Control of Magnetotransport in Quantum Billiards: Theory, Computation and Applications

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In 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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1 Introduction
2 Electrons in LowDimensional Mesoscopic Systems
LandauerBüttiker Formalism
4 Stationary Scattering in Planar Confining Geometries
5 Computational Quantum Transport in Multiterminal and Multiply Connected Structures
6 Magnetoconductance Switching by Phase Modulation in Arrays of Oval Quantum Billiards
EnergyPersistent Scattering in the Deep Quantum Regime
8 Directional Magnetotransport Control in Multiterminal Focusing Quantum Billiards
9 Summary Conclusions and Perspectives
A Green Functions of Leads
B BlockMatrix Inversion and Schur Complement
C Inter and IntraConnection of Modules
D Gauge Transformation of the Greenian
E Natural Units

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About the author (2016)

Christian Morfonios studied physics at Athens University and received his Ph. D. at Hamburg University in the field of electronic transport in mesoscopic structures. Having developed an expertise in computational wave transport, his main current focus is the analysis and simulation of mechanisms underlying the control of electronic conductance in nanoscale circuits.

Prof. Dr. Peter Schmelcher studied physics at the University of Heidelberg and did his PhD in 1990 at the Institute for Physical Chemistry. He did his Habilitation at the University of Heidelberg after a postdoctoral research period at the University of California Santa Barbara. Since 2010 he is full professor for Theoretical Physics at the University of Hamburg and is the head of the research group ‘Fundamental Processes in Quantum Physics’ at the Centre for Optical Quantum Technologies.