Supervisors’ Foreword
Abstract
Publications Related to this thesis Build-up of vibron-mediated electronic correlations in molecular electronics Rémi Avriller, Rubén Seoane Souto, Álvaro Martín Rodero and Alfredo Levy Yeyati. Physical Review B, 99 (12), 121403 (2019).Transient dynamics in interacting nanojunctions within self-consistent perturbation theory Rubén Seoane Souto, Rémi Avriller, Alfredo Levy Yeyati and Álvaro Martín Rodero. New J. Phys. 20, 083039 (2018).Quench dynamics in superconducting nanojunctions: metastability an dynamical Yang-Lee zeros Rubén Seoane Souto, Álvaro Martín Rodero and Alfredo Levy Yeyati. Physical Review B, 96 (16), 165444 (2017).Analysis of universality in transient dynamics of coherent electronic transport Rubén Seoane Souto, Álvaro Martín Rodero and Alfredo Levy Yeyati. Fortschritte der Physik, 65 1600062 (2017).Andreev bound states formation and quasiparticle trapping in quench dynamics revealed by time-dependent counting statistics Rubén Seoane Souto, Álvaro Martín Rodero and Alfredo Levy Yeyati. Physical Review Letters, 117 (26), 267701 (2016).Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime Rubén Seoane Souto, Rémi Avriller, Rosa Carmina Monreal, Álvaro Martín Rodero and Alfredo Levy Yeyati. Physical Review B, 92 (12), 125435 (2015).Dressed tunneling approximation for electronic transport through molecular transistors Rubén Seoane Souto, Alfredo Levy Yeyati, Álvaro Martín Rodero and Rosa Carmina Monreal. Physical Review B, 88 (8), 085412 (2014).
Acknowledgements
Contents
Acronyms
1 General Introduction
1.1 Theory of the Quantum Transport
1.2 Superconductivity at the Nanoscale
1.3 Interactions at the Nanoscale
1.4 Time Dependent Transport
1.4.1 Dynamics of Interacting Nanojunctions
1.5 Current Fluctuations
1.5.1 Full Counting Statistics
1.5.2 Analogy to Equilibrium Statistical Mechanics: Yang–Lee Zeros
1.6 Outline
References
2 Theoretical Framework in the Stationary Regime
2.1 Impurity Level Hamiltonian
2.2 Green Function Formalism
2.2.1 Equilibrium Green Functions
2.2.2 Time-Dependent Green Functions
2.2.3 Non-equilibrium Green Functions
2.2.4 Transport Properties
2.2.5 Interaction Picture
2.3 Electron-Electron Interaction: Anderson Model
2.3.1 Mean Field Approximation
2.3.2 Effects Beyond the Mean Field
2.4 Electron-Phonon Interaction: The Spinless Anderson–Holstein Model
2.4.1 Second Order Perturbation Expansion
2.4.2 Self-consistent Approximations
2.4.3 Polaron-Like Approximations
2.5 Superconducting Nanojunctions
2.5.1 AC-Josephson Effect
2.6 Full Counting Statistics
2.6.1 Non-interacting System
2.6.2 Interaction Effects
2.6.3 Factorial Cumulants
2.6.4 Dynamical Yang–Lee Zeros
References
Part I Transient Dynamics in Normal Nanojunctions
3 Transient Dynamics in Non-interacting Junctions
3.1 Introduction
3.2 Mean Transport Properties
3.3 Full Counting Statistics
3.3.1 Discretized Dyson Equation and the Determinant Formula
3.4 Universal Relation Between Cumulants and Zeros
3.5 Analysis of the Short Time Universality
3.5.1 Single Electrode Junction
3.5.2 Two Electrodes Junction: Coherent Effects
3.5.3 Bidirectional Transport
3.6 Conclusions
References
4 Polaron Effects in Quench Dynamics
4.1 Introduction
4.2 Basic Theoretical Formulation
4.2.1 Single Pole Approximation
4.2.2 Short Time Tunnel Limit
4.3 Evolution of System Population and Current
4.4 Transient Statistics and Waiting Time Distribution
4.5 Conductance and Fano Factor Dynamics at V=nω0
4.6 Conclusions
References
5 Self-consistent Approximations
5.1 Introduction
5.2 Self-consistent Procedure
5.3 Electron–Electron Interaction: The Anderson Model
5.3.1 Hartree–Fock Approximation
5.3.2 Effects of Correlation Beyond Mean-Field
5.4 Electron–Phonon Interaction: Spinless Anderson–Holstein Model
5.4.1 Hartree Approximation
5.4.2 Effects of Correlation Beyond Hartree Approximation
5.5 Electron–Electron and Electron–Phonon Interactions
5.6 Calculation of the Steady State Properties
5.7 Conclusions
References
Part II Transient Dynamics in Superconducting Nanojunctions
6 Quench Dynamics in Superconducting Nanojunctions
6.1 Introduction
6.2 Model and Formalism
6.2.1 Single Pole Approximation
6.3 Quench Dynamics
6.4 AC-Josephson Effect
6.5 Voltage Pulse Initialization
6.6 Conclusions
References
7 Counting Statistics in Superconducting Nanojunctions
7.1 Introduction
7.2 Formalism
7.2.1 Coarse Grained Statistics
7.3 Quench Dynamics
7.3.1 Yang–Lee Zeros and Phase Coexistence
7.4 Finite Bias Voltage Dynamics
7.4.1 Dynamical Yang–Lee Zeros
7.5 Voltage Pulse Initialization
7.6 Coupling to a Bosonic Mode
7.6.1 Model and Formalism
7.6.2 Single Particle Properties
7.6.3 Counting Statistics
7.7 Conclusions
References
Part III General Conclusions and Outlook
8 General Conclusions and Outlook
8.1 Normal Nanojunctions
8.2 Superconducting Nanojunctions
References
Appendix A Numerical Renormalization Group
A.1 Algorithm
A.1.1 Logarithmic Discretization
A.1.2 Recursive Diagonalization
A.1.3 Spectral Properties
A.1.4 Discarded States
A.1.5 Averaging Between Different Band Discretizations
A.2 Holstein Model
Appendix B Toeplitz Matrix Theory
B.1 Basic Mathematical Theory
B.1.1 Block Toeplitz Matrices
B.2 Transport Properties
Appendix C Inverse Free Boson Propagator
Appendix D Interpretation in Terms of Rate Equations
Appendix E Bidirectional Poisson Distribution