Electron-hole hybridization in bilayer graphene

Abstract

Band structure determines the motion of electrons in a solid, giving rise to exotic phenomena when properly engineered. Drawing an analogy between electrons and photons, artificially designed optical lattices indicate the possibility of a similar band modulation effect in graphene systems. Yet due to the fermionic nature of electrons, modulated electronic systems promise far richer categories of behaviors than those found in optical lattices. Here, we uncovered a strong modulation of electronic states in bilayer graphene subject to periodic potentials. We observed for the first time the hybridization of electron and hole sub-bands, resulting in local band gaps at both primary and secondary charge neutrality points. Such hybridization leads to the formation of flat bands, enabling the study of correlated effects in graphene systems. This work may also offer a viable platform to form and continuously tune Majorana zero modes, which is important to the realization of topological quantum computation. Main textBehavior of ballistic electrons in a uniform material resembles that of photons to a high degree [1][2][3][4][5][6][7]35]. For example, electrons follow straight trajectories when considered as particles [16][17][18], while interference effects, such as the Aharonov-Bohm [19][20][21] and Fabry-Perot effects [22], are caused by their wave nature. Due to the conservation of the transverse momentum and the Fermi energy, electron propagation at the boundary of two regions with different carrier densities is subject to reflection and refraction in a way similar to optical rays crossing the boundary of two materials with different refractive indices [23]. Unlike photons, electrons in an atomically thin material can be efficiently manipulated by an artificially designed and applied potential profile that controls the spatial carrier density profile [24][25][26], resulting in graphene electron optics. This opened the way to realizing scenarios that are typically difficult to achieve by traditional optics,

Tuning of the moiré bands in graphene on hexagonal boron nitride by the periodic electrostatic gating

“…Moreover, different sets of resistance patterns may overlap at some gate voltages, where peculiar modulation of the electronic structure and transport properties can occur. The resistance patterns relative to the secondary gaps have indeed been experimentally observed for BLG/BN [45], while their explicit origin remains to be theoretically described. In addition, the variation of the electronic and transport properties of the heterostructures in such devices with the θ is yet to be explored experimentally and theoretically.…”

“…We consider the devices of MLG/BN and BLG/BN with a 1D or 2D patterned top gating structure and a uniform bottom gate, as shown schematically in figure 1(a). Such devices for MLG and BLG have been realized in experiments [45,46]. The 1D top gate is composed of periodically spaced metal wires with a period of about 120 nm and a wire width of 25 nm, and BN is used as the dielectric material between the top gate and graphene with the thickness of 20 nm and between the bottom gate and graphene with the thickness of 10 nm [45].…”

“…In the devices with periodically patterned gating, the electronic and transport properties of MLG/BN may be tuned by the gate voltages. The one-dimensional (1D) or two-dimensional (2D) periodic electrostatic potentials in graphene have recently been realized experimentally through 1D patterned gate [44,45] or 2D patterned dielectric material in the gating structure [46]. Besides MLG/BN, the heterostructure of aligned bilayer graphene and BN (BLG/BN) have also been fabricated in experiments [23,45].…”

“…The one-dimensional (1D) or two-dimensional (2D) periodic electrostatic potentials in graphene have recently been realized experimentally through 1D patterned gate [44,45] or 2D patterned dielectric material in the gating structure [46]. Besides MLG/BN, the heterostructure of aligned bilayer graphene and BN (BLG/BN) have also been fabricated in experiments [23,45]. Then it is important to explore systematically the engineering of the electronic and transport properties of MLG/BN and BLG/BN by such periodic electrostatic potentials.…”

“…In experiments, Fabry-Pérot (FP) interference like resistance maps have been observed in the pristine MLG and BLG devices with a 1D patterned top gate and a uniform bottom gate, where the resistance oscillates with gate voltages [44,45,[47][48][49][50][51][52][53][54][55][56][57][58]. The two gates with opposite signs of voltages induce spatially periodic local electron and hole doping relative to CNP, which results in a periodic electrostatic potential in graphene due to the local quantum capacitance effect [44,45,58]. The devices with a 2D patterned dielectric substrate for a gate and a uniform substrate for another gate can produce 2D periodic electrostatic potentials in graphene [46,59,60].…”