
Introduction to Spintronics
by Bandyopadhyay; Supriyo-
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Summary
Table of Contents
The Early History of Spin | p. 1 |
Spin | p. 1 |
The Bohr planetary model and space quantization | p. 3 |
The birth of "spin" | p. 4 |
The Stern-Gerlach experiment | p. 5 |
The advent of Spintronics | p. 8 |
Problems | p. 10 |
References | p. 13 |
The Quantum Mechanics of Spin | p. 17 |
Pauli spin matrices | p. 19 |
Eigenvectors of the Pauli matrices: spinors | p. 22 |
The Pauli Equation and spinors | p. 23 |
More on the Pauli Equation | p. 25 |
Extending the Pauli Equation - the Dirac Equation | p. 26 |
The time independent Dirac Equation | p. 30 |
Non-relativistic approximation to the Dirac Equation | p. 30 |
Relationship between the non-relativistic approximation to the Dirac Equation and the Pauli Equation | p. 31 |
Problems | p. 31 |
Appendix | p. 33 |
Working with spin operators | p. 36 |
Two useful theorems | p. 36 |
Applications of the Postulates of Quantum Mechanics to a few spin problems | p. 39 |
The Heisenberg Principle for spin components | p. 42 |
References | p. 43 |
The Bloch Sphere | p. 45 |
The spinor and the "qubit" | p. 45 |
The Bloch sphere concept | p. 47 |
Preliminaries | p. 47 |
Connection between the Bloch sphere concept and the classical interpretation of the spin of electron | p. 50 |
Relationship with qubit | p. 51 |
Special spinors | p. 53 |
The spin flip matrix | p. 54 |
Excursions on the Bloch sphere: the Pauli matrices revisited | p. 54 |
Problems | p. 58 |
References | p. 63 |
Evolution of a Spinor on the Bloch Sphere | p. 65 |
Spin-1/2 particle in a constant magnetic field: Larmor precession | p. 65 |
Rotation on the Bloch sphere | p. 67 |
Preparing to derive the Rabi formula | p. 69 |
The Rabi formula | p. 74 |
Spin flip time | p. 75 |
Problems | p. 87 |
References | p. 89 |
The Density Matrix | p. 91 |
The density matrix concept: case of a pure state | p. 91 |
Properties of the density matrix | p. 92 |
Pure versus mixed state | p. 96 |
Concept of the Bloch ball | p. 99 |
Time evolution of the density matrix: case of mixed state | p. 101 |
The relaxation times T1 and T2 and the Bloch equations | p. 105 |
Problems | p. 118 |
References | p. 130 |
Spin Orbit Interaction | p. 131 |
Spin orbit interaction in a solid | p. 134 |
Rashba interaction | p. 134 |
Dresselhaus interaction | p. 136 |
Problems | p. 137 |
References | p. 139 |
Magneto-Electric Subbands in Quantum Confined Structures in the Presence of Spin-Orbit Interaction | p. 141 |
Dispersion relations of spin resolved magneto-electric subbands and eigenspinors in a two-dimensional electron gas in the presence of spin-orbit interaction | p. 141 |
Magnetic field in the plane of the 2-DEG | p. 144 |
Magnetic field perpendicular to the plane of the 2-DEG | p. 152 |
Dispersion relations of spin resolved magneto-electric subbands and eigenspinors in a one-dimensional electron gas in the presence of spin-orbit interaction | p. 153 |
Magnetic field directed along the wire axis (x-axis) | p. 153 |
Spin components | p. 157 |
Magnetic field perpendicular to wire axis and along the electric field causing Rashba effect (i.e., along y-axis) | p. 161 |
Spin components | p. 167 |
Magnetic field perpendicular to wire axis and the electric field causing Rashba effect (i.e., along the z-axis) | p. 168 |
Spin components | p. 170 |
Special case | p. 170 |
Eigenenergies of spin resolved subbands and eigenspinors in a quantum dot in the presence of spin-orbit interaction | p. 171 |
Why are the dispersion relations important? | p. 176 |
The three types of Hall Effect | p. 177 |
Quantum spin-Hall Effect | p. 189 |
Problems | p. 191 |
References | p. 195 |
Spin Relaxation | p. 199 |
The spin-independent spin-orbit magnetic field | p. 201 |
Spin relaxation mechanisms | p. 204 |
Elliott-Yafet mechanism | p. 204 |
D'yakonov Perel' mechanism | p. 207 |
Bir-Aronov-Pikus mechanism | p. 214 |
Hyperfine interactions with nuclear spins | p. 215 |
Spin relaxation in a quantum dot | p. 216 |
Longitudinal and transverse spin relaxation times in a quantum dot | p. 218 |
The Spin Galvanic Effect | p. 223 |
Another example of current flow without a battery | p. 224 |
Problems | p. 228 |
References | p. 238 |
Exchange Interaction | p. 243 |
Identical particles and the Pauli Exclusion Principle | p. 243 |
The Helium atom | p. 244 |
The Heitler-London model of the Hydrogen molecule | p. 253 |
Hartree and Hartree-Fock approximations | p. 256 |
The role of exchange in ferromagnetism | p. 258 |
The Bloch model of ferromagnetism | p. 258 |
The Heisenberg model of ferromagnetism | p. 259 |
The Heisenberg Hamiltonian | p. 260 |
Problems | p. 261 |
References | p. 265 |
Spin Transport in Solids | p. 267 |
The drift-diffusion model | p. 267 |
Derivation of the simplified steady state spin drift-diffusion equation | p. 271 |
