Coulomb and spin blockade effects in nanoscale electronic transport

Bhaskaran Muralidharan, Purdue University

Abstract

Theoretical efforts to evaluate the current-voltage I(V) characteristics of nano-scale devices have mainly employed the non-equilibrium Green's function (NEGF) technique, coupled with appropriate Self Consistent Field (SCF) methods to account for electron-electron interactions. While the NEGF formalism allows a full quantum mechanical treatment of the transport problem, the application of SCF methods is questionable especially in the case where electron interactions dominate. Such cases are often encountered when considering electronic transport through quantum dots and ultrashort molecules, and pose considerable theoretical challenge. One such case is the regime of Coulomb blockade (CB) where the device is strongly interacting but weakly coupled to contacts. In this work, our focus is on interpreting notable transport experiments and novel transport effects in this regime. The NEGF-SCF formalism is highly preferred due to the relative ease with which atomistic electronic structure calculations can be coupled with transport processes, since the compuatational scaling of the one-particle Hamiltonian is linear. However, Coulomb blockaded devices considered here are very difficult to model using the one-particle Hamiltonian, but can be understood very well in terms of the multi-particle space viewpoint. Two types of devices are considered here: (a) Molecular electronic devices: In the first part of this work, we use the multi-particle Hilbert (Fock) space of the exact diagonalized many-electron Hamiltonian of various molecular structures. Using a kinetic equation in Fock space, we identify experimental signatures in the I(V) characteristics of such weakly contacted molecules arising directly from the many-particle excitation spectrum. This approach successfully explains various non-trivial features in the I(V) characteristics that are hard to realize within the NEGF-SCF framework. We then extend this approach to a simpler and more intuitive R-C equivalent by employing an incoherent sum of the many-particle excitations, that aids in understanding the observed experiments. (b) Quantum Dot Devices: The latter part of this work focusses on novel spin correlation and scattering effects in double quantum devices. In several notable experiments, spin correlation effects have revealed novel transport signatures such as regions of multiple Negative Differential Resistances (NDR) in the I(V) characteristics and hysteresis effects. We develop a generic mechanism for multiple NDRs to occur due to "spin blockade" and develop a theory for hysteretic bistability that is induced via feedback from hyperfine scattering of electron spins with the nuclear spins. The resulting Dynamic nuclear polarization forms the essence of various spin-based quantum information schemes that are currently being explored. A deep understanding of non-linear effects in strongly correlated systems will in the future contribute crucially toward theoretical progress in diverse fields where far-out-of-equilibrium dynamics are involved.

Degree

Ph.D.

Advisors

Datta, Purdue University.

Subject Area

Electrical engineering

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