Quantum Confinement in Epitaxial Armchair Graphene Nanoribbons on SiC Sidewalls.

The integration of graphene into devices necessitates large-scale growth and precise nanostructuring. Epitaxial growth of graphene on SiC surfaces offers a solution by enabling both simultaneous and targeted realization of quantum structures. We investigated the impact of local variations in the width and edge termination of armchair graphene nanoribbons (AGNRs) on quantum confinement effects using scanning tunneling microscopy and spectroscopy (STM, STS), along with density-functional tight-binding (DFTB) calculations. AGNRs were grown as an ensemble on refaceted sidewalls of SiC mesas with adjacent AGNRs separated by SiC(0001) terraces hosting a buffer layer seamlessly connected to the AGNRs. Energy band gaps measured by STS at the centers of ribbons of different widths align with theoretical expectations, indicating that hybridization of π-electrons with the SiC substrate mimics sharp electronic edges. However, regardless of the ribbon width, band gaps near the edges of AGNRs are significantly reduced. DFTB calculations successfully replicate this effect by considering the role of edge passivation, while strain or electric fields do not account for the observed effect. Unlike idealized nanoribbons with uniform hydrogen passivation, AGNRs on SiC sidewalls generate additional energy bands with non-pz character and nonuniform distribution across the nanoribbon. In AGNRs terminated with Si, these additional states occur at the conduction band edge and rapidly decay into the bulk of the ribbon. This agrees with our experimental findings, demonstrating that edge passivation is crucial in determining the local electronic properties of epitaxial nanoribbons.

Strain-induced stacking transition in bilayer graphene.

Strain, both naturally occurring and deliberately engineered, can have a considerable effect on the structural and electronic properties of 2D and layered materials. Uniaxial or biaxial heterostrain modifies the stacking arrangement of bilayer graphene (BLG) which subsequently influences the electronic structure of the bilayer. Here, we use density functional theory (DFT) calculations to investigate the interplay between an external applied heterostrain and the resulting stacking in BLG. We determine how a strain applied to one layer is transferred to a second, 'free' layer and at what critical strain the ground-state AB-stacking is disrupted. To overcome limitations introduced by periodic boundary conditions, we consider an approximate system consisting of an infinite graphene sheet and an armchair graphene nanoribbon. We find that above a critical strain of∼1%, it is energetically favourable for the free layer to be unstrained, indicating a transition between uniform AB-stacking and non-uniform mixed stacking. This is in agreement with a simple model estimate based on the individual energy contributions of strain and stacking effects. Our findings suggest that small levels of strain provide a platform to reversibly engineer stacking order and Moiré features in bilayers, providing a viable alternative to twistronics to engineer topological and exotic physical phenomena in such systems.

One-dimensional confinement and width-dependent bandgap formation in epitaxial graphene nanoribbons.

The ability to define an off state in logic electronics is the key ingredient that is impossible to fulfill using a conventional pristine graphene layer, due to the absence of an electronic bandgap. For years, this property has been the missing element for incorporating graphene into next-generation field effect transistors. In this work, we grow high-quality armchair graphene nanoribbons on the sidewalls of 6H-SiC mesa structures. Angle-resolved photoelectron spectroscopy (ARPES) and scanning tunneling spectroscopy measurements reveal the development of a width-dependent semiconducting gap driven by quantum confinement effects. Furthermore, ARPES demonstrates an ideal one-dimensional electronic behavior that is realized in a graphene-based environment, consisting of well-resolved subbands, dispersing and non-dispersing along and across the ribbons respectively. Our experimental findings, coupled with theoretical tight-binding calculations, set the grounds for a deeper exploration of quantum confinement phenomena and may open intriguing avenues for new low-power electronics.

Nonlocal Spin Dynamics in the Crossover from Diffusive to Ballistic Transport.

Improved fabrication techniques have enabled the possibility of ballistic transport and unprecedented spin manipulation in ultraclean graphene devices. Spin transport in graphene is typically probed in a nonlocal spin valve and is analyzed using spin diffusion theory, but this theory is not necessarily applicable when charge transport becomes ballistic or when the spin diffusion length is exceptionally long. Here, we study these regimes by performing quantum simulations of graphene nonlocal spin valves. We find that conventional spin diffusion theory fails to capture the crossover to the ballistic regime as well as the limit of long spin diffusion length. We show that the latter can be described by an extension of the current theoretical framework. Finally, by covering the whole range of spin dynamics, our study opens a new perspective to predict and scrutinize spin transport in graphene and other two-dimensional material-based ultraclean devices.

Ballistic tracks in graphene nanoribbons.

