Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero-energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasi-flat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy, localized states compete with states induced by defects on the superlattice scale in this system which have been proposed as hosts for electron spin qubits. We furthermore suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
Magnetic fields are often used for characterizing transport in nanoscale materials. Recent magnetotransport experiments have demonstrated that ballistic transport is possible in graphene antidot lattices (GALs). These experiments have inspired the present theoretical study of GALs in a perpendicular magnetic field. We calculate magnetotransport through graphene antidot barriers (GABs), which are finite rows of antidots arranged periodically in a pristine graphene sheet, using a tight-binding model and the Landauer-Büttiker formula. We show that GABs behave as ideal Dirac mass barriers for anti…
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken, by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a novel bilayer graphene heterostructure, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band structure engineering can be performed to obtain linearly dispersi…
Nanostructuring of graphene is in part motivated by the requirement to open a gap in the electronic band structure. In particular, a periodically perforated graphene sheet in the form of an antidot lattice may have such a gap. Such systems have been investigated with a view towards application in transistor or waveguiding devices. The desired properties have been predicted for atomically precise systems, but fabrication methods will introduce significant levels of disorder in the shape, position and edge configurations of individual antidots. We calculate the electronic transport properties of…
We explore the effect of antidot size on electronic and magnetic properties of graphene antidot lattices from first-principles calculations. The spin-polarized density of states, band gap, formation energy and the total magnetization of two different equilateral triangular and right triangular antidots with zigzag and mixed zigzag-armchair edges are studied. We find that although the values of band gap, formation energy and the total magnetization of both structures are different, these values may increase when the number of zigzag edges is increased. The armchair edges have no contribution in…
We have investigated the role of pseudospin polarization in electron wave packet dynamics in pristine graphene and in a graphene antidot lattice subject to an external magnetic field. Employing a Green's function formalism, we show that the electron dynamics can be controlled by tuning pseudospin polarization. We find that in Landau quantized pristine graphene both the propagation of an electron wave packet and Zitterbewegung oscillations strongly depend on pseudospin polarization. The electron wave packet is found to propagate in the direction of initial pseudospin polarization. We also show …
Bottom-up fabrication of graphene antidot lattices (GALs) has previously yielded atomically precise structures with sub-nanometer periodicity. Focusing on this type of experimentally realized GAL, we perform density functional theory calculations on the pristine structure as well as GALs with edge carbon atoms substituted with boron or nitrogen. We show that p- and n-type doping levels emerge with activation energies that depend on the level of hydrogenation at the impurity. Furthermore, a tight-binding parameterization together with a Green's function method are used to describe more dilute d…
The ability to localize and manipulate individual quasiparticles in mesoscopic structures is critical in experimental studies of quantum mechanics and thermodynamics, and in potential quantum information devices, e.g., for topological schemes of quantum computation. In strong magnetic field, the quantum Hall edge modes can be confined around the circumference of a small antidot, forming discrete energy levels that have a unique ability to localize fractionally charged quasiparticles. Here, we demonstrate a Dirac fermion quantum Hall antidot in graphene in the integer quantum Hall regime, where…
In order to use graphene for semiconductor applications, such as transistors with high on/off ratios, a band gap must be introduced into this otherwise semimetallic material. A promising method of achieving a band gap is by introducing nanoscale perforations (antidots) in a periodic pattern, known as a graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this paper, we will use the Dirac equation (DE) with a spatially varying mass term to calculate the electronic transport through such structur…
The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antido…
Graphene samples can have a very high carrier mobility if influences from the substrate and the environment are minimized. Embedding a graphene sheet into a heterostructure with hexagonal boron nitride (hBN) on both sides was shown to be a particularly efficient way of achieving a high bulk mobility. Nanopatterning graphene can add extra damage and drastically reduce sample mobility by edge disorder. Preparing etched graphene nanostructures on top of an hBN substrate instead of SiO2 is no remedy, as transport characteristics are still dominated by edge roughness. Here we show that etching full…
A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics processing units, show that disorder that destroys the band gap can give rise to a transport gap caused by Anderson localization. The size of the defect induced transport gap is found to be proportiona…
An experimental method for detection of bound states around an antidot formed from a hole in a graphene sheet is proposed by measuring the ballistic two terminal conductances. In particularly, we consider the effect of bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states. In addition, we develop a new numerical method in which the computational effort is proportional to the linear dimensions, instead of the area of the scatter…
We establish the theoretical foundation of the Floquet graphene antidot lattice, whereby massless Dirac fermions are driven periodically by a circularly polarized electromagnetic field, while having their motion excluded from an array of nanoholes. The properties of interest are encoded in the quasienergy spectra, which are computed non-perturbatively within the Floquet formalism. We find that a rich Floquet phase diagram emerges as the amplitude of the drive field is varied. Notably, the Dirac dispersion can be restored in real time relative to the gapped equilibrium state, which may enable t…
