Foreword |
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vii | |
Preface |
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ix | |
Acknowledgments |
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xiii | |
1 Introduction |
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1 | (26) |
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1.1 What is quantum transport? |
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1 | (7) |
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8 | (5) |
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1.3 Disorder and coherent potential |
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13 | (5) |
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1.4 NECPA-DFT theory and NanoDsim package |
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18 | (3) |
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1.5 A few words about this monograph |
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21 | (6) |
2 The NECPA theory |
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27 | (40) |
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2.1 Two-probe Hamiltonian |
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27 | (3) |
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30 | (2) |
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32 | (3) |
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35 | (4) |
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39 | (4) |
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43 | (5) |
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2.7 Surface Green's function |
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48 | (1) |
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49 | (7) |
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2.9 Current conservation and dephasing effect |
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56 | (5) |
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61 | (6) |
3 The NECPA-LMTO method |
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67 | (46) |
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67 | (2) |
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69 | (3) |
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72 | (1) |
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73 | (1) |
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74 | (2) |
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3.6 LMTO Green's function |
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76 | (3) |
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79 | (2) |
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81 | (5) |
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3.9 Periodicity and Fourier transform |
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86 | (2) |
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3.10 NECPA-LMTO formalism |
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88 | (3) |
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3.11 Self-consistent calculation |
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91 | (12) |
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91 | (2) |
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3.11.2 Step-1 calculate structure constant |
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93 | (1) |
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3.11.3 Step-2 calculate self-energy |
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94 | (1) |
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3.11.4 Step-3 make an initial guess |
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95 | (1) |
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3.11.5 Step-4 calculate atomic orbital |
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96 | (1) |
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3.11.6 Step-5 calculate potential parameter |
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97 | (1) |
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3.11.7 Step-6 solve the NECPA equations |
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98 | (2) |
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3.11.8 Step-7 calculate energy moment |
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100 | (1) |
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3.11.9 Step-8 calculate charge density |
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100 | (1) |
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3.11.10 Step-9 calculate charge and dipole |
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101 | (1) |
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3.11.11 Step-10 calculate atomic potential with DFT |
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102 | (1) |
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3.11.12 Step-11 calculate Madelung potential |
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103 | (1) |
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3.11.13 Step-12 calculate total potential |
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103 | (1) |
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3.12 Post-analysis calculation |
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103 | (5) |
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103 | (1) |
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3.12.2 Transmission coefficient |
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104 | (2) |
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3.12.3 Transmission variation |
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106 | (1) |
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107 | (1) |
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3.12.5 CPA band structure |
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107 | (1) |
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3.13 Miscellaneous issues |
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108 | (5) |
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3.13.1 Spin degree of freedom |
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109 | (1) |
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109 | (1) |
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3.13.3 Linearization center |
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110 | (1) |
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3.13.4 Scalar relativistic equation |
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111 | (1) |
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3.13.5 Wigner-Seitz radius |
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111 | (2) |
4 NanoDsim: the package design |
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113 | (34) |
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113 | (5) |
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4.2 MATLAB: vectorization technique |
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118 | (2) |
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4.3 MATLAB: hybrid programming |
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120 | (5) |
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4.4 MATLAB: object oriented programming |
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125 | (7) |
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4.5 NanoDsim: overall design |
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132 | (2) |
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4.6 NanoDsim: dsim-solvers |
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134 | (4) |
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4.7 NanoDsim: dsim-calculators |
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138 | (1) |
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4.8 NanoDsim: dsim-classes |
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139 | (2) |
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4.9 NanoDsim: supporting libraries |
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141 | (2) |
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4.10 NanoDsim: implementation and debugging |
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143 | (4) |
5 NanoDsim: bulk systems |
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147 | (42) |
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148 | (6) |
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148 | (2) |
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150 | (1) |
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151 | (2) |
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153 | (1) |
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154 | (2) |
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156 | (3) |
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159 | (6) |
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165 | (6) |
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5.6 Complex contour integral |
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171 | (5) |
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176 | (5) |
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181 | (2) |
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5.9 Bulk calculator: band structure |
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183 | (2) |
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5.10 Bulk calculator: density of states |
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185 | (4) |
6 NanoDsim: two-probe systems |
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189 | (58) |
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189 | (4) |
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6.1.1 @class_necpaTwoProbe |
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190 | (2) |
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192 | (1) |
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193 | (2) |
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195 | (11) |
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6.3.1 2d Madelung potential |
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195 | (5) |
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6.3.2 Surface Madelung potential |
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200 | (4) |
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204 | (2) |
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6.4 Surface Green's function |
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206 | (10) |
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6.4.1 Analytically solvable case |
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206 | (3) |
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209 | (3) |
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212 | (2) |
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214 | (2) |
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216 | (3) |
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6.6 k-integral in the Brillouin zone |
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219 | (13) |
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220 | (1) |
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6.6.2 Symmetric k-sampling |
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221 | (5) |
