You are previewing Quantum Transport.
O'Reilly logo
Quantum Transport

Book Description

This book presents the conceptual framework underlying the atomistic theory of matter, emphasizing those aspects that relate to current flow. This includes some of the most advanced concepts of non-equilibrium quantum statistical mechanics. No prior acquaintance with quantum mechanics is assumed. Chapter 1 provides a description of quantum transport in elementary terms accessible to a beginner. The book then works its way from hydrogen to nanostructures, with extensive coverage of current flow. The final chapter summarizes the equations for quantum transport with illustrative examples showing how conductors evolve from the atomic to the ohmic regime as they get larger. Many numerical examples are used to provide concrete illustrations and the corresponding Matlab codes can be downloaded from the web. Videostreamed lectures, keyed to specific sections of the book, are also available through the web. This book is primarily aimed at senior and graduate students.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. Acknowledgements
  8. List of symbols
  9. *1. Prologue: an atomistic view of electrical resistance
    1. 1.1 Energy level diagram
    2. 1.2 What makes electrons flow?
    3. 1.3 The quantum of conductance
    4. 1.4 Potential profile
    5. 1.5 Coulomb blockade
    6. 1.6 Towards Ohm’s law
    7. Exercises
  10. *2. Schrödinger equation
    1. 2.1 Hydrogen atom
    2. 2.2 Method of finite differences
    3. 2.3 Examples
    4. Exercises
  11. *3. Self-consistent field
    1. 3.1 The self-consistent field (SCF) procedure
    2. 3.2 Relation to the multi-electron picture
    3. 3.3 Bonding
    4. 3.4 Supplementary notes: multi-electron picture
    5. Exercises
  12. 4. Basis functions
    1. *4.1 Basis functions as a computational tool
    2. *4.2 Basis functions as a conceptual tool
    3. 4.3 Equilibrium density matrix
    4. 4.4 Supplementary notes
    5. Exercises
  13. 5. Bandstructure
    1. *5.1 Toy examples
    2. *5.2 General result
    3. *5.3 Common semiconductors
    4. 5.4 Effect of spin–orbit coupling
    5. 5.5 Supplementary notes: the Dirac equation
    6. Exercises
  14. 6. Subbands
    1. *6.1 Quantum wells, wires, dots, and “nanotubes”
    2. *6.2 Density of states
    3. *6.3 Minimum resistance of a wire
    4. 6.4 Velocity of a (sub)band electron
    5. Exercises
  15. 7. Capacitance
    1. *7.1 Model Hamiltonian
    2. 7.2 Electron density/density matrix
    3. *7.3 Quantum vs. electrostatic capacitance
    4. 7.4 Supplementary notes: multi-band effective mass Hamiltonian
    5. Exercises
  16. *8. Level broadening
    1. 8.1 Open systems
    2. 8.2 Local density of states
    3. 8.3 Lifetime
    4. 8.4 What constitutes a contact (reservoir)?
    5. Exercises
  17. 9. Coherent transport
    1. *9.1 Overview
    2. 9.2 Density matrix
    3. 9.3 Inflow/outflow
    4. *9.4 Transmission
    5. *9.5 Examples
    6. Exercises
  18. 10. Non-coherent transport
    1. 10.1 Why does an atom emit light?
    2. 10.2 Examples
    3. 10.3 Inflow and outflow
    4. 10.4 Supplementary notes: phonons
    5. Exercises
  19. 11. Atom to transistor
    1. 11.1 Quantum transport equations
    2. *11.2 Physics of Ohm’s law
    3. *11.3 Where is the heat dissipated?
    4. *11.4 Where is the voltage drop?
    5. Exercises
  20. 12. Epilogue
  21. Appendix: advanced formalism
    1. A.1 Correlation functions
    2. A.2 Non-equilibrium density matrix
    3. A.3 Inflow and outflow
    4. A.4 Inelastic flow
    5. A.5 Coulomb blockade/Kondo resonance
  22. MATLAB codes used to generate text figures
  23. Further reading
  24. References
  25. Index