Index
Introduction . . . . 1
Description of the physical system . . . . 5
Green’s functions . . . 20
Building the Green’s function of a complex system . . . . 40
Analysis of possible implementation strategies . . . 62
Choice of the algorithm and performance review . . . 92
Conclusion . . . . 115
Bibliography . . . . 117
1. Description of the physical system . . . . 5
1.1 Introduction . . . . 5
1.2 Mesoscopic systems . . . . 5
1.3 Single band envelope function and effective mass approximation 10 1.4 Condcutance . . . 15
1.5 Shot noise . . . 17
1.6 Current mapping . . . 18
2. Green’s functions . . . 20
2.1 Introduction . . . 20
2.2 Mathematical interpretation of Green’s function . . . 20
2.3 An interpretation for the Green’s function in solid state physics 26 2.4 Tight binding model . . . 31
2.5 Application of Green’s function to the problem to be simulated 34 3. Building the Green’s function of a complex system . . . . 40
3.1 Introduction . . . 40
3.2 The recursive Green’s function technique . . . 40
3.2.1 Coupling two slices togheter . . . 43
3.2.2 Green’s function for a finite slice and semiinfinite chain . . . 48
3.3 Probe iteration and the Metalidis-Bruno approach . . . 56
4. Analysis of possible implementation strategies . . . 62
4.1 Introduction . . . 62
4.2 Decreasing the size of the system . . . 62
4.3 Simple Algorithm (SA) . . . 63
4.4 Block Algorithm (BA) . . . 67
4.5 Memory Algorithm (MA) . . . 71
4.5.1 Storage needs of the Memory Algorithm . . . 77
4.6 Metalidis-Bruno Algorithm (MBA) . . . 80
4.6.1 Metalidis-Bruno Algorithm by Column (MBAC) . . . 81
4.6.2 Metalidis-Bruno Algorithm by Slice (MBAS) . . . 84
4.7 Exploiting repetitions . . . 88
5. Choice of the algorithm and performance review . . . 92
5.1 Introduction . . . 92
5.2 Comparison of the possible algorithms . . . 92
5.3 Structure of the program . . . 98
5.4 Final considerations and output examples . . . . 100
Conclusion . . . . 115