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6.6.3 Time-reversal symmetry |
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226 | (6) |
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232 | (5) |
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6.8 Fermi level alignment |
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237 | (2) |
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6.9 Two-probe calculator: transmission coefficient |
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239 | (2) |
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6.10 Verification of the implementation |
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241 | (6) |
7 NanoDsim: optimization and parallelization |
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247 | (36) |
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247 | (3) |
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250 | (3) |
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253 | (8) |
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253 | (1) |
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254 | (3) |
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257 | (3) |
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260 | (1) |
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7.4 Principal layer algorithm |
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261 | (8) |
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7.4.1 Retarded Green's function |
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261 | (4) |
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7.4.2 Lesser Green's function |
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265 | (1) |
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7.4.3 Transmission coefficient |
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266 | (1) |
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267 | (2) |
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7.4.5 Implementation details |
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269 | (1) |
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7.5 MATLAB interface to MPI |
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269 | (3) |
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272 | (2) |
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274 | (2) |
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276 | (2) |
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278 | (5) |
8 Kaleidoscope of the physics in disordered systems |
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283 | (36) |
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8.1 Simple examples: bulk Cu, Fe, Co, Ni |
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283 | (3) |
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8.2 CPA vs supercell: Cu/Co alloy |
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286 | (2) |
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8.3 Si with uniaxial strain |
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288 | (4) |
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8.4 Band offset of GaAs/Al Ga1-x As heterojunctions |
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292 | (2) |
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8.5 NECPA vs supercell: Cu/Co interface |
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294 | (4) |
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8.6 Si transistors with localized doping |
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298 | (4) |
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8.7 Graphene transistors with disorder scattering |
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302 | (5) |
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8.8 Fe/MgO/Fe tunnel junctions |
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307 | (4) |
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8.9 Cu films with surface scattering |
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311 | (4) |
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315 | (4) |
Appendix |
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319 | |
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319 | (1) |
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A.2 Phase diagram of the toy model |
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320 | (4) |
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A.3 Classical transport vs quantum transport |
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324 | (10) |
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A.3.1 Drift-Diffusion model |
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325 | (2) |
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A.3.2 Effective-Mass model |
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327 | (6) |
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333 | (1) |
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A.4 Lehmann spectrum of NEGF |
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334 | (5) |
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A.5 Low concentration approximation |
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339 | (6) |
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A.5.1 Multiple scattering theory |
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339 | (3) |
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A.5.2 Transmission coefficient and transmission variation |
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342 | (3) |
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A.6 Scattering states approach |
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345 | (10) |
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345 | (2) |
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347 | (3) |
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A.6.3 Transmission coefficient |
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350 | (2) |
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A.6.4 Further discussion: group velocity |
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352 | (1) |
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A.6.5 Further discussion: number of modes |
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352 | (1) |
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A.6.6 Further discussion: numerical issues |
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353 | (2) |
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355 | (1) |
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A.7 Density matrix in clean bulk systems |
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355 | (2) |
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A.8 Connection to the CPA-NVC theory |
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357 | (1) |
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A.9 Explicit expressions of XC-functionals |
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358 | (5) |
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A.9.1 LDA: Perdew and Zunger (1981) |
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359 | (1) |
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A.9.2 GGA: Perdew, Burke, and Ernzerhof (1996) |
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360 | (1) |
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A.9.3 MBJ: Tran and Blaha (2009) |
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361 | (2) |
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363 | (1) |
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A.10 Complex-valued and real-valued spherical harmonics |
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363 | (2) |
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365 | (1) |
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A.12 Eigensolutions of TST and TSC matrices |
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366 | (2) |
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A.13 Proof of the Wronskian identity |
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368 | (1) |
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369 | (1) |
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A.15 Transmission coefficient in the LMTO method |
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370 | (3) |
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A.16 Specular scattering vs diffusive scattering |
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373 | (3) |
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A.17 Fill the space with atomic spheres |
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376 | (4) |
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A.17.1 Regular structures |
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376 | (2) |
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A.17.2 Irregular structures |
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378 | (2) |
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A.18 Symmetric k-sampling |
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380 | (5) |
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385 | (1) |
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386 | (3) |
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A.21 Modified Fermi pole summation technique |
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389 | (2) |
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A.22 Field effect transistor with gate terminals |
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391 | (2) |
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A.23 Algorithms for solving the Poisson equation |
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393 | (9) |
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A.23.1 Numerical discretization |
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393 | (2) |
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A.23.2 Algorithms in 1d case |
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395 | (3) |
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A.23.3 Algorithms in 2d and 3d cases |
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398 | (1) |
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A.23.4 Nonorthogonal Poisson box |
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399 | (1) |
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A.23.5 Nonlinear Poisson equation |
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400 | (2) |
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A.24 Locality in nonequilibrium |
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402 | (1) |
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403 | (4) |
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A.26 Preconditioner designed for quantum transport |
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407 | (4) |
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A.27 Content of the affiliated CD |
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411 | |
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411 | (1) |
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A.27.2 ResearchCode package |
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411 | |