Non-linear conductance in mesoscopic weakly disordered wires -- Interaction and magnetic field asymmetry

Abstract

We study the non-linear conductance $\mathcal{G}\sim {\partial }^{2}I/\partial V^2{|}_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim 0.006E_{\mathrm{Th}}^{-1}$ (and $⟨\mathcal{G}⟩=0$), where $E_{\mathrm{Th}}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, ${\mathcal{G}}_a\sim 0.001(g{E}_{\mathrm{Th}}{)}^{-1}$, where $g\gg 1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_{\phi }\ll L$, where $L_{\phi }$ is the phase coherence length, we get $\mathcal{G}\sim (L_{\phi }/L{)}^{7/2}{E}_{\mathrm{Th}}^{-1}$, and ${\mathcal{G}}_a\sim (L_{\phi }/L{)}^{11/2}(g{E}_{\mathrm{Th}}{)}^{-1}\ll \mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_{\phi }\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim (L_T/L)(L_{\phi }/L{)}^{7/2}{E}_{\mathrm{Th}}^{-1}$ (the result is dominated by the effect of screening) and ${\mathcal{G}}_a\sim (L_T/L{)}^2(L_{\phi }/L{)}^{7/2}(g{E}_{\mathrm{Th}}{)}^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

RevTeX, 39 pages, 38 pdf figures ; v2: Sections II, VII, VIII & IX reorganised, refs added ; v3: Table I updated, Appendices B & C extended, to appear in Phys. Rev. B

References in corpus (13)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Functionals of the Brownian motion, localization and metric graphs
• Magnetic field asymmetry of mesocopic dc rectification in Aharonov Bohm rings
• Dephasing due to electron-electron interaction in a diffusive ring
• Rectification and nonlinear transport in chaotic dots and rings
• Magnetoasymmetric transport in a mesoscopic interferometer: From the weak to the strong coupling regime
• Signature of the electron-electron interaction in the magnetic field dependence of nonlinear I-V characteristics in mesoscopic conductors
• Quantum oscillations in mesoscopic rings and anomalous diffusion
• Ergodic vs diffusive decoherence in mesoscopic devices
• Magnetic-field symmetries of mesoscopic nonlinear conductance
• Al'tshuler-Aronov correction to the conductivity of a large metallic square network
• $\zeta$-regularised spectral determinants on metric graphs
• Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations

Cited by in corpus (8)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Non-linear ballistic response of quantum spin-Hall edge states
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Detailed study of nonlinear cooling with two-terminal configurations of topological edge states
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures
• Readout of quantum screening effects using a time-dependent probe
• Thermoelectric cooling properties of a quantum Hall Corbino device
• Conductance matrix symmetries of multiterminal semiconductor-superconductor devices