The adsorption effects of small molecules (H$_{2}$O, CO, NH$_{3}$, NO$_{2}$) and large molecules (Tetracyanoquinodimethane (TCNQ) and Tetrafluoro-tetracyanoquinodimethane (F4TCNQ)) on electronic and magnetic properties of two triangular graphene antidot lattices (GALs), $[10,3,6]_{RTA}$ and $[10, 5]_{ETA}$, are investigated by means of first-principles calculations. We find that CO, NO$_{2}$, TCNQ, and F4TCNQ molecules are chemisorbed by both antidots, whereas NH$_{3}$ is physisorbed (chemisorbed) by $[10, 5]_{ETA}$ ($[10,3,6]_{RTA}$) structure. H$_{2}$O, CO, NH$_{3}$ molecules reveal no signi…
Tunable inter-edge interactions in a bilayer graphene quantum Hall antidot
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Research Center for Functional Materials, National Institute for Materials Science（国立材料研究所功能材料研究中心）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（国立材料研究所国际纳米材料架构中心）；Institute of Experimental and Applied Physics and Halle-Berlin-Regensburg Cluster of Excellence CCE, University of Regensburg（雷根斯堡大学实验与应用物理研究所及哈勒-柏林-雷根斯堡卓越集群CCE）；Center for Quantum Science and Engineering (QSE Center), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
Ideal graphene antidot lattices are predicted to show promising band gap behavior (i.e., $E_G\simeq 500$ meV) under carefully specified conditions. However, for the structures studied so far this behavior is critically dependent on superlattice geometry and is not robust against experimentally realistic disorders. Here we study a rectangular array of triangular antidots with zigzag edge geometries and show that their band gap behavior qualitatively differs from the standard behavior which is exhibited, e.g, by rectangular arrays of armchair-edged triangles. In the spin unpolarized case, zigzag…
Graphene antidot lattices (GALs) are two-dimensional (2D) monolayers with periodically placed holes in otherwise pristine graphene. We investigate the electronic properties of symmetric and asymmetric GAL structures having hexagonal holes, and show that anisotropic 2D GALs can display a dimensional crossover such that effectively one-dimensional (1D) electronic structures can be realized in two-dimensions around the charge neutrality point. We investigate the transport and thermoelectric properties of these 2D GALs by using non-equilibrium Green function (NEGF) method. Dimensional crossover ma…
The edge states which were observed on a linear edge of graphene may also persist on a curved edge. We calculate the elastic transport scattering cross section on a graphene nanohole supporting the edge states. Resonant peaks in the gate voltage dependence of conductivity of graphene with such nanoholes are obtained. Position and height of the resonances are determined by the localization depth of the quasibound edge states, and width -- by their lifetime. The scattering amplitude near the resonant energies has a strong valley asymmetry. We evaluate the effect of moderate edge rippling, inhomo…
Ballistic transport was studied in a multiple-band system consisting of an antidot lattice of AB-stacked trilayer graphene. The low temperature magnetoresistance showed commensurability peaks arising from matching of the antidot lattice period and radius of cyclotron orbits for each mono- and bilayer-like band in AB stacked trilayer graphene. The commensurability peak of the monolayer-like band appeared at a lower magnetic field than that of the bilayer-like band, which reflects the fact that the Fermi surface of the bilayer-like band is larger than that of monolayer-like band. Rotation of the…
Charge carrier scattering is critical to the electrical properties of two-dimensional materials such as graphene, transition metal dichalcogenide monolayers, black phosphorene, and tellurene. Beyond pristine two-dimensional materials, further tailored properties can be achieved by nanoporous patterns such as nano- or atomic-scale pores (antidots) across the material. As one example, structure-dependent electrical/optical properties for graphene antidot lattices (GALs) have been studied in recent years. However, detailed charge carrier scattering mechanism is still not fully understood, which h…
Structural manipulation at the nanoscale breaks the intrinsic correlations among different energy carrier transport properties, achieving high thermoelectric performance. However, the coupled multifunctional (phonon and electron) transport in the design of nanomaterials makes the optimization of thermoelectric properties challenging. Machine learning brings convenience to the design of nanostructures with large degree of freedom. Herein, we conducted comprehensive thermoelectric optimization of isotopic armchair graphene nanoribbons (AGNRs) with antidots and interfaces by combining Green's fun…
Commensurability oscillations in the magnetotransport of periodically patterned systems, emerging from the interplay of cyclotron orbit and the pattern periodicity, are a benchmark of mesoscopic physics in electron gas systems. Exploiting similar effects in 2D materials would allow exceptional control of electron behaviour, but is hindered by the requirement to maintain ballistic transport over large length scales. Recent experiments have overcome this obstacle and observed distinct magnetoresistance commensurability peaks for perforated graphene sheets (antidot lattices). Interpreting the exa…
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料科学研究所纳米材料国际中心）；Center for Quantum Science and Engineering (QSE Center), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
The magneto-resistance of antidot lattices shows pronounced peaks, which became a hallmark of ballistic electron transport. While most studies agree that they reflect the interplay of regular and chaotic motion in the quasi-classical dynamics, the exact mechanism has been surprisingly controversial. Inspired by recent experiments on graphene antidot lattices showing that the effect survives strong impurity scattering, we give a new explanation of the peaks linked to a fundamental relation between collision times and accessible phase space volumes, accounting for their robustness. Due to the fu…
The influence of periodic edge vacancies and antidot arrays on the thermoelectric properties of zigzag graphene nanoribbons is investigated. Using the Green's function method, the tight-binding approximation for the electron Hamiltonian and the 4th nearest neighbor approximation for the phonon dynamical matrix, we calculate the Seebeck coefficient and the thermoelectric figure of merit. It is found that, at a certain periodic arrangement of vacancies on both edges of zigzag nanoribbon, a finite band gap opens and almost twofold degenerate energy levels appear. As a result, a marked increase in…
We propose systems that allow a tuning of the phonon transmission function T($ω$) in graphene nanoribbons by using C$^{13}$ isotope barriers, antidot structures, and distinct boundary conditions. Phonon modes are obtained by an interatomic fifth-nearest neighbor force-constant model (5NNFCM) and T($ω$) is calculated using the non-equilibrium Green's function formalism. We show that by imposing partial fixed boundary conditions it is possible to restrict contributions of the in-plane phonon modes to T($ω$) at low energy. On the contrary, the transmission functions of out-of-plane phonon modes c…
