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Final Report Summary - CANTOR (Carbon-nanotube-based terahertz-to-optics rectenna)

The main goal of the project is to combine the efforts of scientific teams from Britain, Israel and Belarus in developing a theoretical basis for the use of carbon nanotube antennas for rectification and detection of electromagnetic radiation in terahertz and optical ranges. To reach the main project goal, we will combine the efforts of the international consortium on the following objectives:
- To extend the Landauer-Büttiker theory of electron transport to the case of photon-dressed electrons;
- To analyze theoretically the rectenna performance with photon-dressed electrons as working
- To estimate thermodynamically the ultimate rectenna efficiency stipulated by the entropy transfer in photo-assisted tunneling.

The Project Consortium joins representatives of different scientific communities under the common roof of interdisciplinary research in theoretical modeling of nanorectenna which contributes to the problem of the solar energy conversion to electricity. The combined effort of teams with the different background and experience provides the complementarity/synergy between the partners stimulating the generation of new knowledge directly related to quantum optics of carbon nanostructures and aimed towards the progress in sunlight conversion into electric power.
The main scientific results obtained within the four-year period of the project in accordance with the project tasks and deliverables are as follows:

We carried out physical analysis of the rectification mechanism and established its relation to the process of generation of terahertz radiation by Rabi oscillations in a two-level system with broken inversion symmetry. Localized modes in the form of single-peaked fundamental and vortex-like stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and rectification properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nanorectenna, which should be stable against imperfections. Our novel results illustrate possibilities to control its operation by means of optical tools. Soliton-based nanorectennas are shown to be promising for applications in solar cells and detectors of terahertz and optical radiation. We extended the Landauer- Büttiker theory of electron transport to the case of ballistic electron transport over the 1D insulator layer sandwiched between two metals. The shape of the tunneling barrier is determined by the work function difference between these two metals, the applied bias voltage, and the electron affinities and thicknesses of the insulators. The described system provides rectification of the driving electromagnetic radiation.

As a major step towards the nanorectenna theory, we investigated two typical electromagnetic interference problems, namely, coupling and matching in nanoscale circuits composed of nano-interconnects and quantum devices in entangled state. Nano-interconnects under consideration are implemented by using carbon nanotubes or metallic nanowires (NWs), while quantum devices are represented by semiconductor quantum dots. The equivalent circuits of such nanocircuits contain additional elements arising at nanoscale due to quantum effects. As a result, the notions of coupling and impedance matching are reconsidered. Two examples are studied: in the first one, electromagnetically coupled NWs are connected to classical lumped devices; in the second one, electromagnetically uncoupled transmission lines are terminated on quantum devices in entangled states. In both circuits, the electromagnetic interference features differ both qualitatively and quantitatively from their classical analogs. We also demonstrated the existence of quantum coupling due to the entanglement, which exists in spite of the absence of classical electromagnetic coupling. The entanglement also modifies the matching condition introducing a dependence of the optimal value of load impedance on the line length.
We studied the fundamental thermodynamic limitation of the rectenna efficiency. It was shown that the fundamental thermodynamic limitation of the rectenna efficiency is governed by the generation of the heat flux and coherence flux in nano-gaps. We have modeled a nanorectenna as a 1D tight-binding chain of two-level systems coupled through common dissipative Markovian reservoirs. We have shown that even for a few systems in a chain, a density matrix of this chain evolves according to the classical heat transfer equation or, alternatively, can be described by the classical random walk equation. However, the dynamics of the chain induces quantum correlations between the rectenna elements. The dynamics is non-trivial and can be tailored by choosing the initial state of this one-dimensional chain to model much more complex systems. The anomalous thermodynamic behaviour contradicting Fourier law was demonstrated. Besides the energy transport occurring in one dimension (along the rectenna), there is an additional motion. The Fourier law always breaks down in the presence of an additional motion (the simplest example is convection in liquids). In our case this additional motion is a flow of quantum coherence along the rectenna.

One of the main project achievements was developing of the model of electron transport through the nano-rectenna. As a model, we consider scatterers of electrons connected to two leads, treated as electron-photon reservoirs in the thermodynamic equilibrium with the scattering center. Applying the Landauer- Büttiker formalism generalized to the case of dressed electrons, we evaluate the relaxation rates of the rectenna transporting electrons dressed by photon states of electromagnetic radiation. We demonstrated theoretically and experimentally that such systems can perform optical equalization to smooth multimode light or act as a distributor, guiding it into selected channels. Quantum thermodynamically, these systems can act as catalytic coherent reservoirs. This opens the way of the entropy transfer and high-efficient generation of the heat flux. The engineering of coupling via a common reservoir generates a vast array of novel structures for future potential applications in solar cell energy industry.

We also analyzed dynamics of coupled quantum systems. It has been found, noisy coupling between individual quantum systems leads to diffusive lossless energy transfer and retain quantum character of stationary states. Diffusive dynamics persists even in the case where additional noise suppresses all unitary excitation exchange: arbitrarily strong local dephasing, while destroying quantum correlations, does not affect energy transfer. The noisy coupling opens a new way of the high-efficient type of energy transfer, which makes it promising for applications in solar energetic. We showed that the observable values of the electromagnetic field in the far- and near-field zones emitted and absorbed by the quantum nanoantenna are coupled via uncertainty relations of the Heisenberg type. The similar uncertainty inequalities have been obtained for the electric currents in the different branches of the quantum networks. On this basis we determined the fundamental physical limitations of quantum antennas efficiency. The process of generation of terahertz radiation by Rabi oscillations in two-level system with broken inversion symmetry, predicted in Task 2.1 is generalized to the generation of terahertz radiation by Rabi-Bloch oscillations in the chains of two-level real or artificial atoms coupled via inter-atomic tunneling and driven by both dc and ac voltages. The coupling of artificial atoms is modeled by the 2x2 electron interatomic scattering and analyzed basing on the Landauer- Büttiker theory of electron ballistic transport.

For modeling nano-rectenna as an electromagnetic macroscopic scatterer with an embedded mesoscopic objects we developed the theory based on a synthesis of the integral equation technique of classical electrodynamics and the quantum transport formalism. We formulated Hallén-type integral equations, where the canonical integral operators from wire antenna theory are combined with special terms responsible for the mesoscopic structure. The mesoscopic structure is analyzed on a basis of the Landauer- Büttiker theory of ballistic electron transport. By means of this theory, it has been shown that stand-alone finite-length carbon tube with a short low-conductive section is promising for the realization of nanoantennas in the terahertz frequency range.

During the period of the project the Consortium organized a set of knowledge transfer events in accordance with project milestones. These events included 2 international workshops and four special sessions at major international conferences.

Over the four-year period CANTOR consortium members published three book chapters and over 35 papers in peer-reviewed journals and conference proceedings, delivered over 40 oral presentations at international conferences and workshops. At least 24 talks at the international conferences were invited ones.

In summary, the project has made a significant contribution towards the fast developing area of science and engineering of new artificial materials for solar energy conversion. It has outlined new directions for technological development.

Reported by

United Kingdom


Life Sciences
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