In the present work, we investigate how structural defects in graphene can change its transport properties. In particular, we show that breaking of the sublattice symmetry in a graphene monolayer overcomes the Klein effect, leading to confined states of massless Dirac fermions. Experimentally, this corresponds to chemical bonding of foreign atoms to carbon atoms, which attach themselves to preferential positions on one of the two sublattices. In addition, we consider the scattering off a tensor barrier, which describes the rotation of the honeycomb cells of a given region around an axis perpendicular to the graphene layer. We demonstrate that in this case the intervalley mixing between the Dirac points emerges, and that Klein tunneling occurs.
Guided by the analogy to Mie scattering of light on small particles we show that the propagation of a Dirac-electron wave in graphene can be manipulated by a circular gated region acting as a quatum dot. Large dots enable electron lensing, while for smaller dots resonant scattering entails electron confinement in quasibound states. Forward scattering and Klein tunneling can be almost switched off for small dots by a Fano resonance arising from the interference between resonant scattering and the background partition.
Using advanced ab-initio calculations, we describe the formation and confinement of a two-dimensional electron gas in short-period ($\simeq$4 nm) Nb-doped SrTiO$_3$ superlattices as function of Nb doping. We predict complete two-dimensional confinement for doping concentrations higher than 70%. In agreement with previous observations, we find a large thermopower enhancement at room temperature. However, this effect is primarily determined by dilution of the mobile charge over a multitude of weakly occupied bands. As a general rule, we conclude that thermopower in similar heterostructures will …
We study by first-principles calculations a densely packed island of organic molecules (F4TCNQ) adsorbed on graphene. We find that with electron doping the island naturally forms a p-n junction in the graphene sheet. For example, a doping level of ~ 3 * 10^{13} electrons per cm^2 results in a p-n junction with 800 meV electrostatic potential barrier. Unlike in a conventional p-n junction in graphene, in the case of the junction formed by an adsorbed organic molecular island we expect that the Klein tunneling is inhibited, even without an applied external magnetic field. Here Klein tunneling is…
Graphene quantum dots (GQDs) not only have potential applications on spin qubit,but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to…
The inherent asymmetry of the electric transport in graphene is attributed to Klein tunneling across barriers defined by $\textit{pn}$-interfaces between positively and negatively charged regions. By combining conductance and shot noise experiments we determine the main characteristics of the tunneling barrier (height and slope) in a high-quality suspended sample with Au/Cr/Au contacts. We observe an asymmetric resistance $R_{\textrm{odd}}=100-70$ $Ω$ across the Dirac point of the suspended graphene at carrier density $|n_{\rm G}|=0.3-4 \cdot 10^{11}$ cm$^{-2}$, while the Fano factor displays …
Massless Dirac particles cannot be confined by an electrostatic potential. This is a problem for making graphene quantum dots but confinement can be achieved with a magnetic field and here, general conditions for confined and deconfined states are derived. There is a class of potentials for which the character of the state can be controlled at will. Then a confinement-deconfinement transition occurs which allows the Klein paradox to be probed experimentally in graphene dots.
Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g. quantum dots or quantum point contacts.
Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated-electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomoge…
Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hallbar magnetic focusing set-ups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular 'edgeless' Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or m…
The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality. While electron optics such as lensing and focusing have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge due to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resona…
The 8-\textit{Pmmn} borophene is one kind of new elemental monolayer, which hosts anisotropic and tilted massless Dirac fermions (MDF). The planar \textit{p-n} junction (PNJ) structure as the basic component of various novel devices based on the monolayer material has attracted increasing attention. Here, we analytically study the transport properties of anisotropic and tilted MDF across 8-\textit{Pmmn} borophene PNJ. Similar to the isotropic MDF across graphene junctions, perfect transmission exists but its direction departures the normal direction of borophene PNJ induced by the anisotropy a…
Realizing magnetism in graphene/carbon nanostructures is a decade-long challenge. The magnetic edge state and half metallicity in zigzag graphene nanoribbons are particularly promising [Y.-W. Son, et al., Nature 444, 347 (2006)]. However, its experimental realization has been hindered by the stringent requirement of the mono-hydrogenated zigzag edge. Using first-principle calculations, we predict that free-carrier doping can overcome this challenge and realize ferromagnetism and half-metallicity in narrow graphene nanoribbons of general types of edge structures. This magnetism exists within th…
Resonant tunneling transport in polar heterostructures is intimately connected to the polarization fields emerging from the geometric Berry-phase. In these structures, quantum confinement results not only in a discrete electronic spectrum, but also in built-in polarization charges exhibiting a broken inversion symmetry along the transport direction. Thus, electrons undergo highly asymmetric quantum interference effects with respect to the direction of current flow. By employing doping to counter the broken symmetry, we deterministically control the resonant transmission through GaN/AlN resonan…
When a single-layer graphene sheet is contacted with metallic electrodes, tunnel barriers are formed as a result of the doping of graphene by the metal in the contact region. If the Fermi energy level is modulated by a gate voltage, the phenomenon of Klein tunneling results in specific features in the conductance and noise. Here we obtain analytically exact solutions for the transmission and reflection probability amplitudes using a trapezoidal potential barrier, allowing us to calculate the differential conductance and the Fano factor for a graphene sheet in the ballistic regime. We put in ev…
Superconductivity can be induced in a normal material via the leakage of superconducting pairs of charge carriers from an adjacent superconductor. This so-called proximity effect is markedly influenced by graphene unique electronic structure, both in fundamental and technologically relevant ways. These include an unconventional form of the leakage mechanism the Andreev reflection and the potential of supercurrent modulation through electrical gating. Despite the interest of high-temperature superconductors in that context, realizations have been exclusively based on low-temperature ones. Here …
It is of keen interest to researchers understanding different approaches to confine massless Dirac fermions in graphene, which is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene p-n boundaries with an angle 34. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in …
The band gap of two-dimensional (2D) semiconductors can be efficiently tuned by gate electric field, which is so called the Stark effect. We report that doping, which is essential in realistic devices, will substantially change the Stark effect of few-layer transition metal dichalcogenides in unexpected ways. Particularly in bilayer structures, because of the competition between strong quantum confinement and intrinsic screening length, electron and hole dopings exhibit surprisingly different Stark effects: doped electrons actively screen the external field and result in a nonlinear Stark effe…
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative $k \rightarrow -i\partial_x$ skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken …
Solid state electronics relies on the intentional introduction of impurity atoms or dopants into a semiconductor crystal and/or the formation of junctions between different materials (heterojunctions) to create rectifiers, potential barriers, and conducting pathways. With these building blocks, switching and amplification of electrical currents and voltages is achieved. As miniaturization continues to ultra-scaled transistors with critical dimensions on the order of ten atomic lengths, the concept of doping to form rectifying junctions fails and heterojunction formation becomes extremely diffi…
Recently the graphene/SiC interface has emerged as a versatile platform for the epitaxy of otherwise unstable, monoelemental, two-dimensional (2D) layers via intercalation. Intrinsically capped into a van der Waals heterostructure with overhead graphene, they compose a new class of quantum materials with striking properties contrasting their parent bulk crystals. Intercalated silver presents a prototypical example where 2D quantum confinement and inversion symmetry breaking entail a metal-to-semiconductor transition. However, little is known about the associated unoccupied states, and control …
Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or quantization of energy levels However, creating confining structures with nanometer precision in shape, size and location, remains as an experimental challenge, both for top-down and bottom-up approaches. Moreover, Klein tunneling, offering an escape route to graphene electrons, limits the efficiency of electrostatic confinement. Here, a scanning tunneling mic…
The metal-graphene contact resistance is a technological bottleneck for the realization of viable graphene based electronics. We report a useful model to find the gate tunable components of this resistance determined by the sequential tunneling of carriers between the 3D-metal and 2D-graphene underneath followed by Klein tunneling to the graphene in the channel. This model quantifies the intrinsic factors that control that resistance, including the effect of unintended chemical doping. Our results agree with experimental results for several metals.
