Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

• Published in: Physical review. B 2021-07, Vol.104 (3), p.1, Article 035432
• Main Authors: Laubscher, Katharina, Weber, Clara S., Kennes, Dante M., Pletyukhov, Mikhail, Schoeller, Herbert, Loss, Daniel, Klinovaja, Jelena
• Format: Article
• Language: English
• Subjects: Adiabatic flow; Charge density waves; Ground state; Nanowires; Quantum Hall effect
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.104.035432

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors ν = 1 / ( 2 l + 1 ) , where l is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has 2 l + 1 different branches that cannot be connected adiabatically, reflecting the ( 2 l + 1 ) -fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.