Solid State Physics

Integration of concepts and insights on different physical properties already learned in previous courses and use them as an essential part of the development of physics of solids.

Knowing the properties of crystalline solids in terms of their constituent-atoms (red) and electrons, their state of motion or interactions between them.

To promote the interest and the student's ability to catalog and model the phenomena underlying the properties of crystalline solids, and understand the main approaches (adiabatic, harmonic, independent particles, mean field, etc.) used in this discipline.

Understand and estimate the order of magnitude of the main properties of crystalline solids and related quantities.

Enhance the student's perception of physically different systems but show analogies, allowing the application of solutions already known to new phenomena.

Encourage and train students in the use of bibliographical sources for obtaining documentation of the subjects studied or data needed to solve problems.

Develop the skills of analysis and synthesis of the student, as well as oral and written communication.

LEARNING RESULTS. The student will demonstrate:
- To have knowledge of the properties of crystalline solids in terms of their constituents - atoms (lattice) and electrons - of their state of motion and of the interactions between them.
- Know the main models developed to explain the phenomena underlying the properties of crystalline solids, as well as a good understanding of the main approaches used in this discipline.
- Have the ability to apply the knowledge acquired about models, approaches, etc. to the solution of issues related to the physics of crystalline solids.
- Have knowledge and ability to make estimates in view of the main properties of crystalline solids and associated magnitudes and ease of handling of the aforementioned orders of magnitude.
- Have the ability to search and manage bibliography and sources of information related to the physics of solids.
- Be able to analyze and synthesize, as well as oral and written communication of studies, results, etc.

1. CRYSTAL STRUCTURES. Periodic distribution of atoms. Basic types of lattices. Examples of structures. Holes in structures. Defects in Crystals: vacancies, dislocations.
2. THE RECIPROCAL LATTICE AND X-RAY DIFFRACTION. Systems of lattice plains: Miller indices. Reciprocal lattice. Wave diffraction by crystals. Brillouin zones. The geometrical structure factor of a basis.
3. COHESIVE ENERGY OF CRYSTALS. Crystals of noble gases. Ionic crystals. Covalent crystals. Cohesion in metals.
4. DYNAMICS OF LATTICES. Vibrations in monoatomic and polyatomic crystals. Quantization of vibrations: phonons. Vibrations in ionic crystals. Inelastic dispersion of phonons.
5. THERMAL PROPERTIES OF LATTICES. Density of normal modes. Lattice heat capacity. Thermal expansion. Lattice thermal conductivity.
6. FERMI GAS OF FREE ELECTRONS. Fundamental state. Heat capacity of the free electron gas. Electrical and thermal conductivity. Wiedemann-Franz law. Hall effect and magnetoresistance. Optical properties.
7. ENERGY BANDS. Schrödinger equation in a periodic potential: Bloch states. Models of nearly free electrons and tight-binding electrons. Other methods for calculating band structure. Fermi surfaces. Metals and insulators.
8. SEMICLASSICAL DYNAMICS OF BLOCH ELECTRONS. Equations of motion. Effective mass. Motion in an electric field. Motion in a magnetic field.
9. SEMICONDUCTORS. Carrier Statistics. Doping of semiconductors. Influence of impurities on the carriers concentration. Conductivity and mobility. Inhomogeneous semiconductors: p-n junction.
10. MAGNETISM. Diamagnetism: Langevin equation. Paramagnetism: Curie law. Exchange interaction. Ferromagnetic order. Ferromagnetic domains: hysteresis. Antiferromagnetic and ferrimagnetic order.
11. SUPERCONDUCTIVITY. Meissner effect and persistent currents. Critical magnetic fields. BCS and Ginzburg-Landau theories. Magnetic Flux Quantization. Josephson effect. High-temperature superconductors.

Basic:

1. C. Kittel.
Introducción a la Física del Estado Sólido, Ed. Reverté (3ª edición española 1993).
2. N.W. Ashcroft and N.D. Mermin.
Solid State Physics, Ed. Holt, Rinehart and Winston, Philadelphia 1975.
3. J. Maza, J. Mosqueira y J.A. Veira, Física del Estado Sólido, Manuais Universitarios (USC, 2008).
4. J. Maza, J. Mosqueira y J.A. Veira.
Física del Estado Sólido. Ejercicios resueltos, Manuais Universitarios (USC, 2009).
5. L. Mihály and M.C. Martin.
Solid State Physics. Problems and solutions, Ed. Wiley-VCH (2ª edición 2009).


Complementary:

- P.V. Pavlov y A.F. Jojlov, Física del Estado Sólido, Ed. MIR, 1987.
- H.M. Rosenberg, El estado sólido, Ed. Alianza Universidad, 1991.
- H.E. Hall, Física del Estado Sólido, Ed. Limusa, 1978.
- H. Ibach and H. Lüth, Solid-State Physics, Ed. Springer-Verlag, 1991.
- G. Burns, Solid State Physics, Ed. Academic Press, 1985.
- J. S. Blakemore, Solid State Physics, Cambridge University Press, London 1985.
- J. M. Ziman, Principios de la Teoría de Sólidos, Ed. Selecciones Científicas 1969.
- H.J. Goldsmid, Problemas de Física del Estado Sólido, Ed. Reverté 1975.
- J. Piqueras y J.M. Rojo
Problemas de Introducción a la Física del Estado Sólido, Ed.Alhambra, 1980.

Online resources:
- Notes and presentations of the subject in the virtual campus

BASIC:
- That the students have demonstrated to possess and understand knowledge in an area of study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply knowledge coming from the vanguard of their field of study.
- That students know how to apply their knowledge to their work or vocation in a professional manner and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
- That students have the ability to gather and interpret relevant data (usually within their area of study) to make judgments that include a reflection on relevant issues of a social, scientific or ethical nature.

GENERAL:
- Possess and understand the most important concepts, methods and results of the different branches of Physics, with a historical perspective of their development.
- To have the capacity to gather and interpret data, information and relevant results, obtain conclusions and issue reasoned reports on scientific, technological or other problems that require the use of knowledge of Physics.
- Apply both acquired theoretical and practical knowledge and the ability to analyze and abstract in the definition and approach of problems and in the search for their solutions both in academic and professional contexts.

TRANSVERSAL:
- Acquire analysis and synthesis capacity.
- Have capacity for organization and planning.
- Develop critical reasoning.

SPECIFIC:
- Have a good understanding of the most important physical theories, locating in their logical and mathematical structure, their experimental support and the physical phenomenon that can be described through them.
- Be able to clearly handle orders of magnitude and make appropriate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.
- Be able to perform the essentials of a process or situation and establish a work model of it, as well as perform the required approaches in order to reduce the problem to a manageable level. He will demonstrate critical thinking to build physical models.
- Understand and master the use of mathematical and numerical methods most commonly used in Physics
- Be able to manage, search and use bibliography, as well as any source of relevant information and apply it to research projects and technical development projects

The core content of the course will be addressed in the expositive lectures. Each topic will begin with a brief introduction of their content, positioning in the global context of the subject, and in general in the ones of the Degree in Physics, and will conclude with a summary highlighting the most important aspects. The general outline of the lectures will be:
- Definition / Description of the system or physical property under study indicating the relevant observables, their orders of magnitude, and so on.
- Assumptions, approximations, simplifications, etc.. to be used in developing the subject in order to elaborate a mathematical model.
- Comparison of results followed from the models with the experimental ones and discussion of the limitations of such models, possible extensions, etc.
There are published by the USC a course manual (reference No. 3) with the contents of each course topics presented following the above scheme which make not necessary that students take full note of teacher explanations. In fact, most of the mathematical developments related to the contents of the subject are omitted in the expositive lectures because they can be followed in that manual. In addition, the material used for the presentations will be available for students.

The interactive classes will address the explanation, both conceptual and development aspects, of the exercises provided to students. There is also a workbook with solved problems (reference No. 4) published by the USC, so these classes are not merely devoted to the resolution of exercises (which the student can see in that manual) but will be centered on the assumptions, approximations, etc. underlying the learned models, on the use and familiarization with orders of magnitude, and so on. The workbook also includes a collection of exercises (mostly taken from exams of other courses of similar content to this) accompanied by their solution (but not their development) with the purpose that students can follow a continuous process of self-evaluation. This activity will allow both teacher and students to check the level of understanding and familiarization with the worked topics. In addition, in these sessions will be periodically proposed exercises or questions of relatively short answer (there are formulated for during a normal class) to be realized by students, in writing, individually and that will serve as material for their continuous evaluation.

The tutoring sessions will be addressed to the control of the students comprehension or familiarization on the contents of the course as well as in the resolution of doubts and in a personalized guide in learning the subject.

Attendance to lectures and tutorial sessions are voluntary, although assistance will be taken into account for the final rating.

The evaluation system consists of two complementary parts:

a) continuous assessment, which will represent 40% of the final grade, and which will consist of the delivery and / or realization of exercises in class time.

b) evaluation through a face-to-face final exam that will be carried out on the official dates established by the center

The student's grade at the first opportunity will correspond to the maximum between the grade of the final exam and the average of the grades obtained in the continuous evaluation (40% of the grade) and the final exam (60% of the grade). The same rule applies to the second opportunity, for which continuous evaluation is maintained.

In cases of fraudulent performance of exercises or tests, the collection in the Standard for evaluating the academic performance of students and reviewing grades will apply.

Hours
-Expository classes: 32
-Interactive classes: 24
-Customized tutorials: 4


-Personal work: 90, divided as follows
Individual or group autonomous study: 50
Writing exercises, conclusions or other works: 5
Recommended readings, library activities or similar: 10
Preparation of oral presentations, debates or similar: 20
Attendance at talks, exhibitions and other recommended activities: 5

For a proper comprehension of the subject it is recommended to have attended the courses of Electromagnetism, Thermodynamics and Kinetic Theory, Statistical Physics and Quantum Physics.
The availability of textbooks well suited to the contents of the subject can facilitate the student individual work. The workbook edited by USC contains the explained solutions for the problems included in the Bulletin provided to students. It is however recommended that students try to solve the exercises yourself, using what they learn in lectures and use the manual only in the most difficult cases or for the verification of results. It is also recommended that in addition to the possible use of this workbook students use other texts on the subject, in particular References 1 and 2.