Quasiparticle dynamics in ballistic weak links under weak voltage bias: an elementary treatment |
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| Authors: | Herbert Kroemer |
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| Institution: | 1. Department of Environmental Engineering, College of Environment & Resources, Zhejiang University, Hangzhou 310058, Zhejiang, People’s Republic of China;2. Department of Civil, Construction and Environmental Engineering, Marquette University, Milwaukee, WI 53233, USA;1. Department of Chemistry, National Institute of Technology Hamipur, Hamirpur 177005, H.P., India;2. Department of Mechanical Engineering & Materials Science and Engineering Program, State University of New York (SUNY), Binghamton, NY 13902-6000, USA;1. German Aerospace Center (DLR), German Remote Sensing Data Center (DFD), Oberpfaffenhofen, D-82234 Wessling, Germany;2. Chair for Remote Sensing, Institute for Geography and Geology, University of Wuerzburg, Am Hubland, D-97074 Wuerzburg, Germany;3. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA;1. Henan Center for Outstanding Overseas Scientists, Henan University, Kaifeng 475004, PR China;2. Henan Province Engineering Research Center of Green Anticorrosion Technology for Magnesium Alloys, Henan University, Kaifeng, Henan 475004, PR China;3. College of Chemistry and Chemical Engineering, Henan University, Kaifeng, Henan 475004, PR China |
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| Abstract: | A simple one-dimensional model for SNS weak links in the ballistic limit is presented. In the presence of a bias voltage, the quasiparticle state at any given instant of time is described as a superposition of that particular set of phase-dependent Andreev bound states that belongs to the specific phase difference present at that instant between the superconducting banks. The treatment—basically a form of adiabatic perturbation theory—has a strong formal similarity to the treatment of the k -space dynamics of an electron in a periodic potential under perturbation by an external electric field, sufficiently strong to cause transitions across the energy gaps between bands (Zener tunneling). It is shown that the quasiparticle wavefunction retains its phase information during analogous transitions between Andreev bands. The experimental observation of Shapiro steps at one-half the canonical voltage follows naturally from the model, along with some of the experimental properties of these steps, especially their much weaker temperature dependence, compared to the canonical steps. |
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