Wave-particle duality of electrons with spin-momentum locking
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Wave-particle duality of electrons with spin-momentum locking Double-slit interference and single-slit diffraction effects of electrons on the surface of three-dimensional topological insulators Dario Bercioux1,2,a , Tineke L. van den Berg1,b , Dario Ferraro3,4,5 , Jérôme Rech3 , Thibaut Jonckheere3 , Thierry Martin3 1 2 3 4
Donostia International Physics Center (DIPC), Manuel de Lardizbal 4, 20018 San Sebastián, Spain IKERBASQUE, Basque Foundation of Science, 48011 Bilbao, Basque Country, Spain Aix Marseille Univ, Universitá de Toulon, CNRS, CPT, Marseille, France Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genoa, Italy 5 SPIN-CNR, Via Dodecaneso 33, 16146 Genoa, Italy Received: 3 July 2020 / Accepted: 5 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We investigate the effects of spin-momentum locking on the interference and diffraction patterns due to a double- or single-slit in an electronic Gedankenexperiment. We show that the inclusion of the spin-degree-of-freedom, when coupled to the motion direction of the carrier—a typical situation that occurs in systems with spin–orbit interaction—leads to a modification of the interference and diffraction patterns that depend on the geometrical parameters of the system.
1 Introduction The wave-particle duality is one of the fundamental paradigms introduced by quantum mechanics, which tells us that every particle or quantum entity may be described as either a particle or a wave [1]. In one of his “Lectures on physics” books, Feynman et al. [2] proposed to verify the wave nature of electrons by performing a thought experiment analogous to the one conducted by Thomas Young, performed in the first decade of the 1800s to show the wave nature of light. The first experiment implementing the Young experiment with electrons was realized by Jönsson [3,4] contemporaneously with the preparation of Feynman’s lecture notes; these results were confirmed a few years later by a team of researchers at the University of Bologna [5]. In this experiment, the two slits of the setup by Jönsson were substituted by a biprism. Further refinement came after more than a decade with an experiment performed at the Hitachi lab by Tonomura et al. [6]. The readers of the magazine “Physics World” of the Institute of Physics selected these experiments to be the most beautiful ones in physics of the past century [7]. Although this type of research has now been in large part delegated to the educational framework [8,9], several groups in recent years tried to push the limits of the understanding
a e-mail: [email protected] (corresponding author) b e-mail: [email protected]
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of the validity of the wave-particle duality towards large quantum objects and molecules. One of the most complex attempts was realized by considering interference and diffraction of large C60 molecules [10–12]. This experiment was a breakthro
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