PhD Thesis:

“On the effects of the many-body interactions and decoherence in the conductance of nano-devices”(Original title:(Spanish) "Sobre los efectos de la decoherencia y las interacciones de muchos cuerpos en la conductividad de nanodispositivos")

by Luis E. F. Foà Torres

(born in Córdoba in 1978)

Presented to the Facultad de Matemáticas, Astronomía y Física, Universidad Nacional de Córdoba, Argentina (School of Mathematics, Astronomy and Physics of the Córdoba National University, Argentina) in partial fulfillment of the requirements for the degree of Doctor in Physics.

Advisor: Prof. Dr. Horacio M. Pastawski

Córdoba, Argentina, August 2004

Abstract

Nanodevicesare electronic components of mesoscopic scale. Due to their small dimensions, they constitute a playground to study fundamental issues concerning thequantum coherenceof the electrons and the nature of their interactions. The focus of this thesis is the study of the effects of electron-phonon and electron-electron interactions in the conductance ofnanodevices, as well as the interplay between coherent and decoherent effects.First, we consider the emergence of

decoherencewithin a single-particle picture. We show that, in presence of a complex spectrum, anti-resonances (i.e. transmission zeroes) act as a precursor for dephasing enabling the crossover to a fully decoherent transport. This general scenario is illustrated by studying a quantum dot coupled to a cavity containing a finite, but large, number of states using a Hamiltonian formulation. In the case where the coupling is weak and the cavity has a sufficiently dense spectrum, a complex structure of resonances and anti-resonances emerge leading to phase randomization. The natural energy resolution at the electrodes leads to the same conductances as those obtained by adding a fictitious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence.The main part of this thesis is devoted to the study of the

electron-phonon interaction in nano-devices. Using suitable models, the problem of one electron interacting with phonons is solved exactly. This is achieved by mapping the many-body problem into a one-body problem with an expanded dimensionality. Our quantum coherent framework allows us to study many-body interference effects. Particular emphasis is given to the occurrence of anti-resonances as a result of these interferences. The phase fluctuations of the elastically transmitted wave are also studied. As an application we analyze the emission of the longitudinal optical phonons required to operate aphonon laser (SASER). We show that the phonon assisted tunneling peak can be strongly enhanced by an appropriate election of the geometrical parameters of the device (barrier height and width). This choice is done in order to achieve a symmetry condition for the rates of build up and decay of the resonant state in the Fock space.Finally, we consider the statistics of conductance peak heights in quantum dots in the Coulomb blockade regime. Using a coherent framework, we analyze the corrections due to the finite magnitude of the line-width of the dot levels at low temperatures. Our results show an improved agreement with recent experiments.

## Publications associated to this thesis

Articles:

L. E. F. Foa Torres, H. M. Pastawski, and E. Medina.

Antiresonances as precursors of decoherence.

EPL (Europhysics Letters)73, 164 (2006). (7 pages)

L. E. F. Foa Torres, C. H. Lewenkopf, and H. M. Pastawski.

Coherent versus Sequential Electron Tunneling in Quantum Dots.

Physical Review Letters91, 116801 (2003). (4 pages)H. M. Pastawski,

L. E. F. Foa Torres, and E. Medina.

Electron-phonon interaction and electronic decoherence in molecular conductors.

Chemical Physics281, 257 -278 (2002). (22 pages)

Special issue on molecular electronics, Edited by Mark Ratner and S. Yaliraki.

L. E. F. Foa Torres, H. M. Pastawski, and S. S. Makler.

An ultrasound emitter based on assisted tunneling.

Solid State Communications124, 363-371 (2002). (8 pages)

L. E. F. Foa Torres, H. M. Pastawski, and S. S. Makler.

Tuning a resonance in Fock space: Optimization of phonon emission in a resonant-tunneling device.

Physical Review B64, 193304 (2001). (4 pages)I. Camps, S. S. Makler, H. M. Pastawski, and

L. E. F. Foa Torres

GaAs − Alx Ga1−x As double-barrier heterostructure phonon laser: A full quantum treatment.

Physical Review B64, 125311 (2001). (13 pages)

Proceedings

L. E. F. Foa Torres, C. H. Lewenkopf, and H. M. Pastawski.

Conductance fluctuations in Coulomb-Blockaded dots: From the sequential theory to a quantum coherent description.

Proceedings of “The 15th International Conference on Electronic Properties of Two-Dimensional Systems”, Nara, Japan.

Physica E22, 526-529 (2004).

L. E. F. Foa Torres, H. M. Pastawski, and S. S. Makler.

Electron-Phonon interaction in electronic tunneling: from sequential rate equations to a coherent description.

Proceedings of the “10th Brazilian Workshop on Semiconductor Physics”.

Braz. Journal of Phys.32, 300-302 (2002).

L. E. F. Foa Torres, H. M. Pastawski, and S. S. Makler.

Resonances in Fock Space: Optimization of a SASER Device.

Proceedings of “The VI Latin American Workshop on Non-Linear Phenomena LAWNP99”.

Physica A283, 297-301 (2000).