Quantum dragon solutions for electron transport through nanostructures based on rectangular graphs

Abstract

Electron transport through nanodevices of atoms in a single-layer rectangular arrangement with free (open) boundary conditions parallel to the direction of the current flow is studied within the singleband tight binding model. The Landauer formula gives the electrical conductance to be a function of the electron transmission probability, ( ) E , as a function of the energy E of the incoming electron. A quantum dragon nanodevice is one which has a perfectly conducting channel, namely  = ( ) E 1 for all energies which are transmitted by the external leads even though there may be arbitrarily strong electron scattering. The rectangular single-layer systems are shown to be able to be quantum dragon devices, both for uniform leads and for dimerized leads. The quantum dragon condition requires appropriate lead-device connections and correlated randomness in the device. F .

Order amidst disorder in semi-regular, tatty, and atypical random nanodevices with locally correlated disorder

“…For most nanodevice with more than one type of atom on a graph the analysis of this paper needs to be generalized to leads which have more than one atom in the lead unit cell. This generalization has already been accomplished for quantum dragon nanodevices that had randomness correlated across the device [22,23]. Therefore, there should be no problems with generalizing to quantum dragons with only locally correlated randomness.…”

“…Alternatively, the electron transmission can be calculated using a related ansatz method [22,23,32,33] for matrices of size (N + 1) × (N + 1). These two methods have been shown to be equivalent mathematically [23], as expected from physical considerations. The calculations in this paper used the NEGF method.…”

“…Alternatively it can be obtained by using standard NEGF methods [27][28][29][30][31] to obtain the same result using only matrices with the size of the Hamiltonian (N × N ). Alternatively, the electron transmission can be calculated using a related ansatz method [22,23,32,33] for matrices of size (N + 1) × (N + 1). These two methods have been shown to be equivalent mathematically [23], as expected from physical considerations.…”

“…and may have arbitrarily strong disorder but still have T (E) = 1 for all −2<E<2 and order amidst disorder. We term these atypical disordered nanodevices quantum dragon nanodevices [22,23]. All previous quantum dragon nanodevices had disorder correlated throughout the nanodevice, either all vertices within a slice had Hamiltonian parameters globally correlated, or each of the slices were identical.…”

Order amidst disorder for two-dimensional nanoribbons with various boundary conditions

“…We previously studied the case of free boundary conditions (k 1 = k 2 = 0) and demonstrated quantum dragon nanoribbons [16] for both uniform and dimerized leads, but did not analyze order amidst disorder in the LDOS and did not calculate the bond currents.…”