High quality graphene nanoribbons epitaxially grown on the sidewalls of silicon carbide (SiC) mesa structures stand as key building blocks for graphene-based nanoelectronics. Such ribbons display 1D single-channel ballistic transport at room temperature with exceptionally long mean free paths. Here, using spatially-resolved two-point probe (2PP) measurements, we selectively access and directly image a range of individual transport modes in sidewall ribbons. The signature of the independently contacted channels is a sequence of quantised conductance plateaus for different probe positions. These result from an interplay between edge magnetism and asymmetric terminations at opposite ribbon edges due to the underlying SiC structure morphology. Our findings demonstrate a precise control of transport through multiple, independent, ballistic tracks in graphene-based devices, opening intriguing pathways for quantum information device concepts.

Conductance quantization suppression in the quantum Hall regime.

Conductance quantization is the quintessential feature of electronic transport in non-interacting mesoscopic systems. This phenomenon is observed in quasi one-dimensional conductors at zero magnetic field B, and the formation of edge states at finite magnetic fields results in wider conductance plateaus within the quantum Hall regime. Electrostatic interactions can change this picture qualitatively. At finite B, screening mechanisms in narrow, gated ballistic conductors are predicted to give rise to an increase in conductance and a suppression of quantization due to the appearance of additional conduction channels. Despite being a universal effect, this regime has proven experimentally elusive because of difficulties in realizing one-dimensional systems with sufficiently hard-walled, disorder-free confinement. Here, we experimentally demonstrate the suppression of conductance quantization within the quantum Hall regime for graphene nanoconstrictions with low edge roughness. Our findings may have profound impact on fundamental studies of quantum transport in finite-size, two-dimensional crystals with low disorder.

Scale-invariant large nonlocality in polycrystalline graphene.

The observation of large nonlocal resistances near the Dirac point in graphene has been related to a variety of intrinsic Hall effects, where the spin or valley degrees of freedom are controlled by symmetry breaking mechanisms. Engineering strong spin or valley Hall signals on scalable graphene devices could stimulate further practical developments of spin- and valleytronics. Here we report on scale-invariant nonlocal transport in large-scale chemical vapor deposition graphene under an applied external magnetic field. Contrary to previously reported Zeeman spin Hall effect, our results are explained by field-induced spin-filtered edge states whose sensitivity to grain boundaries manifests in the nonlocal resistance. This phenomenon, related to the emergence of the quantum Hall regime, persists up to the millimeter scale, showing that polycrystalline morphology can be imprinted in nonlocal transport. This suggests that topological Hall effects in large-scale graphene materials are highly sensitive to the underlying structural morphology, limiting practical realizations.

Electron Interference in Ballistic Graphene Nanoconstrictions.

We realize nanometer size constrictions in ballistic graphene nanoribbons grown on sidewalls of SiC mesa structures. The high quality of our devices allows the observation of a number of electronic quantum interference phenomena. The transmissions of Fabry-Perot-like resonances are probed by in situ transport measurements at various temperatures. The energies of the resonances are determined by the size of the constrictions, which can be controlled precisely using STM lithography. The temperature and size dependence of the measured conductances are in quantitative agreement with tight-binding calculations. The fact that these interference effects are visible even at room temperature makes the reported devices attractive as building blocks for future carbon based electronics.

Graphene Nanobubbles as Valley Filters and Beam Splitters.

The energy band structure of graphene has two inequivalent valleys at the K and K^{'} points of the Brillouin zone. The possibility to manipulate this valley degree of freedom defines the field of valleytronics, the valley analogue of spintronics. A key requirement for valleytronic devices is the ability to break the valley degeneracy by filtering and spatially splitting valleys to generate valley polarized currents. Here, we suggest a way to obtain valley polarization using strain-induced inhomogeneous pseudomagnetic fields (PMFs) that act oppositely on the two valleys. Notably, the suggested method does not involve external magnetic fields, or magnetic materials, unlike previous proposals. In our proposal the strain is due to experimentally feasible nanobubbles, whose associated PMFs lead to different real space trajectories for K and K^{'} electrons, thus allowing the two valleys to be addressed individually. In this way, graphene nanobubbles can be exploited in both valley filtering and valley splitting devices, and our simulations reveal that a number of different functionalities are possible depending on the deformation field.

Theoretical analysis of a dual-probe scanning tunneling microscope setup on graphene.

Experimental advances allow for the inclusion of multiple probes to measure the transport properties of a sample surface. We develop a theory of dual-probe scanning tunneling microscopy using a Green's function formalism, and apply it to graphene. Sampling the local conduction properties at finite length scales yields real space conductance maps which show anisotropy for pristine graphene systems and quantum interference effects in the presence of isolated impurities. Spectral signatures in the Fourier transforms of real space conductance maps include characteristics that can be related to different scattering processes. We compute the conductance maps of graphene systems with different edge geometries or height fluctuations to determine the effects of nonideal graphene samples on dual-probe measurements.