The fate of disorder in twisted bilayer graphene near the magic angle

Abstract

In disordered lattices, itinerant electrons typically undergo Anderson localization due to random phase interference, which suppresses their motion. By contrast, in flat-band systems where electrons are intrinsically localized owing to their vanishing group velocity, the role of disorder remains elusive. Twisted bilayer graphene (TBG) at the magic angle $\sim 1.1^\circ$ provides a representative flat-band platform to investigate this problem. Here, we perform an atomistic tight-binding quantum transport calculation on the interplay between disorder and flat-bands in TBG devices. This non-phenomenological approach provides direct evidence that moderate disorder enhances conductance, whereas stronger disorder restores localization, revealing a disorder-driven delocalization-to-localization transport behavior. The underlying physical mechanism is understood by an effective inter-moir{é} tunneling strength via spectral flow analysis of a disordered TBG cylinder. Moreover, by comparing magic-angle and large-angle TBG, we demonstrate qualitatively distinct disorder responses tied to the presence of flat-bands. Our quantitative results highlight the unconventional role of disorder in flat-band moir{é} materials and offer insights into the observation of the fractional quantum anomalous Hall effect in disordered moir{é} systems.

Figures (4)

• Figure 1: (a) Schematic diagram of the two-terminal transport device with a rectangular TBG flake sandwiched between two metallic leads (shown in dark). The moiré length is denoted as $L_m$. (b) Band structure of the TBG along $\rm \overline{K}-\overline{\Gamma}-\overline{M}-\overline{K}'$ in the moiré Brillouin zone. Here a commensurate twist angle $\theta \approx 1.12^\circ$ is chosen, characterized by two integer numbers $m=29, n=30$. (c) Ensemble-averaged conductance $\langle G \rangle$ as a function of the disorder strength $W$. Here for the red (blue) curve, the Fermi energy $E_F$ is set at the dispersive conduction (valence) band, as marked by the red (blue) dashed line in the band structure of (b). For the black curve, $E_F$ is set at the flat band ($E_F=0$). For the sake of comparison, $\langle G \rangle$ at $E_F=0$ has been amplified by 50 times. The transport parameters are: $N=55, L=261$, $\eta_c=0.5$ meV. $\langle G \rangle$ is averaged over 100 configurations for the dispersive bands, and over 500 configurations for the flat-bands.
• Figure 2: $\langle G \rangle$ as a function of $E_F$ at different disorder strength $W$. Inset: zoom-in plot of the curves near the CNP. Curves in the inset are averaged over 500 configurations while others are averaged over 100 configurations. The parameters are: $N=55, L=261$, $\eta_c=0.5$ meV.
• Figure 3: Numerical results for twist angle $\theta \approx 3.15^{\circ}$, characterized by two commensurate numbers $m=10$ and $n=11$. $\langle G \rangle$ versus $W$ at different $E_F$. $\langle G \rangle$ at $E_F=0$ is amplified by 30 times. The inset shows the band structure of a quasi-1D TBG nanoribbon with flat cutoff boundaries with width $N=23$.
• Figure 4: (a) Distribution of LDOSs on the bottom layer of the central TBG flake shown in Fig. 1(a). Here the energy and disorder strength are labeled on the top right part inside each panel as $(E, W)$. The inset in the middle panel illustrates the broadening of wavefunctions inside the TBG nanoflake for different values of disorder strength $W$. The white dashed circles indicate the region of the localized wavefunctions. (b) and (c): Spectral flow of a periodic clean and disordered TBG ribbon as shown in the inset of (d). For (c) one disorder configuration with disorder strength $W=2.7$ eV is chosen, and the lowest energy bands close to the CNP are labeled by number 1 to 4 in energy-ascending order. (d) The ensemble-averaged effective inter-QD tunneling strength $\langle |\tilde{t}_n| \rangle$ of the disordered moiré supercell ribbon (shown in the inset), as a function of $W$ for the four lowest energy bands marked in (c). (e) $\langle |\tilde{t}_n| \rangle$ versus $W$ at twist angle $\theta \approx 3.15^{\circ}$. To obtain $\langle |\tilde{t}_n| \rangle$ 21 points of $\phi$ are adopted. The other parameters are: $N=55$, $\theta \approx 1.12^{\circ}$ and $\eta_c=0.5$ meV for (a-d), and $N=23$ for (e). For each $W$, 100 configurations are considered.