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Register a new userImaging electrostatically confined Dirac fermions in graphene quantum dots
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Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and transmission at these novel potential barriers should affect the quantum interference of electronic wavefunctions near these boundaries. Here we report the use of scanning tunneling microscopy (STM) to map the electronic structure of Dirac fermions confined by circular graphene pn junctions. These effective quantum dots were fabricated using a new technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer. Inside such graphene quantum dots we observe energy levels corresponding to quasi-bound states and we spatially visualize the quantum interference patterns of confined electrons. Dirac fermions outside these quantum dots exhibit Friedel oscillation-like behavior. Bolstered with a theoretical model describing relativistic particles in a harmonic oscillator potential, our findings yield new insight into the spatial behavior of electrostatically confined Dirac fermions.
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We report on transport characteristics of quantum dot devices etched entirely in graphene. At large sizes, they behave as conventional single-electron transistors, exhibiting periodic Coulomb blockade peaks. For quantum dots smaller than 100 nm, the peaks become strongly non-periodic indicating a major contribution of quantum confinement. Random peak spacing and its statistics are well described by the theory of chaotic neutrino (Dirac) billiards. Short constrictions of only a few nm in width remain conductive and reveal a confinement gap of up to 0.5eV, which demonstrates the in-principle possibility of molecular-scale electronics based on graphene.
We present realistic simulations of quantum confinement effects in ballistic graphene quantum dots with linear dimensions of 10 to 40 nm. We determine wavefunctions and energy level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be potentially characterized by the distribution of measured Coulomb blockade peaks.
The dynamics of low energy charge carriers in a graphene quantum dot subjected to a time-dependent local field is investigated numerically. In particular, we study a configuration where a Coulomb electric field is provided by an ion traversing the graphene sample. A Galerkin-like numerical scheme is introduced to solve the massless Dirac equation describing charge carriers subjected to space- and time-dependent electromagnetic potentials and is used to evaluate the field induced interband transitions. It is demonstrated that as the ion goes through graphene, electron-hole pairs are generated dynamically via the adiabatic pair creation mechanism around avoided crossings, similar to electron-positron pair generation in low energy heavy ion collisions.
We present an electrostatically defined few-electron double quantum dot (QD) realized in a molecular beam epitaxy grown Si/SiGe heterostructure. Transport and charge spectroscopy with an additional QD as well as pulsed-gate measurements are demonstrated. We discuss technological challenges specific for silicon-based heterostructures and the effect of a comparably large effective electron mass on transport properties and tunability of the double QD. Charge noise, which might be intrinsically induced due to strain-engineering is proven not to affect the stable operation of our device as a spin qubit. Our results promise the suitability of electrostatically defined QDs in Si/SiGe heterostructures for quantum information processing.
Graphene has raised high expectations as a low-loss plasmonic material in which the plasmon properties can be controlled via electrostatic doping. Here, we analyze realistic configurations, which produce inhomogeneous doping, in contrast to what has been so far assumed in the study of plasmons in nanostructured graphene. Specifically, we investigate backgated ribbons, co-planar ribbon pairs placed at opposite potentials, and individual ribbons subject to a uniform electric field. Plasmons in backgated ribbons and ribbon pairs are similar to those of uniformly doped ribbons, provided the Fermi energy is appropriately scaled to compensate for finite-size effects such as the divergence of the carrier density at the edges. In contrast, the plasmons of a ribbon exposed to a uniform field exhibit distinct dispersion and spatial profiles that considerably differ from uniformly doped ribbons. Our results provide a road map to understand graphene plasmons under realistic electrostatic doping conditions.
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