$G_Q$-corrections in Circuit Theory of Quantum Transport

Abstract

We develop a finite-element technique that allows one to evaluate correction of the order of $G_Q$ to various transport characteristics of arbitrary nanostructures. Common examples of such corrections are weak localization effect on conductance and universal conductance fluctuations. Our approach, however, is not restricted to conductance only. It allows in the same manner to evaluate corrections to noise characteristics, superconducting properties, strongly non-equilibrium transport and transmission distribution. To enable such functionality, we consider Green functions of arbitrary matrix structure. We derive a finite-element technique from Cooperon and Diffuson ladders for these Green's functions. The derivation is supplemented with application examples. Those include transitions between ensembles and Aharonov-Bohm effect.

arXiv comment16 pages, 9 figures

References in corpus (12)

• Random-Matrix Theory of Quantum Transport
• Quantum Effects in Coulomb Blockade
• Finite-element theory of transport in ferromagnet-normal metal systems
• Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems
• Novel Circuit Theory of Andreev Reflection
• Circuit Theory for Full Counting Statistics in Multi-Terminal Circuits
• Keldysh action for disordered superconductors
• Conductance Fluctuations, Weak Localization, and Shot Noise for a Ballistic Constriction in a Disordered Wire
• "Electro-flux" effect in superconducting hybrid Aharonov-Bohm rings
• Universality of Weak Localization in Disordered Wires
• Fluctuations of Transmission Distribution in Disordered Conductors
• Statistics of Transmission Eigenvalues for a Disordered Quantum Point Contact

Cited by in corpus (7)

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• Transfer matrix approach to the persistent current in hybrid normal-superconducting rings
• Mesoscopic fluctuations of the supercurrent in diffusive Josephson junctions
• Mesoscopic fluctuations of spin currents
• Temperature and magnetic-field dependence of the quantum corrections to the conductance of a network of quantum dots
• Semiclassical electron transport at the edge of a 2D topological insulator: Interplay of protected and unprotected modes
• Weak localization, Aharonov-Bohm oscillations and decoherence in arrays of quantum dots