General information:
Code:
UBPJO-253
Name:
Computational methods for nanosystems and correlated electron systems
Profile of education:
Academic (A)
Lecture language:
English
Semester:
Spring
Course homepage:
 
Responsible teacher:
dr inż. Zegrodnik Michał (michal.zegrodnik@agh.edu.pl)
Academic teachers:
dr Biborski Andrzej (biborski@agh.edu.pl)
dr inż. Zegrodnik Michał (michal.zegrodnik@agh.edu.pl)
Module summary

The principal purpose of the module is to provide students with basic knowledge and skills in the modelling of nano-systems.

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Skills
M_U001 Basic skills in the modelling of nano-systems within the framework of non-commercial calculation package(s) such as KWANT. - Project
M_U002 Carrying out calculations on High Performance Cluster by using the queueing system - Activity during classes
M_U003 Application of numerical methods to quantum mechanical problems: optimization, diagonalization, multidimensional integration etc. - Examination
Knowledge
M_W001 Quantum mechanical description of nanosystems: - Schroedinger equation for a particle in quantum well - description of electron transport through nanostructures - electron transport in the presence of magnetic field - the role of electronic interactions - basic knowledge of Second Quantization formalism - Examination
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Skills
M_U001 Basic skills in the modelling of nano-systems within the framework of non-commercial calculation package(s) such as KWANT. - - - - - - - - + - -
M_U002 Carrying out calculations on High Performance Cluster by using the queueing system - - - - - - - - + - -
M_U003 Application of numerical methods to quantum mechanical problems: optimization, diagonalization, multidimensional integration etc. - - - - - - - - + - -
Knowledge
M_W001 Quantum mechanical description of nanosystems: - Schroedinger equation for a particle in quantum well - description of electron transport through nanostructures - electron transport in the presence of magnetic field - the role of electronic interactions - basic knowledge of Second Quantization formalism - - - - - - - - + - -
Module content
Workshops:
Computational methods for nanosystems and correlated electron systems

The classes will cover neccesery theoretical formalism and computer laboratory excercises with the use of high performance cluster. The emphasis will be placed on discussing the principal experimental effects in the field of physics of nanostructures and then carrying out numerical calculations on the computer which reproduce the given effect. Selected problems are to be solved by the students as calculation projects with the use of the KWANT package (https://kwant-project.org/).

The topics covered by the course include: Quantum size effect (two-dimensional electron gas, quantum wells, quantum dots and quantum wires); Description of electron transport through nanostructures (ballistic transport and diffusive transport, Landauer Formula, Tsu-Esaki model, quantum point contact); Electron transport in the presence of magnetic field (Landau levels, quantum Hall effect, quantum rings and Aharonov-Bohm effect); Coulomb blockade and the influence of electronic interactions on the features of the system; Introduction to the description of many electron systems in the representation of second quantization; Selected calculation methods dedicated to correlated electron systems formulated in the representation of second quantization.

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 80 h
Module ECTS credits 3 ECTS
Workshops participation 30 h
Contact hours 5 h
Preparation for classes 15 h
Completion of a project 15 h
Examination or Final test 15 h
Additional information
Method of calculating the final grade:

workshop classes (active participation in the classes, project) – 60% of the final grade , exam – 40% of the final grade.

Prerequisites and additional requirements:

Basic knowledge in quantum mechanics:
- Schroedinger equation, wave function
- quantization of physical quantities (energy, angular momentum etc.)
Basic knowledge in mathematics and algebra:
- integral calculus, differential equations
- lineral algebra: matrix operations, eigenproblem
Basic knowledge in linux operating system

Recommended literature and teaching resources:

1. Yuli V. Nazarov, Yaroslav M. Blenter, “Quantum transport Introduction to Nanoscience”, Cambridge University Press 2009

2. Supriyo Datta, “Quantum Transport: Atom to Transistor”, Cambridge University Press, 2005

3. C.W.J.Beenakker, H.van Houten, “Quantum Transport in Semiconductor Nanostructures”, Solid State Physics, Volume 44, 1991, Pages 1-228

4. C. Kittel, “Wstęp do fizyki ciała stałego”, Warszawa : Państwowe Wydawnictwo Naukowe, 1976.

5. Neil W. Ashcroft, N. David Mermin , “Fizyka ciała stałego”, Warszawa : Państwowe Wydawnictwo Naukowe, 1986

6. J. Spalek, “Wstęp do fizyki materii skondensowanej”, Warszawa: Państwowe Wydawnictwo Naukowe 2015

Scientific publications of module course instructors related to the topic of the module:

1. Dot-ring nanostructure: Rigorous analysis of many-electron effects
A. Biborski, A. P. Kądzielawa, A. Gorczyca-Goraj, E. Zipper, M. M. Maśka and J. Spałek
Scientific Reports 6, 29887 (2016)
tekst: http://dx.doi.org/10.1038/srep29887

2. Interplay between quantum confinement and Fulde–Ferrell–Larkin–Ovchinnikov phase in superconducting nanofilms
P. Wójcik, M. Zegrodnik
Physica E 83, 442-449 (2016)
tekst: http://dx.doi.org/10.1016/j.physe.2016.01.020

3. Fulde-Ferrell state induced by the orbital effect in a superconducting nanowire
P. Wójcik, M. Zegrodnik, J. Spałek
PHYSICAL REVIEW B 91, 224511 (2015)
tekst: http://dx.doi.org/10.1103/PhysRevB.91.224511

4. Orbital effect on the in-plane critical field in free-standing superconducting nanofilms
P. Wójcik, M. Zegrodnik
Physica Status Solidi B 252, 2096-2103 (2015)
tekst: http://dx.doi.org/10.1002/pssb.201552067

Additional information:

None