Topological charge pumping in twisted bilayer graphene

Abstract

We show that a sliding motion between the two layers of a moiré superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to moiré superlattices, and may find applications in nanogenerators and nanomotors.The emergence of long-wavelength moiré superlattices in van der Waals heterostructures has generated widespread interest in condensed matter physics. These superlattices can strongly modify the low-energy spectrum of charge carriers, giving rise to a wide range of spectacular quantum phenomena such as Hofstadter butterfly [1][2][3], superconductivity [4][5][6], Mott insulators [7,8], and moiré excitons [9][10][11][12]. A notable recent advance in experimental techniques is the demonstration of in situ control of the moiré superlattice in rotatable heterostructures, including twisted bilayer graphene [13] and graphene/BN heterostructures [14]. These results point to the exciting possibility of dynamical control of quantum states in van der Waals heterostructures, in which the moiré superlattice should be treated as a timedependent potential.In a van der Waals heterostructure, the moiré superlattice is formed by incommensurate stacking of atomic layers. A complete description of the stacking requires both the twist angle (θ) and the relative shift (s). In principle, a variation in either θ or s will make the moiré potential time-dependent. However, while varying the twist angle can lead to a drastic change of the moiré potential and hence a strong modification of the electronic structure, a relative shift does not change the overall shape of the moiré superlattice and the static electronic structure is shift independent (for small twist angles) [15][16][17][18][19]. Because of this, so far little attention has been paid to the shift-dependence of the moiré superlattice.In this Letter we consider the dynamical consequence of the relative shift in a van der Waals heterostructure. We show that a sliding motion between the two layers of a moiré superlattice will induce an electric current. In particular, when the Fermi energy lies in one of the minigaps, the system realizes a two-dimensional version of the topological Thouless pump [20]. We first give a general argument of this phenomena by analyzing the motion of the moiré potential and the symmetry of the heterostructures. Interestingly, we find that a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers [ Fig. 1(a)]. This result is further confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene, where (a) (c) (b) sliding FIG. 1. (a) A relative shif...

Tunable Layer Circular Photogalvanic Effect in Twisted Bilayers

“…We begin with an AB stacked bilayer graphene, then twist one of the layers around a point where the top and bottom lattice points overlap. At arbitrary twisting angle except when θ = nπ/3, the resulting structure, whether commensurate or incommensurate, always respects the chiral D 3 or D 6 group [20][21][22][23].…”

Topological invariants in two-dimensional quasicrystals

“…The result coincides with the adiabatic moiré pumping in the previous works. [26][27][28] The argument is also applicable to the quasicrystal gaps at θ = 30 • . Here the zone quantum numbers take the form Q m,n = (m, n, 2n, −n, n, m) [Eq.…”

“…26 The integers C i1 and C i2 are expressed as the first Chern numbers. [26][27][28] The Bloch Hamiltonian for the commensurate approximant can be written as H(k 1 , k 2 ; φ 1 , φ 2 , φ 3 , φ 4 ) where k l = k • a c l /|a c l | (l = 1, 2) is the component of the Bloch wavevector along a c l , and φ i (i = 1, 2, 3, 4) is the phase factors for the potential slide [Eq. (21)].…”

“…Quasiperiodic systems can also have energy gaps [5][6][7][8] , while the lack of the Bloch bands makes the definition of topological numbers a nontrivial problem. Several theoretical works have been devoted to topological characterization of various one-dimensional (1D) [9][10][11][12][13][14][15][16][17][18][19][20] and two-dimensional (2D) quasiperiodic systems [21][22][23][24][25][26][27][28] . In particular, one-dimensional quasicrystals are characterized by the adiabatic charge pumping, where the number of the transfered charge under a relative slide of a single periodic structure to the other is given by the first Chern number, in an analogous manner to the quantum Hall effect.…”

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

“…The need for the generic twist angle theory becomes apparent if we consider an out of equilibrium system. In this context, optical Floquet engineering [18,19] and the Thouless pump [20] physics of TBG have been studied. Since a theory based on commensurate approximation [21] is not enough to capture the incommensurate nature for any twisted angle, there is a need to develop a geometric theory for generic twisted angle.…”