Persistent currents on graphs

Abstract

We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix which describes the topology of the graph. In certain limits, they are obtained by simple counting of the nodes and their connectivity. We relate the average current of a disordered graph with interactions and the non-interacting current of the same graph with clean 1D wires. A similar relation exists for orbital magnetism in general.

4 pages, 3 figures, to appear in Physical Review Letters

References in corpus (2)

• Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems
• Thermodynamics and Transport in Mesoscopic Disordered Networks

Cited by in corpus (30)

• Observation of Persistent Currents in Mesoscopic Connected Rings
• Spectral determinant on quantum graphs
• Unitary stochastic matrix ensembles and spectral statistics
• Explicitly solvable cases of one-dimensional quantum chaos
• Functionals of the Brownian motion, localization and metric graphs
• Transmission through quantum networks
• Scattering theory on graphs
• Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
• Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
• Eigenstate Structure in Graphs and Disordered Lattices
• Weak localization in multiterminal networks of diffusive wires
• Spin Fluctuation and Persistent Current in a Mesoscopic Ring Coupled to a Quantum Dot
• Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
• Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network
• Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders
• From quantum graphs to quantum random walks
• Quantum oscillations in mesoscopic rings and anomalous diffusion
• Dimensional crossover in quantum networks: from macroscopic to mesoscopic Physics
• Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant
• Non-linear conductance in mesoscopic weakly disordered wires -- Interaction and magnetic field asymmetry
• Thermal noise and dephasing due to electron interactions in non-trivial geometries
• Spectra of regular quantum graphs
• Charge and currents distribution in graphs
• On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
• Al'tshuler-Aronov correction to the conductivity of a large metallic square network
• $\zeta$-regularised spectral determinants on metric graphs
• Persistent Currents in Helical Structures
• Large diamagnetic persistent currents
• Persistent Currents in Normal Metal Rings (Yale PhD thesis)
• Importance of individual scattering matrix elements at Fano resonances