Friedel oscillations in disordered quantum wires: Influence of e-e interactions on the localization length

Abstract

The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the disorder. Scaling of the average Friedel oscillations by this exponential term collapses the disordered samples data on the clean results. We show that the length scale governing the exponential decay may be associated with the Anderson localization length and thus be used as a convenient way to determine the dependence of the localization length on disorder and interactions. The localization length decreases as a function of the interaction strength, in accordance with previous predictions.

7 pages, 7 figures

References in corpus (13)

• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Metal-insulator transition in two-dimensional electron systems
• Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems
• One-dimensional transport in polymer nanofibers
• Electron Transport in a Multi-Channel One-Dimensional Conductor: Molybdenum Selenide Nanowires
• Metal-insulator transitions and the effects of electron-electron interactions in two-dimensional electron systems
• Functional renormalization group for Luttinger liquids with impurities
• Dephasing and weak localization in disordered Luttinger liquid
• Occupation of a resonant level coupled to a chiral Luttinger liquid
• Quantum creep and variable range hopping of one-dimensional interacting electrons
• Disorder and Interactions in 1D Systems
• A level coupled to a 1D interacting reservoir : A DMRG study
• From Luttinger liquid to Altshuler-Aronov anomaly in multi-channel quantum wires

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• Interacting resonant level coupled to a Luttinger liquid: Universality of thermodynamic properties
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• Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states
• Capacitance of a resonant level coupled to Luttinger liquids
• Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
• The Friedel oscillations in the presence of transport currents
• Density of states of a dissipative quantum dot coupled to a quantum wire
• Disorder effect on the Friedel oscillations in a one-dimensional Mott insulator
• Anderson localization: a density matrix approach