Topological charge pumping by a sliding moiré pattern

Fujimoto, Manato; Koschke, Henri; Koshino, Mikito

doi:10.1103/physrevb.101.041112

Cited by 35 publications

(27 citation statements)

References 59 publications

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“…And, for simplicity, we further require that both the two moiré interfaces in the DTFLG will restore to a AA configuration when θ = 0, which is the most possible case as suggested in the recent experiment 1 . It is noted that, in the double twisted moiré heterostructures, the kind of moiré interface will influence the band structures 27,29,31,72 . Here, we leave the DTFLGs with other kinds of moiré interface to future works.…”

Section: Model and Methodsmentioning

confidence: 99%

Moire Band Structures of the Double twisted Few Layer Graphene

Liang,

Xiao,

et al. 2021

Preprint

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Section: Model and Methodsmentioning

confidence: 99%

Moire Band Structures of the Double twisted Few Layer Graphene

Liang,

Xiao,

et al. 2021

Preprint

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“…( 17), we conclude ∆P i = m i , i.e., m i electrons passed through any cross section of the system. The integers m 1 and m 2 coincide with the first Chern numbers 11,26,29,30 , as presented in Appendix A.…”

Section: A 1d Systemsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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. 11,26,29,30 Recent developments in the study of 2D materials gave rise to a new class of 2D quasicrystals controlled by twist. [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] When two atomic layers are overlaid with an arbitrary rotation angle, the periodicities of the individual layers do not generally match, and the entire system becomes quasi-periodic.…”

Section: Introductionmentioning

confidence: 99%

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Topological invariants in two-dimensional quasicrystals

Koshino¹,

Oka²

2021

Preprint

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We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones defined in the redundant periodicities. These integers can be expressed as the second Chern numbers, by considering an adiabatic charge pumping under a relative slide of different periodicities, and using a formal relationship to the four-dimensional quantum Hall effect. The integers are independent of commensurability of the multiple periods, and invariant under arbitrary continuous deformations such as a relative rotation of twisted periodicities.

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“…Note added.-Recently, we became aware of Ref. [26], which obtained the same result of topological charge pumping in twisted bilayer graphene mainly using the tight-binding approach, while our analysis is base on the continuum model.…”

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confidence: 96%

Topological charge pumping in twisted bilayer graphene

Zhang

Gao

2020

Phys. Rev. B

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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...

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Topological charge pumping by a sliding moiré pattern

Cited by 35 publications

References 59 publications

Moire Band Structures of the Double twisted Few Layer Graphene

Moire Band Structures of the Double twisted Few Layer Graphene

Topological invariants in two-dimensional quasicrystals

Topological charge pumping in twisted bilayer graphene

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