## Control of Magnetotransport in Quantum Billiards: Theory, Computation and ApplicationsIn this book the coherent quantum transport of electrons through two-dimensional mesoscopic structures is explored in dependence of the interplay between the confining geometry and the impact of applied magnetic fields, aiming at conductance controllability. After a top-down, insightful presentation of the elements of mesoscopic devices and transport theory, a computational technique which treats multiterminal structures of arbitrary geometry and topology is developed. The method relies on the modular assembly of the electronic propagators of subsystems which are inter- or intra-connected providing large flexibility in system setups combined with high computational efficiency. Conductance control is first demonstrated for elongated quantum billiards and arrays thereof where a weak magnetic field tunes the current by phase modulation of interfering lead-coupled states geometrically separated from confined states. Soft-wall potentials are then employed for efficient and robust conductance switching by isolating energy persistent, collimated or magnetically deflected electron paths from Fano resonances. In a multiterminal configuration, the guiding and focusing property of curved boundary sections enables magnetically controlled directional transport with input electron waves flowing exclusively to selected outputs. Together with a comprehensive analysis of characteristic transport features and spatial distributions of scattering states, the results demonstrate the geometrically assisted design of magnetoconductance control elements in the linear response regime. |

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### Contents

1 | |

2 Electrons in LowDimensional Mesoscopic Systems | 15 |

LandauerBüttiker Formalism | 37 |

4 Stationary Scattering in Planar Confining Geometries | 59 |

5 Computational Quantum Transport in Multiterminal and Multiply Connected Structures | 102 |

6 Magnetoconductance Switching by Phase Modulation in Arrays of Oval Quantum Billiards | 149 |

EnergyPersistent Scattering in the Deep Quantum Regime | 173 |

8 Directional Magnetotransport Control in Multiterminal Focusing Quantum Billiards | 192 |

### Other editions - View all

Control of Magnetotransport in Quantum Billiards: Theory, Computation and ... Christian Morfonios,Peter Schmelcher No preview available - 2016 |

### Common terms and phrases

2DEG 2DES amplitudes asymptotic attached leads backscattered ballistic band blocks boundary channel coherent computational confining potential connected corresponding coupling density Dyson equation edge effect eigenstates electron billiard electron transport equation Fano resonances Fermi energy field strength finite flux gauge geometry Green function Greenian grid Hamiltonian hard-wall heterostructure impurity inner leads interface interference intra-connection inversion lattice LDOS lead openings Lett librator magnetic field magnetotransport mesoscopic Mesoscopic Systems modes module Morfonios multiple multiterminal open quantum oscillations outer leads oval parameter Phys propagator quantum billiard quantum dots quantum transport quantum wire regime Rotter S-matrix Schmelcher Schrödinger equation Schur complement Sect self-energy semi-infinite leads semiconductor setup slice soft wall soft-wall spatial spectral Springer structure subband switching ratio symmetry terminals tight-binding transmission coefficients transmission function transmission spectra transport device transversal transversal modes two-terminal voltage wave function width zero