Chaotic Dirac billiard in graphene quantum dots

Chaotic Dirac billiard in graphene quantum dots

| L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. H. Hill, K. S. Novoselov, A. K.Geim
This study reports on the transport characteristics of quantum dot devices fabricated entirely in graphene. These devices exhibit different behaviors depending on their size. For larger devices (submicron), they function as conventional single-electron transistors (SETs), showing periodic Coulomb blockade (CB) oscillations. For smaller devices (less than 100 nm), the CB peaks become non-periodic, indicating significant quantum confinement effects. The random spacing of these peaks is well described by the theory of chaotic neutrino (Dirac) billiards. Short constrictions in these devices, as narrow as a few nanometers, remain conductive and exhibit a confinement gap of up to 0.5 eV, demonstrating the potential for molecular-scale electronics based on graphene. The exceptional electronic properties of graphene, combined with its potential in various applications, have led to rapid interest in this material. One of the most discussed directions is its use as a base for nanoscale electronic circuits. This study reports on quantum dot (QD) devices made entirely from graphene, including their central islands, quantum barriers, source and drain contacts, and side-gate electrodes. Three operational regimes are identified based on device size: large (submicron) devices behave as conventional SETs, intermediate-sized devices enter the quantum regime with strong quantization, and very small devices exhibit chaotic behavior. The quantum confinement in graphene leads to unique properties, such as a large confinement energy (δE) compared to other materials. This results in significant level splitting in graphene-based QDs, allowing studies of relativistic-like quantum effects in confined geometries. The observed strong level repulsion in QDs is a clear signature of quantum chaos, known as "neutrino billiards." The conductance of the smallest devices is dominated by individual constrictions, which exhibit a confinement gap of up to 0.5 eV and good transistor action at room temperature. The devices were fabricated using graphene crystallites prepared by micromechanical cleavage on an oxidized Si wafer. High-resolution electron-beam lithography was used to define a mask for plasma etching, allowing precise control over the device geometry. The devices were tested over a wide range of temperatures, revealing different behaviors depending on the size of the central island. For smaller devices, the spacing between CB peaks varied significantly, indicating the importance of quantum confinement. The observed level statistics in these devices agree well with the predictions for chaotic Dirac billiards, indicating the presence of quantum chaos. The study also highlights the potential of graphene for molecular-scale electronics, with devices demonstrating high conductivity, stability, and the ability to operate at room temperature. The results demonstrate the unique properties of graphene-based quantum dots and their potential for future electronic applications.This study reports on the transport characteristics of quantum dot devices fabricated entirely in graphene. These devices exhibit different behaviors depending on their size. For larger devices (submicron), they function as conventional single-electron transistors (SETs), showing periodic Coulomb blockade (CB) oscillations. For smaller devices (less than 100 nm), the CB peaks become non-periodic, indicating significant quantum confinement effects. The random spacing of these peaks is well described by the theory of chaotic neutrino (Dirac) billiards. Short constrictions in these devices, as narrow as a few nanometers, remain conductive and exhibit a confinement gap of up to 0.5 eV, demonstrating the potential for molecular-scale electronics based on graphene. The exceptional electronic properties of graphene, combined with its potential in various applications, have led to rapid interest in this material. One of the most discussed directions is its use as a base for nanoscale electronic circuits. This study reports on quantum dot (QD) devices made entirely from graphene, including their central islands, quantum barriers, source and drain contacts, and side-gate electrodes. Three operational regimes are identified based on device size: large (submicron) devices behave as conventional SETs, intermediate-sized devices enter the quantum regime with strong quantization, and very small devices exhibit chaotic behavior. The quantum confinement in graphene leads to unique properties, such as a large confinement energy (δE) compared to other materials. This results in significant level splitting in graphene-based QDs, allowing studies of relativistic-like quantum effects in confined geometries. The observed strong level repulsion in QDs is a clear signature of quantum chaos, known as "neutrino billiards." The conductance of the smallest devices is dominated by individual constrictions, which exhibit a confinement gap of up to 0.5 eV and good transistor action at room temperature. The devices were fabricated using graphene crystallites prepared by micromechanical cleavage on an oxidized Si wafer. High-resolution electron-beam lithography was used to define a mask for plasma etching, allowing precise control over the device geometry. The devices were tested over a wide range of temperatures, revealing different behaviors depending on the size of the central island. For smaller devices, the spacing between CB peaks varied significantly, indicating the importance of quantum confinement. The observed level statistics in these devices agree well with the predictions for chaotic Dirac billiards, indicating the presence of quantum chaos. The study also highlights the potential of graphene for molecular-scale electronics, with devices demonstrating high conductivity, stability, and the ability to operate at room temperature. The results demonstrate the unique properties of graphene-based quantum dots and their potential for future electronic applications.
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