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Correlation Effects in Nanostructures

Doctoral thesis, 2006

In this Ph.D. thesis I present the background and provide
further details to the work presented in the appended papers. The background consists of brief overviews of Kondo physics, Luttinger liquid theory, and conformal field theory. My own research is divided into three parts: the first deals with the interplay between Luttinger and Kondo physics (described in Papers I and II), the second
addresses scanning tunneling microscopy (STM) response of a Luttinger liquid with an edge or an impurity (described in Paper III), and the third explores the boundary Green's function of 1D electrons in the spin-incoherent regime (described in Paper IV).
In Papers I and II a setup is proposed which allows for a
controlled study of Kondo and Luttinger liquid physics. It
consists of a quantum box, biased by a gate voltage, and side-coupled to a quantum wire by a point contact. Close to the degeneracy points of the Coulomb blockaded box the setup can be described as a Luttinger liquid interacting with an effective Kondo impurity. Using boundary conformal field theory techniques we predict that for the case of spin-polarized electrons the differential capacitance of the box will exhibit distinctive Luttinger liquid scaling with temperature and gate voltage. In the limit of zero magnetic field the Luttinger liquid behavior gets masked by two-channel Kondo screening, leading to a logarithmic scaling of the differential capacitance with temperature
and gate voltage. These effects should be possible to study
experimentally, using the recently developed single-electron
transistor (SET) electrometer technique.
In Paper III the finite-temperature local spectral weight (LSW) of a Luttinger liquid with a hard wall boundary is calculated. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the combined effect of electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence
the STM response of one-dimensional electron systems
at low temperatures and voltage bias. Applications to STM on
single-walled carbon nanotubes are also discussed.
Paper IV, finally, presents a study of the spin-incoherent regime of 1D strongly interacting electrons. For sufficiently low densities the potential energy dominates the kinetic energy, and one can easily reach the
spin-incoherent regime where the spin exchange energy is much less than the temperature. We have generalized the description of the spin-incoherent regime to account for the presence of a boundary. By calculating the exact Green's function we find that the charge sector critical exponent is highly sensitive to the boundary, strongly modifying the tunneling of electrons close to it. Our approach also allows for a detailed description of the crossover between boundary and bulk regimes.

conformal field theory

Coulomb blockade

Wigner crystal.

Strongly correlated electrons

Kondo effect

bosonization

Luttinger liquid

STM

single-electron transistor

10.00 Kollektorn, Kemivägen 9, MC2, Chalmers.

Opponent: Professor Avraham Schiller, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel