Electronic structure of solids

This course deals with the fundamental concepts to understand the electronic structure of solids from the point of view of single-particle models (band-theory type). The study will focus on the simplest models that allow to analyse the electronic properties and its consequences in the physical properties observed in different types of materials of scientific and technological interest.

The specific aims of the course will be:

- To handle the concepts of band structure, representation of Brillouin zones, density of states.
- Being able to give a simple image of the electronic structure of a material given its crystalline structure and its composition by means of a tight-binding model.
- To understand the different approximations that are necessary for the study by means of analytical or computational models of the electronic structure properties of different crystalline solids.
- Being able to understand a current scientific article that describes the electronic structure of a solid-state material.


Expected learning outcome of the course:

In this course the student will acquire and practise a series of basic competencies, desirable in any basic degree, and specific competences in the field of the electronic structure of solids and its possible consequences in the technology.

Amgon the specific competencies we highlight:

- Knowing and handling the key concepts in Electronic Structure, such as density of states, reciprocal space, energy bands.
- Resolving simple problems related with these fundamental concepts. Understanding the concept of hopping to nearest neighbours and its relationship with the band structure.
- Understanding the basic electronic structure of some examples of real solid-state materials.
- Understanding the relatiosnship between structure and electronic structure.
- Understanding the results of an electronic structure calculation obtained through either a tight-binding model or a DFT calculation.
- Understanding the different limits where the electronic structure of a material can be analyzed: the ionic limit, the covalent limit and the electon gas (metallic limit).

1. Basic concepts

- Atomic Physics. The periodic table.
- Diatomic molecules. Electronegativity.
- Bond order. Bond energy.
- Linear chain. Rings. Infinite systems.
- Density of states: total and local. Moments theorem.
- Cells in 2D and 3D. Bands. Bond order. Bond energy.
- Types of bonds in solids.
- Energy gaps and metallicity.

2. The electron gas. Theory of metals.

- Fermi-Dirac distribution.
- Density of states.
- Specific heat.
- Electrical conductivity.
- Thermal conductivity.
- Nearly-free electrons.
- Screening.
- Exchange. Hartree-Fock theory.
- Structures.

3. Covalent bond.

- Structures. Directional bonding.
- Tetrahedral bond. Hybrid orbitals.
- Tight-binding approximation. Selection of the hopping parameters.
- Relevant questions applied to real materials.

4. The ionic bond.

- Electronegativity. Origin of the gap.
- Madelung theory.
- Crystal field theory.
- Structures and materials.

5. Calculation schemes.

- Density functional theory.
- Exchange-correlation functional.
- LAPW method.
- Defining "ab initio": from the structure to the electronic structure.
- Self-consistency. Codes.
- Applications. Results and importance.

6. Experimental techniques.

- Spectroscopy: ARPES, XAS, PES.
- Measuring the Fermi surface: Shubnikov - de Haas, de Haas - van Alphen.

7. Beyond band-structure theory.

- Mott insulators.
- Hubbard model.
- Anderson localization.
- Polarons.

8. Current problems in Electronic Structure Theory.

- Journal clubs.
- Topology.
- Correlated systems.
- Graphene.

Basic bibliography:

A.P. Sutton, Electronic Structure of Materials, Clarendon Press. Oxford (1993). (A70 373).

Complementary bibliography:

R.G. Parr, W. Yang, Density Functional Theory, Clarendon Press. Oxford University Press (1989). (A20 106).
N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College (1976). (3 A70 7).
W.A. Harrison, Electronic Structure and the Properties of Solids: the Physics of the Chemical Bond, New York, Dover (1989). (A70 255).
W.A. Harrison, Elementary Electronic Structure, Singapore: World Scientific (1999). (3 A70 69).
R. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press (2004). (A70 447).
S.H. Simon, "The Oxford Solid State Basics", Oxford University Press (2013). (3 A70 116).
David J. Griffiths, "Introduction to Quantum Mechanics", 2nd Edition, Prentice Hall (2005). (3 A03 148).
G. Grosso, G. Parravicini, "Solid State Physics", 2nd Edition, Oxford University Press (2014). (3 A70 55).

BASIC

CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context

CB7 - Knowledge about how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study

CB8 - Ability to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments

CB9 - Ability to communicate conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way

CB10 - Learning skills allowing to continue studying in a way that will be largely self-directed or autonomous.

GENERAL

CG01 - Acquire the ability to perform team research work.

CG02 - Be able to analyze and synthesize.

CG03 - Acquire the ability to write texts, articles or scientific reports according to publication standards.

CG04 - Become familiar with the different modalities used to disseminate results and disseminate knowledge in scientific meetings.

CG05 - Apply knowledge to solve complex problems.

TRANSVERSAL

CT01 - Ability to interpret texts, documentation, reports and academic articles in English, scientific language par excellence.

CT02 - Develop the capacity to make responsible decisions in complex and / or responsible situations.

SPECIFIC


CE08 - Acquire an in-depth knowledge of the structure of matter in the low energy regime and its characterization ..

CE09 - Master the set of tools necessary to analyze the different states of matter.

The teaching activities will be of several types: theory classes, seminars (both on the board and using the available computational resources), problem solving classes. The participation of the student will be essential in the seminars and problem soving classes. Likewise, students will have office hours at their disposal for the individual discussion of all the doubts that arise on the content of the course.

The attendance to the classes will be mandatory and the evaluation will be continuous. This will be carried out through reviews of the recent literature on different aspects of Electronic Structure theory or through computational personal works (either tight-binding model or DFT-based calculations).


There will be also an examination in the date scheduled by the deanship for those students that do not pass the continuous evaluation or want to increase their mark.

The fraudulent performance of any exercise or test required in the
evaluation of a subject will imply the qualification of failure in the
corresponding call, regardless of the disciplinary process that may be
followed against the offending student. It is considered fraudulent,
among others, the performance of plagiarized work or work obtained from
sources accessible to the public without reworking or reinterpretation
and without citation of the authors and sources.

Distribution of hours
Theory Seminar. Practical Office hours Personal work and other act. Total work of student
17 8 5 1 44 75

A basic knowledge of Solid State Physics and Quantum Mechanics will be required to follow the lectures.

In case of fraudulent behaviour, the University Regulations for the evaluation of the academic performance of students will be applied:
Article 16. Fraudulent performance of exercises or tests.
The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failure in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among others, the performance of plagiarized work or work obtained from sources accessible to the public without reworking or reinterpretation and without citation of the authors and sources.