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Control of Magnetotransport in Quantum Billiards: Theory, Computation and Applications 1st ed. 2017 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 252 pages, aukštis x plotis: 235x155 mm, weight: 4044 g, 48 Illustrations, color; 1 Illustrations, black and white; X, 252 p. 49 illus., 48 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 927
  • Išleidimo metai: 17-Nov-2016
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319398318
  • ISBN-13: 9783319398310
Kitos knygos pagal šią temą:
Control of Magnetotransport in Quantum Billiards: Theory, Computation and Applications 1st ed. 2017Didesnis paveikslėlis
  • Formatas: Paperback / softback, 252 pages, aukštis x plotis: 235x155 mm, weight: 4044 g, 48 Illustrations, color; 1 Illustrations, black and white; X, 252 p. 49 illus., 48 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 927
  • Išleidimo metai: 17-Nov-2016
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319398318
  • ISBN-13: 9783319398310
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319398310.html
Raktažodžiai:
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 condu

ctance 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.

Introduction.- Electrons in mesoscopic low-dimensional systems.- Coherent electronic transport: Landauer-Büttiker formalism.- Stationary scattering in planar confining geometries.- Computational quantum transport in multiterminal and multiply connected structures.- Magnetoconductance switching by phase modulation in arrays of oval quantum billiards.- Current control in soft-wall electron billiards: energy-persistent scattering in the deep quantum regime.- Directional transport in multiterminal focusing quantum billiards.- Summary, conclusions, and perspectives.
1 Introduction
1(14)
1.1 Electron Waves at the Nanoscale
1(2)
1.2 Open Quantum Billiards
3(2)
1.3 Taming Wave Propagation in the Deep Quantum Regime
5(2)
1.4 The Necessity of Efficient Computational Techniques
7(1)
1.5 Outline of the Book
8(7)
References
9(6)
2 Electrons in Low-Dimensional Mesoscopic Systems
15(22)
2.1 Two-Dimensional Electron Systems
15(6)
2.1.1 Band Structure and Effective Mass
15(2)
2.1.2 Heterojunctions and Band Engineering
17(2)
2.1.3 Modulation Doping and Band Diagram
19(2)
2.2 Coherent Transport Devices
21(6)
2.2.1 Shaping the 2D Electron System
21(2)
2.2.2 Mesoscopic Length Scales
23(2)
2.2.3 Approximations to the Hamiltonian
25(2)
2.3 Magnetoelectric Subbands and Transport Channels
27(5)
2.4 Density of States
32(5)
References
34(3)
3 Coherent Electronic Transport: Landauer-Buttiker Formalism
37(22)
3.1 Leads and Reservoirs
37(2)
3.2 Scattering Matrix and Transmission Function
39(8)
3.2.1 Lead Eigenmodes
39(1)
3.2.2 Transmission Amplitudes and Coefficients
40(3)
3.2.3 Connected Scatterers
43(3)
3.2.4 Two-Terminal System
46(1)
3.3 Two-Terminal Landauer Formula
47(6)
3.3.1 General Case of Coherent Transport
47(3)
3.3.2 Linear Response Regime
50(2)
3.3.3 Transmission as Conductance
52(1)
3.4 Multiterminal Conductance
53(6)
3.4.1 Current from Scattering States
54(1)
3.4.2 Conductance Matrix
55(1)
3.4.3 Current and (Fictitious) Voltage Probes
56(1)
References
57(2)
4 Stationary Scattering in Planar Confining Geometries
59(44)
4.1 In-Plane Hamiltonian
59(2)
4.2 Greenian Formulation of Scattering
61(16)
4.2.1 Green Functions
61(5)
4.2.2 Scattering Matrix from Greenian
66(6)
4.2.3 Elements of Formal Scattering Theory
72(5)
4.3 Non-Hermitian Approach to Scattering
77(13)
4.3.1 Decomposition of Configuration Space
77(2)
4.3.2 Effective Scattering Hamiltonian for Finite System
79(6)
4.3.3 Connection to Electronic Transport
85(5)
