Abstract
The self-consistent quantum-electrostatic (also known as Poisson-Schrödinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent even in highly non-linear regimes. We illustrate our approach with both a calculation of the compressible and incompressible stripes in the integer quantum Hall regime as well as a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.
Highlights
Where we have introduced the local density of states (LDOS), ρi(E)
Solving the local quantum problem obtained with the Quantum adiabatic approximation implies calculating the integrated local density of states (ILDOS) as a function of the chemical potential for every site of the quantum system Q
One could use the adiabatic approximation such as in [4] where the 3D LDOS is replaced by the solution of 2D problems that depend on the third dimension
Summary
The control of quantum-mechanical systems in condensed matter has reached a level of maturity where researchers seek to further develop these systems into full-fledged quantum technologies that provide the building blocks for complex devices. The most sophisticated approaches use different predictorcorrector algorithms where an approximate problem (often within the Thomas-Fermi approximation) is solved to obtain predictions of the solution which are corrected iteratively by solving the full equations [20,21,22,23,24,25,26] These approaches have been successful in various contexts, in particular when the temperature is not too low [27] or when the density of states is rather smooth, they fail spectacularly even in simple situations where the density of states has rapid variations in energy such as in the quantum Hall regime. The first is the study of the compressible/incompressible stripes in the quantum Hall effect (Sec. 9) and the second is the calculation of the conductance in a quantum point contact geometry (Sec. 10)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
