Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: I. Spectral properties

Abstract

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when $K_c>1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunnel density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.

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Cited by in corpus (10)

• Junctions of multiple quantum wires with different Luttinger parameters
• Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states
• The tunneling conductance between a superconducting STM tip and an out-of-equilibrium carbon nanotube
• Spectral properties of interacting helical channels driven by Lorentzian pulses
• Enhancement of tunneling density of states at a Y junction of spin-1/2 Tomonaga Luttinger liquid wires
• Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: II. Transport properties
• Minimal alternating current injection into carbon nanotubes
• Local density of states of a quarter-filled one-dimensional Mott insulator with a boundary
• Extrinsic thermoelectric response of coherent conductors
• Renormalization flow of a weak extended backscattering Hamiltonian in a non-chiral Tomonaga-Luttinger liquid