2008/04/10 by Xavier Waintal, Geneviève Fleury, Genevieve Fleury +5 · 28 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Combinatorics #Condensed matter physics #Diamagnetism #Dimension (graph theory) #Electron #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Paramagnetism #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Sign (mathematics) #cond-mat.mes-hall #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevlett.101.106804
published in Physical Review Letters 101(10), 106804 (American Physical Society) · 4 pages, 4 figures
arxiv created 2008/04/10 · openalex publication_date 2008/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.