Evolution of the electronic band structure of twisted bilayer graphene upon doping

Abstract

The electronic band structure of twisted bilayer graphene develops van Hove singularities whose energy depends on the twist angle between the two layers. Using Raman spectroscopy, we monitor the evolution of the electronic band structure upon doping using the G peak area which is enhanced when the laser photon energy is resonant with the energy separation of the van Hove singularities. Upon charge doping, the Raman G peak area initially increases for twist angles larger than a critical angle and decreases for smaller angles. To explain this behavior with twist angle, the energy separation of the van Hove singularities must decrease with increasing charge density demonstrating the ability to modify the electronic and optical properties of twisted bilayer graphene with doping.

Electrically Tunable Gauge Fields in Tiny-Angle Twisted Bilayer Graphene

“…Introducing one extra layer of complexity, twisted bilayer graphene (TBG) is known to host a plethora of new interesting phenomena [20][21][22][23][24][25][26][27][28][29][30], stemming from the appearance of a new scale: the Moiré length L M [31][32][33][34][35][36][37]. The physics of TBG strongly depends on the angle α between the two layers.…”

A Markov theoretic description of stacking-disordered aperiodic crystals including ice and opaline silica

“…A fruitful direction of future theoretical work may be to extend the theory so far explored to crystals composed of infinitely many kinds of layer, which could be applied to a crystal composed of layers that are identical to their immediate predecessor up to some rotation, translation, change in curvature, or shift orthogonal to the basel plane, which takes one of infinitely many values. Such crystals possess so-called turbostratic disorder, and include a range of materials including smectites (Ufer et al, 2008), (Ufer et al, 2009), carbon blacks (Shi, 1993) (Zhou et al, 2014) and possibly n-layer graphene; a novel material that has captured the attention of the nanoscience community (Razado-Colambo et al, 2016) (Huang et al, 2017). Such an extension of existing theory may be achievable by replacing the transition matrix (an operator on a finite dimensional vector space) with a transition operator on an infinite dimensional Banach space.…”

A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene

“…Aside from carbon blacks, it is now well known (Huang et al, 2017;Razado-Colambo et al, 2016) that layers of graphene can be stacked on top of one another with a rotation between them adopting an angle 2 ½À 6 ; 6 , taking one of an uncountable infinity of values. The rotation can adopt any angle, but the sixfold rotational symmetry of graphene allows us to work in the restricted range 2 ½À 6 ; 6 .…”

“…Carbon blacks therefore comprise a Markov chain of layers with infinite state space, and are therefore not fully understood by the analysis of chains with finite state space explored by Riechers et al (2015) Varn & Crutchfield (2016) and Hart et al (2018). The properties of carbon blacks are well worth exploring, as the material has many applications including the moderation of neutrons (Zhou et al, 2014), lithium-ion batteries (Shi, 1993), and the manufacture of rubber (Ungár et al, 2002) Aside from carbon blacks, it is now well known (Huang et al, 2017) (Razado-Colambo et al, 2016) that layers of graphene can be stacked atop one another with rotation between them adopting an angle θ ∈ [− π 6 , π 6 ] taking one of an uncountable infinity of values. The rotation can adopt any angle, but the 6 fold rotational symmetry of graphene allows us to work in the restricted range θ ∈ [− π 6 , π 6 ].…”

“…An illustration of the superlattice produced when a pair of layers differ by an angle θ 1 is shown in Figure 1. The electronic properties of moiré graphene are rich and exotic, and have become subject of a huge international research effort; see for example Huang et al (2017), Razado-Colambo et al (2016) Brown et al (2012), Havener et al (2012), or Cao et al (2018), where the most recent authors identified a magic angle where a twisted bilayer becomes a superconductor. Though the moiré angles are importantly distinct from the other rotation angles, the latter are still of interest, in fact Bistritzer & MacDonald (2011) have remarked that for all other angles θ, a twisted bilayer has no unit cell, but has instead a quasi-periodic structure with its own set of properties.…”