Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials.

Beilstein Journal of Nanotechnology
Daniela Dragoman

Abstract

A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction transverse to that of electron propagation. The difference between the propagation lengths necessary to obtain a fractional Fourier transform of a given order in these two cases could be seen as a manifestation of the Berry phase. The Fourier transform of the electron wave function is a particular case of the fractional Fourier transform. If the input and output wave functions are discretized, this configuration implements in one step the discrete fractional Fourier transform, in particular the discrete Fourier transform, and thus can act as a coprocessor in integrated logic circuits.

References

Sep 29, 2000·Science·M A TopinkaA C Gossard
Nov 11, 2005·Nature·K S NovoselovA A Firsov
May 18, 2011·Nano Letters·Alexander S MayorovA K Geim
Jul 5, 2011·Optics Letters·Alejandro CámaraMariá L Calvo
Nov 7, 2015·Nanotechnology·Daniela Dragoman, Mircea Dragoman
Feb 18, 2016·Nanoscale·F YesilkoyJ Brugger
Jan 4, 2017·Journal of Physics. Condensed Matter : an Institute of Physics Journal·F LibischJ Burgdörfer
Jul 7, 2017·Reports on Progress in Physics·G Wendin

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