Electronic Spectrum of Twisted Graphene Layers under Heterostrain

Abstract

We demonstrate that stacking layered materials allows a strain engineering where each layer is strained independently, which we call heterostrain. We combine detailed structural and spectroscopic measurements with tight-binding calculations to show that small uniaxial heterostrain suppresses Dirac cones and leads to the emergence of flat bands in twisted graphene layers (TGLs). Moreover, we demonstrate that heterostrain reconstructs, much more severely, the energy spectrum of TGLs than homostrain for which both layers are strained identically, a result which should apply to virtually all van der Waals structures opening exciting possibilities for straintronics with 2D materials.

Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene

“…The AA region spectra show a series of pronounced peaks (indicated by numbers) with nearly equal energy spacing. Surprisingly, these peaks are typically different from those of TBG in the absence of external magnetic field [10,16,22,23], but rather similar to the Landau levels of a two dimensional electron gas in graphene under strong external magnetic field [24,25]. In stark contrast, these resonances are hardly found in the AB re-gion.…”

“…Figure 1a shows an STM topography image with hexagonal symmetry moiré patterns. The atomic structure of the moiré pattern can be determined explicitly by the topography image [16,20,21]. Here we follow the same rules to identify the twist angle in Fig.…”

“…The as-shown moiré pattern unit cell contains 57964 atoms that is too large even for state-ofthe-art first-principles methods. Therefore, we adopted a widely used full tight-binding model of bilayer graphene with an angle dependent Hamiltonian [9,16]. Figure 1c shows the calculated local density of states by utilizing the Lanczos recursion method in real space [26].…”

“…Figure 3a shows the topography image with severely distorted moiré pattern. Such distorted moiré structures are due to the existence of uniaxial heterostrain, where the moiré pattern can serve as a magnifying glass [16,20,21,28]. Namely, when the honeycomb lattice is slightly strained, the resulting moiré pattern is significantly distorted, in which the twist angle and strain can be determined by the STM images.…”

A First‐Principles Study of Electronic Properties of Twisted MoTe2

“…In a rotated bilayer, the superposition of two honeycomb lattices generates a unit cell with a longer period and forms Moire patterns . The transmission electron microscopy (TEM) studies have identified the corresponding Moire patterns in the twisted 2H‐MoS 2 with a specific angle . However, since the larger unit cell of the twisting system greatly increases the computational load, the first‐principles calculations are limited to specific twist angles rather than random directions.…”