The semiclassical model | p. 274 |
Spin transport in a quantum wire: Monte Carlo simulation | p. 276 |
Monte Carlo simulation | p. 277 |
Specific examples: temporal decay of spin polarization | p. 278 |
Specific examples: spatial decay of spin polarization | p. 280 |
Upstream transport | p. 280 |
Concluding remarks | p. 283 |
Problems | p. 285 |
References | p. 285 |
Passive Spintronic Devices and Related Concepts | p. 287 |
Spin valve | p. 287 |
Spin injection efficiency | p. 289 |
Stoner-Wohlfarth model of a ferromagnet | p. 290 |
A simple two resistor model to understand the spin valve | p. 294 |
More advanced treatment of the spin valve | p. 297 |
A transfer matrix model | p. 304 |
Application of the Jullière formula to extract the spin diffusion length in a paramagnet from spin valve experiments | p. 319 |
Spin valve experiments | p. 319 |
Hysteresis in spin valve magnetoresistance | p. 320 |
Giant magnetoresistance | p. 323 |
Applications of the spin valve and GMR effects | p. 326 |
Spin accumulation | p. 331 |
Spin injection across a ferromagnet/metal interface | p. 336 |
Spin injection in a spin valve | p. 341 |
Spin extraction at the interface between a ferromagnet and a semiconductor | p. 347 |
Problems | p. 353 |
References | p. 356 |
Hybrid Spintronics: Active Devices Based on Spin and Charge | p. 361 |
Spin-based transistors | p. 361 |
Spin field effect transistors (Spinfet) | p. 363 |
Particle viewpoint | p. 366 |
Wave viewpoint | p. 368 |
The effect of scattering on the Datta-Das SPINFET | p. 369 |
The transfer characteristic of the Datta-Das transistor | p. 370 |
Sub-threshold slope | p. 372 |
The effect of non-idealities | p. 374 |
The quantum well SPINFET | p. 377 |
The SPINFET based on the Dresselhaus spin-orbit interaction | p. 378 |
Device performance of SPINFETs | p. 382 |
Comparison between MISFET and SPINFET | p. 383 |
Comparison between HEMT and SPINFET | p. 385 |
Power dissipation estimates | p. 387 |
Other types of SPINFETs | p. 387 |
The non-ballistic SPINFET | p. 387 |
The spin relaxation transistor | p. 390 |
The importance of the spin injection efficiency | p. 392 |
Transconductance, gain, bandwidth and isolation | p. 396 |
Silicon SPINFETs | p. 397 |
Spin Bipolar Junction Transistors (SBJT) | p. 398 |
GMR-based transistors | p. 400 |
The all-metal spin transistor | p. 400 |
The spin valve transistor | p. 403 |
Concluding remarks | p. 406 |
Problems | p. 407 |
References | p. 409 |
Monolithic Spintronics: All-Spin Logic Processors | p. 413 |
Monolithic spintronics | p. 413 |
Bit stability and fidelity | p. 414 |
Reading and writing single spin | p. 415 |
Single Spin Logic | p. 416 |
The universal Single Electron Logic gate: the NAND gate | p. 416 |
The input dependent ground states of the NAND gate | p. 418 |
Ground state computing with spins | p. 426 |
Energy dissipation issues | p. 432 |
Energy dissipated in the gate during switching | p. 432 |
Energy dissipated in the clocking circuit | p. 436 |
Comparison between hybrid and monolithic spintronics | p. 436 |
Concluding remarks | p. 437 |
Problems | p. 437 |
References | p. 439 |
Quantum Computing with Spins | p. 443 |
The quantum inverter | p. 443 |
Can the NAND gate be switched without dissipating energy? | p. 448 |
Universal reversible gate: the Toffoli-Fredkin gate | p. 453 |
Dynamics of the T-F gate | p. 455 |
A-matrix | p. 456 |
Quantum gates | p. 456 |
The strange nature of true quantum gates: the 'square root of NOT' gate | p. 457 |
Qubits | p. 458 |
Superposition states | p. 460 |
Quantum parallelism | p. 461 |
Universal quantum gates | p. 463 |
2-qubit universal quantum gates | p. 464 |
A 2-qubit "spintronic" universal quantum gate | p. 464 |
The silicon quantum computer based on nuclear spins | p. 464 |
Quantum dot-based spintronic model of universal quantum gate | p. 466 |
Conclusion | p. 468 |
Problems | p. 469 |
References | p. 470 |
A Quantum Mechanics Primer | p. 475 |
Blackbody radiation and quantization of electromagnetic energy | p. 475 |
Blackbody radiation | p. 475 |
The concept of the photon | p. 476 |
Wave-particle duality and the De Broglie wavelength | p. 479 |
Postulates of quantum mechanics | p. 482 |
Interpretation of the Heisenberg Uncertainty Principle | p. 488 |
Time evolution of expectation values: the Ehrenfest Theorem | p. 491 |
Some elements of semiconductor physics: particular application in nanostructures | p. 493 |
Density of states: bulk (3-D) to quantum dot (0-D) | p. 493 |
The Rayleigh-Ritz variational procedure | p. 507 |
The transfer matrix formalism | p. 512 |
Linearly independent solutions of the Schrödinger equation | p. 513 |
Concept of Wronskian | p. 514 |
Concept of transfer matrix | p. 515 |
Cascading rule for transfer matrices | p. 515 |
Problems | p. 520 |
References | p. 521 |
Index | p. 523 |
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