Electron–Phonon Interaction in Cylindrical Nanostructures

Abstract

The superconductivity properties of cylinder with nano cross-section are investigated. In the nearest neighbours approximation, electron Hamiltonian of cylinder decays onto two independent Hamiltonians. One corresponds to electrons which propagate along chains parallel to the axis of cylinder. Second correspond to electrons moving in discs. The electron-phonon interaction Hamiltonians are found and superconductive properties were examined in the frames of BCS approach. It was shown that superconductive temperature in chains is several Kelvins, while in discs it can be higher for two orders of magnitude. It is also shown that magnetic field produced by electron currents in discs is of the order of thousand Tesla, i.e., extremely high.

Stabilization of Excitonic Hamiltonian

“…Consequently, we must quote boundary conditions which correspond to absence of molecules with indices n = −1 and n = N + 1, i.e., [8][9] …”

“…a + nf a nf = a + nf a n0 a + n0 + a + n0 a n0 a nf = a + nf a n0 a + n0 a nf + a + nf a + n0 a n0 a nf = P + n P n (8) Delivered The results (8) are obtained because the term a + nf a + n0 a n0 a nf is equal to zero in subspace h 1 . From (8) and (6) it follows that a n0 = 1 − P + n P n (9) Due to (8) and (9) it is clear that Pauli operators at one lattice point behave as Fermi operator.…”

“…From (8) and (6) it follows that a n0 = 1 − P + n P n (9) Due to (8) and (9) it is clear that Pauli operators at one lattice point behave as Fermi operator. For different lattice point they are defined over different space coordinates and therefore for different lattice point they commute, i.e., they behaves as bosons.…”