Energy-independent total quantum transmission of electrons through nanodevices with correlated disorder

Abstract

In nanostructures with no appreciable scattering, electrons propagate ballistically, and hence have energy-independent total quantum transmission. For an incoming electron of energy $E$, the probability $\mathcal{T}(E)$ of transmission is obtained from the solution of the time-independent Schr\"odinger equation. Ballistic transport hence corresponds to $\mathcal{T}(E)=1$. We show that there is a wide class of nanostructures with correlated disorder that have $\mathcal{T}(E)=1$ for all propagating modes, even though they can have strong scattering. We call these nanostructures quantum dragons. An exact mathematical mapping for quantum transmission valid for a large class of atomic arrangements is presented within the single-band tight-binding model. Quantum transmission through a nanostructure is exactly mapped onto quantum transmission through a one-dimensional chain. The mapping is applied to carbon nanotubes in the armchair and zigzag configurations, Bethe lattices, conjoined Bethe lattices, Bethe lattices with hopping within each ring, and tubes formed from rectangular and orthorhombic lattices. The mapping shows that tuning tight-binding parameters to particular correlated values gives $\mathcal{T}(E)=1$ for all the systems studied. A quantum dragon has the same electrical conductivity as a ballistic nanodevice, namely, in a four-terminal measurement the electrical resistance is zero, while in a two-terminal measurement for the single-channel case, the electrical conductivity is equal to the conductance quantum ${G}_{0}=2{e}^{2}/h$, where $h$ is Planck's constant and $e$ the electron charge. We find $\mathcal{T}(E)=1$ is ubiquitous but occurs only on particular surfaces in the tight-binding parameter space.