We demonstrate a fabrication scheme for clean suspended structures using chemical-vapor-deposition-grown graphene and a dry transfer method on lift-off-resist-coated substrates to facilitate suspended graphene nanoelectronic devices for technology applications. It encompasses the demands for scalable fabrication as well as for ultra-fast response due to weak coupling to environment. The fabricated devices exhibited initially a weak field-effect response with substantial positive ($p$) doping which transformed into weak negative ($n$) doping upon current annealing at the temperature of 4 Kelvin…
Experimental realization of graphene-based stadium-shaped quantum dots (QDs) have been few and incompatible with scanned probe microscopy. Yet, direct visualization of electronic states within these QDs is crucial for determining the existence of quantum chaos in these systems. We report the fabrication and characterization of electrostatically defined stadium-shaped QDs in heterostructure devices composed of monolayer graphene (MLG) and bilayer graphene (BLG). To realize a stadium-shaped QD, we utilized the tip of a scanning tunneling microscope to charge defects in a supporting hexagonal bor…
We investigate the effect of a non-magnetic donor impurity located at the surface of the SnTe topological crystalline insulator. In particular, the changes on the surface states due to a Sb impurity atom are analyzed by means of ab initio simulations of pristine and impurity-doped SnTe. Both semi-infinite and slab geometries are considered within the first-principles approach. Furthermore, minimal and Green's function continuum models are proposed with the same goal. We find that the Dirac cones are shifted down in energy upon doping; this shift strongly depends on the position of the impurity…
The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of…
Massless Dirac fermions in graphene provide unprecedented opportunities to realize the Klein paradox, which is one of the most exotic and striking properties of relativistic particles. In the seminal theoretical work [Katsnelson et al., Nat. Phys. 2 620 (2006)], it was predicted that the massless Dirac fermions can pass through one-dimensional (1D) potential barriers unimpededly at normal incidence. Such a result seems to preclude confinement of the massless Dirac fermions in graphene by using 1D potential barriers. Here, we demonstrate, both experimentally and theoretically, that massless Dir…
We have investigated the Fock-Darwin states of the massless chiral fermions confined in a graphitic parabolic quantum dot. In the light of the Klein tunneling, we have analyzed the condition for confinement of the Dirac fermions in a cylindrically-symmetric potential. New features of the energy levels of the Dirac electrons as compared to the conventional electronic systems are dicussed. We have also evaluated the dipole-allowed transitions in the energy levels of the dots. We propose that in the high magnetic field limit, the band parameters can be accurately determined from the dipole-allowe…
Due to Klein tunneling, electrostatic confinement of electrons in graphene is not possible. This hinders the use of graphene for quantum dot applications. Only through quasi-bound states with finite lifetime has one achieved to confine charge carriers. Here we propose that bilayer graphene with a local region of decoupled graphene layers is able to generate bound states under the application of an electrostatic gate. The discrete energy levels in such a quantum blister correspond to localized electron and hole states in the top and bottom layers. We find that this layer localization and the en…
The absence of a band-gap in graphene limits the gate modulation of its electron conductivity, both in regular graphene as well as in PN junctions, where electrostatic barriers prove transparent to Klein tunneling. We demonstrate a novel way to directly open a gate-tunable transmission gap across graphene PN junctions (GPNJ) by introducing an additional barrier in the middle that replaces Klein tunneling with regular tunneling, allowing us to electrostatically modulate the current by several orders of magnitude. The gap arises by angularly sorting electrons by their longitudinal energy and fil…
Periodic arrays of antidots, i.e. nanoscale perforations, in graphene enable tight confinement of carriers and efficient transport barriers. Such barriers evade the Klein tunneling mechanism by being of the mass rather than electrostatic type. While all graphene antidot lattices (GALs) may support directional barriers, we show, however, that a full transport gap exists only for certain orientations of the GAL. Moreover, we assess the applicability of gapped graphene and the Dirac continuum approach as simplified models of various antidot structures showing that, in particular, the former is an…
High-mobility graphene hosting massless charge carriers with linear dispersion provides a promising platform for electron optics phenomena. Inspired by the physics of dielectric optical micro-cavities where the photon emission characteristics can be efficiently tuned via the cavity shape, we study corresponding mechanisms for trapped Dirac fermionic resonant states in deformed micro-disk graphene billiards and directed emission from those. In such graphene devices a back-gate voltage provides an additional tunable parameter to mimic different effective refractive indices and thereby the corres…
