Quantum Interference at the Twist Boundary in Graphene

Abstract

We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the ! 0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles.

Many‐body effects in optical response of graphene‐based structures

“…[79] The calculations of such configurations require invoking of the TB approaches, whereas band electronic structures of bilayers with reasonably small cells were obtained within DFT. [76,80], [81] Both types of computational approaches gave qualitatively similar results indicating that for the twist angles above 108 up to the symmetric point of 308, the dispersion in a twisted bilayer is linear as in single-layer graphene at the K point. The apparent absence of interlayer interaction at the Fermi level was related to the loss of shortrange correlation in misoriented systems.…”

Long-range atomic ordering and variable interlayer interactions in two overlapping graphene lattices with stacking misorientations

“…From a theoretical perspective, twisted bilayer graphene (TBG) has been examined extensively using both continuum [6][7][8][9] and ab-initio [10][11][12][13][14] approaches. These studies have shown that the individual monolayers become significantly decoupled by the rotational faults.…”

Unraveling the Intrinsic and Robust Nature of van Hove Singularities in Twisted Bilayer Graphene by Scanning Tunneling Microscopy and Theoretical Analysis

“…An alternative route for modifying graphene's band structure would be to exploit a rotation between stacked graphene layers [9]. According to calculations, for large angles ( !15 ) the low energy band structure of graphene should be preserved [10][11][12]. For intermediate angles (1 15 ), it is predicted that, while the linear dispersion persists in the vicinity of the Dirac points of both layers, the band velocity is depressed and two saddle points appear in the band structure, giving rise to two logarithmic van Hove singularities (vHs) in the density of states (DOS) [9,[13][14][15][16][17][18].…”