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Variable-range hopping and quantum creep in one dimension.

Thomas Nattermann1, Thierry Giamarchi, Pierre Le Doussal

  • 1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77 D-50937 Köln, Germany.

Physical Review Letters
|August 9, 2003
PubMed
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We discovered quantum creep in disordered one-dimensional systems, showing a unique crossover to linear response. This reveals insights into electronic transport under electric fields.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Disordered Systems

Background:

  • One-dimensional systems like charge-density waves and Luttinger liquids exhibit complex behavior in the presence of disorder.
  • Understanding their nonlinear response to external electric fields is crucial for solid-state physics.

Purpose of the Study:

  • To investigate the quantum nonlinear response of a 1D pinned charge-density wave or Luttinger liquid under an applied electric field.
  • To identify the mechanisms governing transport in such systems, particularly quantum creep and crossover phenomena.

Main Methods:

  • Explicit construction of low-lying metastable states.
  • Analysis of bounce instanton solutions connecting these states.
  • Derivation of the system's response to an electric field.

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Main Results:

  • Demonstration of quantum creep, with a velocity (v) described by the equation v=e^(-c/E(1/2)).
  • Observation of a sharp crossover at a critical electric field (E=E(*)).
  • The crossover leads to a linear response form consistent with variable-range hopping, but solely dependent on electronic degrees of freedom.

Conclusions:

  • The study reveals a novel quantum creep mechanism in disordered 1D systems.
  • A distinct crossover in the electric field response is identified, linked to electronic properties.
  • Findings provide a deeper understanding of charge transport in complex quantum materials.