Relaxation Effects in Twisted Bilayer Graphene: a Multi-Scale Approach

Abstract

We introduce a multi-scale approach to obtain accurate atomic and electronic structures for atomically relaxed twisted bilayer graphene. High-level exact exchange and random phase approximation (EXX+RPA) correlation data provides the foundation to parametrize systematically improved force fields for molecular dynamic simulations that allow to relax twisted layered graphene systems containing millions of atoms making possible a fine sweeping of twist angles. These relaxed atomic positions are used as input for tight-binding electronic band-structure calculations where the distance and angle dependent interlayer hopping terms are extracted from density functional theory calculations and subsequent representation with Wannier orbitals. We benchmark our results against published force fields and widely used tight-binding models and discuss their impact in the spectrum around the flat band energies. We find that our relaxation scheme yields a magic angle of twisted bilayer graphene consistent with experiments between 1.0 • ∼ 1.1 • using commonly accepted Fermi velocities of graphene υF 1.0 ∼ 1.1 × 10 6 m/s that is enhanced by about 14%∼20% compared with often used local density approximation estimates. Finally, we present high-resolution spectral function calculations for comparison with experimental ARPES. Additional force field parameters are provided for hBN-layered materials.

Chirality-induced spin texture switching in twisted bilayer graphene

“…The structural deformations in the mtBLG are one of the key factors in determining the gap between the flat band manifold from the other bands [19,[29][30][31]. Structural relaxations can be calculated by using empirical potentials [19,30,[32][33][34][35] or by first-principles methods [29,31,36,37]. The tBLG at small twist angles shows different regions labeled as AA-stacked and AB/BA-stacked (Bernal-stacked) as shown in Fig.…”

Electronic localization in small-angle twisted bilayer graphene

“…As a consequence, the electronic properties of small-angle TBLG systems are expected to be strongly affected as well. 25,30,33 To confirm this statement, electronic band structures and DOS of TBLG featuring three different twist angles (3.15 • , 1.08 • , and 0.50 • ) are presented in Fig. 1.…”

“…Around θ MA 1 (i.e., 1.08 • here), the electronic structure of reconstructed TBLG clearly exhibits isolated flat bands and strong electron localization peaks in the DOS near the Fermi level, in very good agreement with experiments as well as with previous theoretical works. 8,10,25,30,33 For angles below θ MA 1 , while the electronic structure of ideal lattices still present some partially flat bands, all low-energy bands of relaxed TBLG systems are found to be much more dispersive. Note that in all the reconstructed TBLG systems examined in this work (as more fully presented in Figs.…”

“…However, these smaller magic angles are not observed when using more accurate calculations based on atomistic tight-binding models parameterized by density functional theory. 25,26,29 In fact, the presence of the first magic angle has been demonstrated in several experiments [8][9][10]12 but there is no experimental evidence pointing to the existence of other magic angles < 1.1 • .…”

Stacking and gate tunable topological flat bands, gaps and anisotropic strip patterns in twisted trilayer graphene

“…Research interests in vertical van der Waals (vdW) heterojunctions [9][10][11] in search of strongly correlated flat bands have expanded beyond the twisted bilayer graphene [1][2][3][4][5][6][7][12][13][14], to include systems like twisted double bilayer graphene (tDBG) [15][16][17][18][19], and various forms of twisted trilayer graphene [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] including twisted monolayer-bilayer graphene (tMBG) [20,22,[26][27][28][29][30][31][32][33][34]. Unlike the systems with a single moire twist interface like tBG, tDBG, or tMBG, in twisted trilayer graphene with finite successive interlayer twist angles we have two interfaces giving rise to double moire patterns.…”