We study the thermoelectric properties of rectangular graphene rings connected symmetrically or asymmetrically to the leads. A side-gate voltage applied across the ring allows for the precise control of the electric current flowing through the system. The transmission coefficient of the rings manifest Breit-Wigner line shapes and/or Fano line shapes, depending on the connection configuration, the width of nanoribbons forming the ring and the side-gate voltage. We find that the thermopower and the figure of merit are greatly enhanced when the chemical potential is tuned close to resonances. Such enhancement is even more pronounced in the vicinity of Fano-like antiresonances which can be induced by a side-gate voltage independently of the geometry. This opens a possibility to use the proposed device as a tunable thermoelectric generator.

We investigate the nonequilibrium transport properties of a double quantum dot system connected in parallel to two leads, including intradot electron-electron interaction. In the absence of interactions the system supports a bound state in the continuum. This state is revealed as a Fano antiresonance in the transmission when the energy levels of the dots are detuned. Using the Keldysh nonequilibrium Green's function formalism, we find that the occurrence of the Fano antiresonance survives in the presence of Coulomb repulsion. We give precise predictions for the experimental detection of bound states in the continuum. First, we calculate the differential conductance as a function of the applied voltage and the dot level detuning and find that crossing points in the diamond structure are revealed as minima due to the transmission antiresonances. Second, we determine the thermoelectric current in response to an applied temperature bias. In the linear regime, quantum interference gives rise to sharp peaks in the thermoelectric conductance. Remarkably, we find interaction induced strong current nonlinearities for large thermal gradients that may lead to several nontrivial zeros in the thermocurrent. The latter property is especially attractive for thermoelectric applications.

We report on a novel implementation of the cryo-etching method, which enabled us to fabricate low-roughness hBN-encapsulated graphene nanoconstrictions with unprecedented control of the structure edges; the typical edge roughness is on the order of a few nanometers. We characterized the system by atomic force microscopy and used the measured parameters of the edge geometry in numerical simulations of the system conductance, which agree quantitatively with our low temperature transport measurements. The quality of our devices is confirmed by the observation of well defined quantized 2e2/h conductance steps at zero magnetic field. To the best of our knowledge, such an observation reports the clearest conductance quantization in physically etched graphene nanoconstrictions. The fabrication of such high quality systems and the scalability of the cryo-etching method opens a novel promising possibility of producing more complex truly-ballistic devices based on graphene.

Non-equilibrium molecular dynamics is used to investigate the heat current due to the atomic lattice vibrations in graphene nanoribbons and nanorings under a thermal gradient. We consider a wide range of temperature, nanoribbon widths up to 6 nm and the effect of moderate edge disorder. We find that narrow graphene nanorings can efficiently suppress the lattice thermal conductivity at low temperatures (∼ 100 K), as compared to nanoribbons of the same width.Remarkably, rough edges do not appear to have a large impact on lattice energy transport through graphene nanorings while nanoribbons seem more affected by imperfections. Furthermore, we demonstrate that the effects of hydrogensaturated edges can be neglected in these graphene nanostructures.

Here, the quantization of Dirac fermions in lithographically defined graphene nanoconstrictions is studied. Quantized conductance is observed in single nanoconstrictions fabricated on top of a thin hexamethyldisilazane layer over a Si/SiO2 wafer. This nanofabrication method allows to obtain well defined edges in the nanoconstrictions, thus reducing the effects of edge roughness on the conductance. The occurrence of ballistic transport is proved and several size quantization plateaus are identified in the conductance at low temperature. Experimental data and numerical simulations show good agreement, demonstrating that the smoothening of the plateaus is not related to edge roughness but to quantum interference effects.

We study electronic transport in systems comprising square graphene nanorings with a ferromagnetic insulator layer on top of them. The rings are connected symmetrically or asymmetrically to contacts. The proximity exchange interaction of electrons with magnetic ions results in spin-dependent transport properties. When a nanoring is connected asymmetrically, the occurrence of Fano-like antiresonances in the transmission coefficient can induce abrupt changes in the spin polarisation under minute variations of the Fermi energy. We also demonstrate that the spin polarisation can be efficiently controlled by a side-gate voltage. This opens a possibility to use these effects for fabricating tunable sources of polarised electrons.

We argue that twisted graphene nanoribbons subjected to a transverse electric field can operate as a variety of nonlinear nanoelectronic devices with tunable current-voltage characteristics controlled by the transverse field. Using the density-functional tight-binding method to address the effects of mechanical strain induced by the twisting, we show that the electronic transport properties remain almost unaffected by the strain in relevant cases and propose an efficient simplified tight-binding model which gives reliable results. The transverse electric field creates a periodic electrostatic potential along the nanoribbon, resulting in a formation of a superlattice-like energy band structure and giving rise to different remarkable electronic properties. We demonstrate that if the nanoribbon geometry and operating point are selected appropriately, the system can function as a field-effect transistor or a device with nonlinear current-voltage characteristic manifesting one or several regions of negative differential resistance. The latter opens possibilities for applications such as an active element of amplifiers, generators, and new class of nanoscale devices with multiple logic states.

Recent progress in nanostructuring of materials opens up possibilities to achieve more efficient thermoelectric devices. Nanofilms, nanowires, and nanorings may show increased phonon scattering while keeping good electron transport, two of the basic ingredients for designing more efficient thermoelectric systems. Here we argue that graphene nanorings attached to two leads meet these two requirements. Using a density-functional parametrized tight-binding method combined with Green's function technique, we show that the lattice thermal conductance is largely reduced as compared to that of graphene nanoribbons. At the same time, numerical calculations based on the quantum transmission boundary method, combined with an effective transfer matrix method, predict that the electric properties are not considerably deteriorated, leading to an overall remarkable thermoelectric efficiency. We conclude that graphene nanorings can be regarded as promising candidates for nanoscale thermoelectric devices.