Electric Current Fluctuations in Mesoscopic Systems

The thesis consists of three parts. In the first part, electric current fluctuations in phase-coherent mesoscopic conductors are considered. For a dc transport, electron counting statistics shows that the fluctuations are reduced due to Fermi statistics. Fermi correlations lead to regularity of electron flow, and to binomial counting statitics. For a time-dependent voltage, the phase-coherence of electron transport results in non-trivial behavior of current fluctuations. Current fluctuations due to a pulse of voltage depend on detailed shape of the pulse and the mean square fluctuations diverge if the flux contained in the pulse is not an integer, as a result of Anderson orthogonality catastrophe. In the the second part, current fluctuations in an ultra-small single tunnel junction are considered. Due to the Coulomb interaction, the charging energy tends to suppress the fluctuations whereas quantum fluctuations of charge induced by an electromagnetic environment tend to wipe out the charging energy effect. The interplay of the two effects makes current fluctuations depend on the part of the circuit in which they are measured, and also on the impedance of the environment. For several environments, the current fluctuations are calculated and for each environment, their sensitivity to the measurement scheme is discussed. In the third part, the excitations induced by switching are discussed. Two kinds of perturbations are considered, an on-off operation and a switching-off perturbation. Firstly, the excitations induced by an on-off perturbation depend on the duration time 7 of the perturbation. High frequency modes with inverse frequencies smaller than 7 are significanly affected by the perturbation while low frequency modes are not excited. Secondly, the energy spectrum of the excitations induced by a switchingoff perturbation resembles thermal equilibrium spectrum. However unlike thermal excitations, they are coherent which is manifest in the non-vanishing off-diagonal correlation functions. Thesis Supervisor: Leonid S. Levitov Title: Assistant Professor of Physics Acknowledgements It is a great pleasure to finally have the opportunity to thank the people who made all of this possible. I would like to express my deepest gratitude to my advisor, Leonid Levitov. Leonid has brought my attention to recent developments in mesoscopics, and provided me with many interesting and tractable problems. He was always willing to take time to explain even the most basic facts in condensed matter physics, and shared with me many of his deep physical insights. Most of my understanding and knowledge in the condensed matter physics has been acquired through excellent lectures by professors at MIT and Harvard. I would like to take this opportunity to thank John Joannopolous, Mehran Kardar, Leonid Levitov, and Bertrand Halperin. During my :research works presented in this thesis, I have enjoyed working with my collaborators, Alexi Yakovets, Andrei Shytov, and Michael Reznikov. They have supplied valuable comments and suggested ways to resolve difficulties that caused me to stumble. Also I have benefited from numerous discussions with other graduate students and postdocs including Dongsu Bak, Yong Baek Kim, Don Kim, Ickjin Park, and Kyeongjae Cho. They have exposed me to many interesting developments in their research areas and helped me broaden my interest. In addition, I would like to thank my former and present officemates, Bruce Normand, Menke Ubbens, Mitya Chklovskii, and. Dmitri Ivanov. At various stages of my stay at MIT, I have had a good fortune of having generous mentors. Especially I would like to thank Manfred Sigrist and Peggy Berkovitz. They have given me :pieces of invaluable advice when I was at a loss, and helped me enjoy pleasant days. I would also like to thank all my friends including, but not limited to, Young-Gyu Park, Jae Sang Kim, Seungheon Song, and Sukyoung Chey. Finally I would like to thank my parents, Kwangja and Chongho Lee, and my fiancee, Ji-Kyung Choi, for all the supports and love they have given me. Without them this thesis could not have been written. Biographical Note Hyunwoo Lee was born in Seoul, Korea in 1969 and grew up there. From 1987 to 1990, he attended the Korea Institute of Technology (presently undergraduate course of Korea Advanced Institute of Science and Technology), where he graduated with a bachelor degree in physics. From 1990 to 1996, he attended graduate school at MIT and studied theoretical condensed matter physics under professor Leonid S. Levitov. In the fall of 1996, he will take a post-doctoral position at the Center for Theoretical Physics at Seoul National University in Seoul, Korea. Publications [1] Hyunwoo Lee, L. S. Levitov, and A. V. Shytov, Excitations Induced by Switching Perturbations in Quantum Wires, in preparation. [2] Hyunwoo Lee and L. S. Levitov, Flux Lattices in Layered Superconductors, in preparation. [3] Leonid S. Levitov, Hyunwoo Lee and Gordey B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, preprint, submitted to J. Math. Phys. [4] Hyunwoo Lee and L. S. Levitov, Universality in Phyllotaxis: a Mechanical Theory, to be published in Symmetry in Plants (Cambridge University, Cambridge, 1996). [5] D. A. Ivanov, H.-W. Lee, and L. S. Levitov, Coherent States of Alternating Current, to be published in Phys. Rev. B. [6] Hyunwoo Lee and L. S. Levitov, Current Fluctuations in a Single Tunnel Junction, Phys. Rev. B 53, 7383 (1996). [7] Hyunwoo Lee, L. S. Levitov, and A. Yu. Yakovets, Universal Statistics of Transport in Disordered Conductors, Phys. Rev. B 51, 4079 (1995). [8] Hyunwoo Lee and L. S. Levitov, Estimate of Minimal Noise in a Quantum Conductor, unpublished (cond-mat/9507011). [9] Hyunwoo Lee and L. S. Levitov, Orthogonality Catastrophe in a Mesoscopic Conductor due to a Time-dependent flux, unpublished (cond-mat/9312013).