HMM searches generate promiscuous hits limited to solely the SP/TM part among clearly unrelated proteins. More worryingly, we show explicit examples that the scores of clearly false-positive hits, even in global-mode searches, can be elevated into the significance range just by matching the hydrophobic runs. In the PIR iProClass database v3.74 using conservative criteria, we find that at least between 2.1% and 13.6% of its annotated Pfam hits appear unjustified for a set of validated domain models. Thus, false-positive domain hits enforced by SP/TM regions can lead to dramatic annotation errors where the hit has nothing in common with the problematic domain model except the SP/TM region itself. We suggest a workflow of flagging problematic hits arising from SP/TM-containing models for critical reconsideration by annotation users