Teaching plan for the course unit



Close imatge de maquetació




General information


Course unit name: Solid State Simulation Techniques

Course unit code: 574649

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 3

Single program: S



Estimated learning time

Total number of hours 75


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Lecture with practical component

Face-to-face and online



Supervised project


Independent learning




Learning objectives


Referring to knowledge

  1. To develop a broad and unified perspective of the simulation techniques and their range of applicability for solid-state devices. 

  2. To be aware of the intricacies associated to the study of quantum systems beyond steady-state regime. 

  3. To become acquainted with the basic operation of ab-initio and quantum transport software.



Teaching blocks


1. Energy levels and bands


  1. Many-body problem and Born-Oppenheimer approximation. Density Functional Theory. 

  2.  Tight-binding, k·p method and effective mass equation.

  3. Energy bands: Bulk silicon, silicon quantum wire, and graphene band structures. 

2. Steady state quantum transport


  1. Open quantum systems: Lindblad and stochastic Schrödinger equations. Environment, decoherence and collisions.

  2. Landauer approach. Density matrix. Wigner distribution. Non-equilibrium Green’s functions. Atomistic simulations. 

  3. Quantum dots, resonant tunnelling and Coulomb blockade. 


3. Beyond steady state quantum transport


  1. Strong, weak and multi-time measurements. Time-correlations. 

  2. Landauer-Büttiker approach. Time-dependent density functional theory. Bohmian trajectories.

  3. Transients, high-frequency and quantum noise



Teaching methods and general organization


  1. Lectures where theoretical contents of the subject are presented.

  2. Simulation-based learning.



Official assessment of learning outcomes


  1. Homework and simulation assignments.



Reading and study resources

Consulteu la disponibilitat a CERCABIB


J.M. Thijssen, “Computational Physics”, Cambridge University Press, 2nd ed., Cambridge UK 2007.  EnllaƧ

Richard M. Martin, “Electronic Structure”, Cambridge University Press, 1st ed., Cambridge UK, 2004.  EnllaƧ

Versió electrņnica, 2004  EnllaƧ

Breuer, Heinz-Peter, and Francesco Petruccione. “The theory of open quantum systems.” Oxford University Press on Demand, 2002.   EnllaƧ

Asher Peres, "Quantum Theory: Concepts and Methods", Kluwer, 1st ed., New York, 1995  EnllaƧ

Versió electrņnica, 2002  EnllaƧ

Datta, Supriyo. “Quantum transport: atom to transistor”. Cambridge university press, 2005.   EnllaƧ

Ferry, David K. “An Introduction to Quantum Transport in Semiconductors”. CRC Press, 2017.

Waser, Rainer. “Nanoelectronics and information technology”. Weinheim, Germany: Wiley-VCH Verlag GmbH, 2012.  EnllaƧ


J. C. Slater, G. F. Koster (1954). "Simplified LCAO method for the Periodic Potential Problem". Physical Review. 94 (6): 1498–1524. 



Evan O. Kane (1957). "Band Structure of Indium Antimonide". Journal of Physics and Chemistry of Solids. 1: 249. 



Chao-Xing Liu, Xiao-Liang Qi, HaiJun Zhang, Xi Dai, Zhong Fang and Shou-Cheng Zhang (2010). "Model Hamiltonian for topological insulators". Physical Review B. 82: 045122. 



P. A. Khomyakov, G. Brocks, V. Karpan, M. Zwierzycki, and P. J. Kelly (2005)  “Conductance calculations for quantum wires and interfaces: Mode matching and Green’s functions” Phys. Rev. B 72, 035450



K. Jacobs and D. A. Steck (2006), “A straightforward introduction to continuous quantum measurement” Contemporary Physics,  47 (5) 2006, 279 – 303 



B. Pellegrini  (1986). "Electric charge motion, induced current, energy balance, and noise". Physical Review B.  34(8): 5921–5924



R. Landauer(1998)  “The noise is the signal”  Nature, 392, 658–659.