Current-Induced Reversal of Anomalous Hall Conductance in Twisted Bilayer Graphene

It is observed experimentally that the sign of the Hall resistance can be flipped by a dc electric current in the twisted bilayer graphene (TBG) at $3/4$ filling of the fourfold degenerate conduction flat bands. The experiment implies a switching of the valley polarization (VP) and topology in TBG. Here we present a theory on the current-induced switching of VP and topology. The presence of current in the bulk causes the redistribution of electron occupation in bands near the Fermi energy, which then deforms and shifts the band dispersion due to the Coulomb interaction. Above a critical current, the original occupied and empty bands can be swapped, resulting in the switching of VP and topology.

Figure 1

(a)–(c) Schematic band structures for $\lambda =0$, $\lambda \ge {\lambda }_c$, and $\lambda =0$, respectively. (d)–(f) Free energy profiles correspond to (a)–(c). The two energy bands are labeled by the effective valley index $\pm$. (a) and (c) represent the two degenerate ground states with opposite VP. (b) Obtained from (a) by introducing the current, and (c) is obtained from (b) by removing the current. The current-induced pumping of electrons from the lower band to the upper band is indicated by the arrow and is highlighted in (a). The switching of VP and vanishing of energy barrier in the presence of current is exhibited in (e).

Figure 2

(a) Schematic BZs of the TBG (black hexagon) and of two graphene layers (red and blue hexagons). (b) Low-energy band structure of the TBG along the high-symmetry path. The solid and dashed energy bands are from the $\pm K$ valleys, respectively. The upper flat bands are marked by red color. (c) $n_{\tau }$ (red solid line), $n_s$ (red dashed line), and Hall conductance $G_{xy}$ (blue solid line) are plotted as a function of the temperature $T$.

Figure 3

The four upper fat bands labeled by the valley-spin index $(\tau ,s)$ are shown for the insulating valley-spin-polarized state obtained from the Hartree-Fock approximation. The Chern numbers of the flat bands are displayed. The black hexagon encloses the moiré BZ.

Figure 4

(a) Current density $J$ as a function of $\lambda$ at $T=13\mathrm{K}$. (b), (c) The corresponding order parameters $n_{\tau ,s}$ and Hall conductance $G_{xy}$ as a function of $J$. (d) The dependence of critical current density $J_c$ on $T$. The inset shows ${\lambda }_c$ vs $\sqrt{T_c-T}$.

Figure 5

Density plot of the Hall conductance $G_{xy}$ as a function of current $I$ and magnetic field $B$. The positive and negative $G_{xy}$ are for opposite valley polarization. The black line is the phase boundary extracted from Ref. [7] that separates different valley-polarized states. Here we offset $I$ by the critical current $I_c$ at $B=0$ to make a direct comparison of the phase boundaries.