Ilya Grigorenko

Phonon-mediated tunneling into graphene.

Recent scanning tunneling spectroscopy experiments on graphene reported an unexpected gap of about +/-60 meV around the Fermi level [V. W. Brar, Appl. Phys. Lett. 91, 122102 (2007); 10.1063/1.2771084Y. Zhang, Nature Phys. 4, 627 (2008)10.1038/nphys1022]. Here we give a theoretical investigation explaining the experimentally observed spectra and confirming the phonon-mediated tunneling as the reason for the gap: We study the real space properties of the wave functions involved in the tunneling process by means of ab initio theory and present a model for the electron-phonon interaction, which couples the graphenes Dirac electrons with quasifree-electron states at the Brillouin zone center. The self-energy associated with this electron-phonon interaction is calculated, and its effects on tunneling into graphene are discussed. Good agreement of the tunneling density of states within our model and the experimental dI/dU spectra is found.

Electromagnetic response of broken-symmetry nanoscale clusters.

A microscopic, nonlocal response theory is developed to model the interaction of electromagnetic radiation with inhomogeneous nanoscale clusters. The breakdown of classical continuum-field Mie theory is demonstrated at a critical coarse-graining threshold, below which macroscopic plasmon resonances are replaced by molecular excitations with suppressed spectral intensity.

Plasmonic excitations in tight-binding nanostructures

We explore the collective electromagnetic response in atomic clusters of various sizes and geometries. Our aim is to understand, and hence to control, their dielectric response, based on a fully quantum-mechanical description which captures accurately their relevant collective modes. The electronic energy levels and wave functions, calculated within the tight-binding model, are used to determine the non-local dielectric response function. It is found that the system shape, the electron filling and the driving frequency of the external electric field strongly control the resonance properties of the collective excitations in the frequency and spatial domains. Furthermore, it is shown that one can design spatially localized collective excitations by properly tailoring the nanostructure geometry.

Optimal control of electromagnetic field using metallic nanoclusters

The dielectric properties of metallic nanoclusters in the presence of an applied electromagnetic field are investigated using the non-local linear response theory. In the quantum limit we find a nontrivial dependence of the induced field and charge distributions on the spatial separation between the clusters and on the frequency of the driving field. Using a genetic algorithm, these quantum functionalities are exploited to custom-design sub-wavelength lenses with a frequency-controlled switching capability.

Formation of collective excitations in quasi-one-dimensional metallic nanostructures: Size and density dependence

We investigate theoretically the formation of collective excitations in atomic scale quasi-one dimensional metallic nanostructures. The response of the system is calculated within the linear response theory and random phase approximation. For uniform nanostructures a transition from quantum single particle excitations to classical plasmon scaling is observed, depending on the system length and electron density. We find crucial differences in the scaling behavior for quasi-one dimensional and three-dimensional nanostructures. The presence of an additional modulating on-site potential is shown to localize electrons, leading to the response function that is highly sensitive to the number of electrons at low fillings.

Torsional oscillators and the entropy dilemma of putative supersolid 4He

Solid 4He is viewed as a nearly perfect Debye solid. Yet, recent calorimetry measurements by the PSU group (J. Low Temp. Phys. 138, 853 (2005) and Nature 449, 1025 (2007)) indicate that at low temperatures the specific heat has both cubic and linear contributions. These features appear in the same temperature range where measurements of the torsional oscillator period suggest a supersolid transition. We analyze the specific heat and compare the measured with the estimated entropy for a proposed supersolid transition with 1% superfluid fraction and find that the observed entropy is too small. We suggest that the low-temperature linear term in the specific heat is due to a glassy state that develops at low temperatures and is caused by a distribution of tunneling systems in the crystal. We propose that dislocation related defects produce those tunneling systems. Further, we argue that the reported putative mass decoupling, that means an increase in the oscillator frequency, is consistent with a glass-like transition. The glass scenario offers an alternative interpretation of the torsional oscillator experiments in contrast to the supersolid scenario of nonclassical rotational inertia.

Optimal control of the local electromagnetic response of nanostructured materials: Optimal detectors and quantum disguises.

We consider the problem of optimization of an effective trapping potential in a nanostructure with a quasi-one-dimensional geometry. The optimization is performed to achieve certain target optical properties of the system. We formulate and solve the optimization problem for a nanostructure that serves either as a single molecule detector or as a “quantum disguise” for a single molecule.

The electron–hole superfluidity in two coaxial nanotubes

The superfluid phase and Coulomb drag effect caused by the pairing in a system of spatially separated electrons and holes in two coaxial cylindrical nanotubes are predicted. It is found that the drag resistance as a function of temperature experiences a jump at the critical temperature and can be used for the manifestation of the superfluid transition. It is demonstrated that at sufficiently low temperatures the order parameter and free energy density exhibit a kink due to the electron-hole asymmetry that is controlled by the radii of the nanotubes.

Control of the temporal profile of the local electromagnetic field near metallic nanostructures

We study control of the temporal profile of the local electric field in the vicinity of a small doped semiconductor or metal nanostructure. Unlike in the case of control in a gas or liquid phase, the collective response of electrons in the nanostructure may significantly enhance different frequency components of the external field. This enhancement strongly depends on the geometry of the nanostructure and can substantially modify the temporal profile of the local field. The changes in the amplitude and phase of the local field are studied using linear response theory within the random phase approximation. The inverse problem of finding the external electromagnetic field to generate an arbitrary target temporal profile of the local field, including the time-dependent polarization of the field, is considered and solved. We systematically study the pulse enhancement and shape distortion effects for a set of control pulses of various shapes.

Superfluidity of electron–hole pairs between two critical temperatures

We study a system of spatially separated electrons and holes, assuming the carriers are confined to two parallel planes. The existence of the superfluid state of electron–hole pairs between two critical temperatures is predicted for such system in a case of electron–hole asymmetry caused by the difference in the carrier masses and their chemical potentials. The stability of the superfluid state is studied with respect to the changes of the asymmetry between electrons and holes. It is found that one type of the asymmetry can compensate another one, so the superfluid state is possible in a wide range of the asymmetry parameters when they satisfy a simple linear equation.