Generalized Hamiltonian for Kekulé graphene and the emergence of valley-cooperative Klein tunneling

Valley transport in Kekulé structures of graphene

“…[30,31,40,41] (a) (b) In recent years, the study of valleytronics in Kekulé graphene structures has successfully attracted widespread attention due to its unique valley-coupling effect in the system, [40] which can be used to control the valley transport. [30,31,[47][48][49][50][51][52][53][54][55] In 2021, Bao et al [44] inserted Li [56] atoms between graphene sheets and SiC substrate realizing a Kekulé superlattice structure, and confirmed the breaking of valley chirality symmetry in Kekulé structure [30,31,36,41,50] as well as the generation of a topological phase with valley-orbit coupling. [50] Currently, it has been proposed that the valley-related interaction in the Kekulé structures, [36,44,50] especially the one breaking valley chiral symmetry, can lead to numerous interesting transport properties of valley electrons.…”

“…[30,31,[47][48][49][50][51][52][53][54][55] In 2021, Bao et al [44] inserted Li [56] atoms between graphene sheets and SiC substrate realizing a Kekulé superlattice structure, and confirmed the breaking of valley chirality symmetry in Kekulé structure [30,31,36,41,50] as well as the generation of a topological phase with valley-orbit coupling. [50] Currently, it has been proposed that the valley-related interaction in the Kekulé structures, [36,44,50] especially the one breaking valley chiral symmetry, can lead to numerous interesting transport properties of valley electrons. [30,31,50] Santacruz et al [57] found that valley-momentum coupling in the Y-Kek structure can result in a low attenuation rate and low frequency valley-driven oscillatory motion of the wave packets of Dirac electrons.…”

“…[50] Currently, it has been proposed that the valley-related interaction in the Kekulé structures, [36,44,50] especially the one breaking valley chiral symmetry, can lead to numerous interesting transport properties of valley electrons. [30,31,50] Santacruz et al [57] found that valley-momentum coupling in the Y-Kek structure can result in a low attenuation rate and low frequency valley-driven oscillatory motion of the wave packets of Dirac electrons. The theoretical research by Beenakker et al [40] showed that the Y-Kek graphene can induce valley isospin locking with momentum direction in a parallel or antiparallel configuration.…”

Atomically Thin Current Pathways in Graphene through Kekulé-O Engineering

“…22,23 In order to open a gap in Kekule-Y graphene, it has been proposed using Kekule-Y bilayers or on-site potentials. 24,25 Another Kekulédistortion is a benzene-ring-like bond texture named Kekule-O graphene 26−28 that was recently observed in graphene deposited in SiC with Li intercalations. 29 In this case the electronic structure possesses a band gap proportional to the degree of deformation.…”

“…It has been shown that graphene on a Cu(111) substrate shows Y-shaped bond alternations and is named therefore Kekulé-Y graphene . In this case, the Dirac cones are mapped to the Γ point and remain gapless but can have different Fermi velocities that can be employed to induce birefringence in a spherical pn junction. , In order to open a gap in Kekulé-Y graphene, it has been proposed using Kekulé-Y bilayers or on-site potentials. , Another Kekulé distortion is a benzene-ring-like bond texture named Kekulé-O graphene − that was recently observed in graphene deposited in SiC with Li intercalations . In this case the electronic structure possesses a band gap proportional to the degree of deformation …”