Analytical simulations of the resonant transmission of electrons in a closed nanocircuit for terahertz applications where a tunneling junction is shunted by a metallic nanowire

In the CINT program at Los Alamos we focused ultrafast mode-locked lasers on the tip-sample junction of a scanning tunneling microscope to generate currents at hundreds of harmonics of the laser pulse repetition frequency. Each harmonic had a signal-to-noise ratio of 20 dB and a 10-dB linewidth of 3 Hz. Now we model closed quantum nanocircuits with rectangular, triangular, or delta-function barriers shunted by a beryllium filament for quasi-coherent electron transport over mean-free paths as great as 68 nm. The time-independent Schrödinger equation is solved with the boundary conditions that the wavefunction and its derivative are continuous at both connections. These boundary conditions form a four-by-four complex matrix equation with a column of zeros on the right-hand side because of the closed circuit. The dimensions are chosen such that the determinant is zero for a non-trivial solution. Each model has four parameters: (1) barrier length, (2) height and shape of the barrier, (3) length of the pre-barrier, and (4) the electron energy. Any three are specified and the fourth is varied to bring the determinant to zero on lines or surfaces in the space that is defined by the four parameters. This may provide a compact device to extend our earlier work at CINT.