研究了单层石墨烯超晶格中一维方势垒周期势下广义Goos-Hänchen位移的电子模拟.研究发现，电子束在单层石墨烯超晶格中的横向位移在零- $\bar{k}$带边附近可以是正的，也可以是负的，这与布拉格带边附近的横向位移不同.这些负的和正的光束位移与狄拉克点密切相关。当满足条件$q_A d_A= -q_B d_B= m π$（$m=1,2,3...$）时，当入射能量高于狄拉克点时，可以控制光束位移从负到正，反之亦然。此外，零- $\bar{k}$间隙内的缺陷模可以极大地增强光束位移。这些有趣的现象可以在相对简单的光学装置中得到验证，并在石墨烯基电子波器件中具有潜在的应用。
英文摘要：
Electronic analogue of generalized Goos-Hänchen shifts is investigated in the monolayer graphene superlattice with one-dimensional periodic potentials of square barriers. It is found that the lateral shifts for the electron beam transmitted through the monolayer graphene superlattice can be negative as well as positive near the band edges of zero-$\bar{k}$ gap, which are different from those near the band edges of Bragg gap. These negative and positive beam shifts have close relation to the Dirac point. When the condition $q_A d_A= -q_B d_B= m π$ ($m=1,2,3...$) is satisfied, the beam shifts can be controlled from negative to positive when the incident energy is above the Dirac point, and vice versa. In addition, the beam shifts can be greatly enhanced by the defect mode inside the zero-$\bar{k}$ gap. These intriguing phenomena can be verified in a relatively simple optical setup, and have potential applications in the graphene-based electron wave devices.
The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superl…
A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moiré patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moiré superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple m…
We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding …
Motivated by recent experimental findings on the low-energy spectrum of Kekulé-patterned graphene, the optoelectronic signatures of graphene superlattices with a spatial modulation that triples the size of the unit cell and folds the valleys to the center of the Brillouin zone are studied. For superlattices like those visualized in recent experiments, the optoelectronic response reveals multiple species of carriers distinguished by their effective masses or Fermi velocities. Their signatures are similar to those of systems hosting multifold fermions in which different frequency intervals are d…
We consider graphene superlattice miniband fermions probed by electronic interferometry in magneto-transport experiments. By decoding the observed Fabry-Pérot interference patterns together with our corresponding quantum transport simulations, we find that the Dirac quasiparticles originating from the superlattice minibands do not undergo conventional cyclotron motion but follow more subtle trajectories. In particular, dynamics at low magnetic fields is characterized by peculiar, straight trajectory segments. Our results provide new insights into superlattice miniband fermions and open up nove…
The hybridization of $σ$ and $π$ orbitals of carbon atoms in graphene depends on the surface curvature. Considering a single junction between flat and rippled graphene subsystems, it is found an accumulation of charge in the rippled subsystem due to Klein penetration phenomenon that gives rise to n-p junction. Using this fact, we show that the momentum distribution of electrons in ballisitically propagating beam can be selective without a waveguide, or external electric, and/or magnetic fields in graphene strip under experimentally feasible one-dimensional periodic potential. Such a potential …
A model of a superlattice consisting of alternating strips of single-layer and bilayer graphene is proposed, whose parameters of the energy spectrum can be controlled by changing the external electric field perpendicular to the surface of the sample. Using the Kronig-Penney model, the dispersion equation is obtained, based on the analysis of which the energy spectrum of a graphene superlattice is studied depending on the ratio of the strip widths of single-layer and bilayer graphene. The results of the analytical solution are compared with the results of modeling by methods of the theory of th…
Flat bands emerging in buckled monolayer graphene superlattices have been recently shown to realize correlated states analogous to those observed in twisted graphene multilayers. Here, we demonstrate the emergence of valley topology driven by competing electronic correlations in buckled graphene superlattices. We show, both by means of atomistic models and a low-energy description, that the existence of long-range electronic correlations leads to a competition between antiferromagnetic and charge density wave instabilities, that can be controlled by means of screening engineering. Interestingl…
The time evolution of electron waves in graphene superlattices is studied using both microscopic and 'effective medium' formalisms. The numerical simulations reveal that in a wide range of physical scenarios it is possible to neglect the granularity of the superlattice and characterize the electron transport using a simple effective Hamiltonian. It is verified that as general rule the continuum approximation is rather accurate when the initial state is less localized than the characteristic spatial period of the superlattice. This property holds even when the microsocopic electric potential ha…
One-dimensional (1D) graphene superlattices have been predicted to exhibit zero-energy modes a decade ago, but an experimental proof has remained missing. Motivated by a recent experiment that could possibly shed light on this, here we perform quantum transport simulations for 1D graphene superlattices, considering electrostatically simulated potential profiles as realistic as possible. Combined with the analysis on the corresponding miniband structures, we find that the zero modes generated by the 1D superlattice potential can be further cloned to higher energies, which are also accessible by…
Dirac electrons in graphene have a valley degree of freedom that is being explored as a carrier of information. In that context of "valleytronics" one seeks to coherently manipulate the valley index. Here we show that reflection from a superlattice potential can provide a valley switch: Electrons approaching a pristine-graphene--superlattice-graphene interface near normal incidence are reflected in the opposite valley. We identify the topological origin of this valley switch, by mapping the problem onto that of Andreev reflection from a topological superconductor, with the electron-hole degree…
Non-trivial Berry phase of graphene leads to unusual quantum correction to the conductivity. Berry phase of pi in single layer graphene (SLG) and 2pi in bi-layer graphene (BLG) is expected to reveal weak anti-localization (WAL) and weak localization (WL), respectively. However, experimentally both WAL and WL have been observed in graphene devices depending on the strength of different scattering mechanisms. Graphene superlattice having multiple Dirac cones is expected to exhibit pi to 2pi Berry phase transition from primary Dirac cone (PDC) to cloned Dirac cone (CDC). However, its effect on lo…
Interactions between stacked two-dimensional (2D) atomic crystals can radically change their properties, leading to essentially new materials in terms of the electronic structure. Here we show that monolayers placed on an atomically flat substrate can be forced to undergo a buckling transition, which results in periodically strained superlattices. By using scanning tunneling microscopy and spectroscopy and support from numerical simulations, we show that such lateral superlattices in graphene lead to a periodically modulated pseudo-magnetic field, which in turn creates a post-graphene material…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.
Manipulating the valley degree of freedom to encode information for potential valleytronic devices has ignited a new direction in solid-state physics. A significant, fundamental challenge in the field of valleytronics is how to generate and regulate valley-polarized currents by practical ways. Here, we discover a new mechanism of producing valley polarization in a monolayer transition metal dichalcogenides superlattice, in which valley-resolved gaps are formed at the supercell Brillouin zone boundaries and centers due to the intervalley scattering. When the energy of the incident electron is i…
Stack of correlated insulating states in bilayer graphene kagome superlattice
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室）；ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University（上海科技大学拓扑物理实验室）；Department of Physics and Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）；Department of Physics, University of Oxford（牛津大学物理系）；School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）
Surface plasmon polaritons in planar graphene superlattices with one-dimensional periodic mo-dulation of the band gap were studied. The interminiband contribution to the optical conductivity of this system was found by the equation of motion method for two cases: the Fermi level falls within one of the minigaps and the Fermi level is located within one of the minibands. It was shown that the optical conductivity of the system varies significantly in these cases. The spectra of surface plasmon polaritons in the system differs for them.