4.4 Multi-state Interference Effects
90(13)
4.4.1 Fano Interference
91(4)
4.4.2 Aharonov-Bohm Oscillations
95(3)
References
98(5)
5 Computational Quantum Transport in Multiterminal and Multiply Connected Structures
103(46)
5.1 Computational Schemes for Quantum Transport
103(2)
5.2 From Operators to Matrices
105(7)
5.2.1 Grid Discretization and Tight-Binding Hamiltonian
105(6)
5.2.2 Dispersion Relation
111(1)
5.3 Scattering via Spatial Decomposition
112(11)
5.3.1 Truncation of the Hamiltonian
113(4)
5.3.2 Open System Propagator
117(6)
5.4 Computation of the Propagator
123(7)
5.4.1 Block-Partitioning of the Hamiltonian
123(2)
5.4.2 Standard Recursive Green Function Method
125(1)
5.4.3 Reordered Block-Gaussian Elimination Scheme
126(4)
5.5 Extended Recursive Green Function Method for Multiterminal, Multiply Connected Structures
130(8)
5.5.1 Modular Partitioning
131(2)
5.5.2 Inter-Connection
133(2)
5.5.3 Intra-Connection
135(2)
5.5.4 Computational Efficiency and Considerations
137(1)
5.6 Transport Through Multiterminal and Multiply Connected Billiard Systems
138(11)
5.6.1 Single Three-Terminal Elliptic Billiard
138(4)
5.6.2 Transmission and Localization Patterns in a Looped Multiterminal Structure
142(4)
References
146(3)
6 Magnetoconductance Switching by Phase Modulation in Arrays of Oval Quantum Billiards
149(24)
6.1 System Setup, Approximations and Computational approach
149(3)
6.2 Single Oval Billiard: Transmission Suppression from Selective Eigenstate Interference
152(6)
6.3 Quantum Dot Array: Composite Resonant States and Magnetically Controlled Transmission Bands
158(5)
6.4 Conductance Switching
163(4)
6.5 The Impact of Impurities
167(2)
6.6 Summary and Conclusions
169(4)
References
170(3)
7 Current Control in Soft-Wall Electron Billiards: Energy-Persistent Scattering in the Deep Quantum Regime
173(20)
7.1 Persistent Switching Via Geometric Rescaling at Low Energies
173(3)
7.2 Decoupling of Resonances and Controllable Finite-Temperature Conductance
176(3)
7.3 Closed Billiard Eigenspectrum
179(3)
7.4 Switching Between Collimated and Backscattered Wave Propagation
182(3)
7.5 Conductance Switching in Soft-Wall Billiard Arrays
185(2)
7.6 Billiard Geometry and Soft-Wall Potential Variations
187(2)
7.7 Summary and Conclusions
189(4)
References
190(3)
8 Directional Magnetotransport Control in Multiterminal Focusing Quantum Billiards
193(26)
8.1 From Two-terminal to Multiterminal Conductance Control: Directional Coupling by Wave Guiding and Focusing
194(2)
8.2 Setup and Computational Approach
196(2)
8.3 Symmetries of the Transmission Coefficients
198(2)
8.4 Transmission Spectra at Zero Magnetic Field
200(2)
8.5 Geometry Dependent Mean Transmission
202(5)
8.6 Transmission in a Magnetic Field
207(5)
8.7 Bent Coupled Wires
212(2)
8.8 Directed Conductance
214(2)
8.9 Summary and Conclusions
216(3)
References
217(2)
9 Summary, Conclusions, and Perspectives
219(6)
References
223(2)
A Green Functions of Leads
225(6)
A.1 Green Function of an Infinite Quasi-1D Wire
225(2)
A.2 Interface Green Function of a Semi-Infinite Quasi-1D Wire
227(4)
B Block-Matrix Inversion and Schur Complement
231(6)
B.1 Inversion by Block-Gaussian Elimination
231(3)
B.2 Application to Block-Partitioned Lattice Hamiltonian
234(3)
C Inter- and Intra-Connection of Modules
237(6)
C.1 Inter-Connection Between Two Modules
237(3)
C.2 Intra-Connection of a Module
240(3)
D Gauge Transformation of the Greenian
243(4)
D.1 Gauge Transformation of the Green Function Between Two Different Axial Gauges
243(1)
D.2 Gauge Transformation for the Inter-Connection of Two Modules
244(3)
E Natural Units
247(2)
References
248(1)
Index 249
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.