Quantum Waveguide Transport in Serial Stub and Loop Structures

We have studied the quantum transmission properties of serial stub and loop structures. Throughout we have considered free electron networks and the scattering arises solely due to the geometric nature of the problem. The band formation in these geometric structures is analyzed and compared with the conventional periodic potential scatterers. Some essential differences are pointed out. We show that a single defect in an otherwise periodic structure modifies band properties non trivially. By a proper choice of a single defect one can produce positive energy bound states in continuum in the sense of von Neumann and Wigner. We also discuss some magnetic properties of loop structures in the presence of Aharonov-Bohm flux.Comment: Revtex 3.2 version, 27 pages, figures available on request, To appear in Phys. Rev.

Phase of Aharonov-Bohm oscillations in conductance of mesoscopic systems

Motivated by a recent experiment we analyze in detail the phase of Aharonov-Bohm oscillations across a 1D ring with a stub coupled to one of its arms, in the presence of a magnetic flux. We demonstrate that there are two kinds of conductance extremas. One class of them are fixed at particular flux values and can only change abruptly from a maxima to a minima as incident energy is varied. We show a different mechanism for such abrupt phase change in conductance oscillation. We demonstrate that these extremas can exhibit $``$phase locking". However, the second kind of extremas can shift continuously as the incident energy is varied.Comment: Figure available on reques

Novel interference effects and a new Quantum phase in mesoscopic systems

Mesoscopic systems have provided an opportunity to study quantum effects beyond the atomic realm. In these systems quantum coherence prevails over the entire sample. We discuss several novel effects related to persistent currents in open systems which do not have analogues in closed systems. Some phenomena arising simultaneously due to two non-classical effects namely, Aharonov-Bohm effect and quantum tunneling are presented. Simple analysis of sharp phase jumps observed in double-slit Aharonov-Bohm experiments is given. Some consequences of parity violation are elaborated. Finally, we briefly describe the dephasing of Aharonov-Bohm oscillations in Aharonov-Bohm ring geometry due to spin-flip scattering in one of the arms. Several experimental manifestations of these phenomena and their applications are given.Comment: A revie

Fractional Periodicity of Persistent Currents: A Signature of Broken Internal Symmetry

We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin Hamiltonian holds the explanation to this transition. Numerical diagonalizations are performed to show this explicitely. Persistent currents therefore, provide an easy way to experimentally verify broken internal symmetry in electronic systems.Comment: minor correction

S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.Comment: non

Landauer-B\"uttiker approach for hyperfine mediated electronic transport in the integer quantum Hall regime

The interplay of spin-polarized electronic edge states with the dynamics of the host nuclei in quantum Hall systems presents rich and non-trivial transport physics. Here, we develop a Landauer-B\"uttiker approach to understand various experimental features observed in the integer quantum Hall set ups featuring quantum point contacts. The approach developed here entails a phenomenological description of spin resolved inter-edge scattering induced via hyperfine assisted electron-nuclear spin flip-flop processes. A self-consistent simulation framework between the nuclear spin dynamics and edge state electronic transport is presented in order to gain crucial insights into the dynamic nuclear polarization effects on electronic transport and in turn the electron-spin polarization effects on the nuclear spin dynamics. In particular, we show that the hysteresis noted experimentally in the conductance-voltage trace as well as in the resistively detected NMR lineshape results from a lack of quasi-equilibrium between electronic transport and nuclear polarization evolution. In addition, we present circuit models to emulate such hyperfine mediated transport effects to further facilitate a clear understanding of the electronic transport processes occurring around the quantum point contact. Finally, we extend our model to account for the effects of quadrupolar splitting of nuclear levels and also depict the electronic transport signatures that arise from single and multi-photon processes.Comment: 21 pages, 8 figure

Aharonov-Bohm effect in the presence of evanescent modes

It is known that differential magnetoconductance of a normal metal loop connected to reservoirs by ideal wires is always negative when an electron travels as an evanescent modes in the loop. This is in contrast to the fact that the magnetoconductance for propagating modes is very sensitive to small changes in geometric details and the Fermi energy and moreover it can be positive as well as negative. Here we explore the role of impurities in the leads in determining the magnetoconductance of the loop. We find that the change in magnetoconductance is negative and can be made large provided the impurities do not create resonant states in the systems. This theoretical finding may play an useful role in quantum switch operations.Comment: 9 figures available on reques