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Rita MAGRI
Professore Associato
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Fisica
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Insegnamento: Quantum Physics of Matter
Physics - Fisica (Offerta formativa 2022)
Obiettivi formativi
At the end of the course the student will possess a deep knowledge of its contents and will be able to autonomously apply the learned concepts to each specific physical contest. In detail:
- will be able to connect the behavior of the different materials to their electronic structure
- will be able to interpret the spectroscopic data in terms of the microscopic characteristics of the material.
-will be able to understand what experimental technique is useful to study which physical property
-will know the theory underlying the interaction of matter with electromagnetic field
- will be able to apply quantum mechanics to derive the expression of the response functions, such as the dielectric function and the conductivity, in the linear response regime.
- will know the physics of the quasiparticles due to the matter-electromagnetic interaction such as polaritons and plasmons and how to measure them.
- will know to link the characteristics of the response functions to the properties of the materials.
-will know how models can be used to derive the expression for the electron energy loss functions.
-will know what are the surface modes of the elctromagnetic field and their properties.
To know more about the "Objectives of the course" please give a look at the section "Risultati di apprendimento attesi"
Prerequisiti
Students are expected to be familiar with basic atomic and solid state physics. A good knowledge of a basic course in quantum mechanics is also necessary.
Programma del corso
The course is taught in the first semester of the first year for a total of 48 hours (6 CFU), The list of contents of the course is just indicative and changes may occur depending on the requests and needs of the students.
Review on the optical measurements and on the electron spectroscopies (4 hours)
Normal modes of the electromagnetic field in the vacuum and in a medium. Response functions. Local and not local approximations.Longitudinal and transverse modes. Dispersion relations. Complex wave vector. (4 hours)
Optical Coefficients. Normal and anomalous dispersion. Metamaterials. Optical coefficients of Insulators, Metals and Semiconductors (4 hours)
Transverse and longitudinal dielectric functions. Longitudinal Response. Thomas-Fermi static screening dielectric function. Response function for electron energy loss in trasmission. Survey of EELS spectra (5 hours)
Dielectric function of the Drude Model and its generalization (3 hours)
The dielectric function in the Lorentz model and associated optical properties. Ionic polarization and polariton dispersion relation (4 hours)
Kramers-Kronig Relations. Surface modes of the electromagnetic field. Dispersion Relation of the surface plasmons. Energy lost by an electron in reflection geometry. Surface Loss Function. EELS spectra. Fuchs-Kliever modes. (6 hours)
Kubo-Greenwood Expression for conductivity. Quantum mechanical description of polarization. (4 hours)
Induced density current and dielectric function derivation via density matrix operator. (4 hours)
Longitudinal dielectric function. Interband and intraband contributions to the dielectric function. K.P method (2 hours)
Mass tensor. Direct band gap materials. Absorption coefficient. Joint Density of States. Absorption Onset for direct Interband Transitions (4 hours)
Excitons. Solution of the SchroedingerEquation. Exciton radius. Excitonic levels. (2 hours)
Static screening . Lindhard dielectric function (2 hours)
Response functions for linear isotropic media, propagation equation. Electromagnetic field modes in a medium. Transverse and longitudinal electromagnetic field modes. Optical coefficients. Optical spectra of materials. Energy conservation in dispersive media. Longitudinal and transverse dielectric functions. Energy loss spectra. Drude Lorentz model. Kramers-Kronig relations. Surface modes of the electromagnetic field. Dispersion and dissipation in linear media. Kubo-Greenwood formula. Theory of absorption between band states. Joint density of states. Direct and indirect transitions. Excitonic states. Electromagnetic field quantization. Hamiltonian of the electromagnetic field interacting with many electron systems. General theory of absorption and emission.
The student's degree of learning will be evaluated by means of a written test consisting in the solving of exercises and a oral exam.
Metodi didattici
Frontal lectures ordinarily(*) through slide projection and writing on the blackboard. The lessons will be about the contents listed in "Contenuti del corso". Questions and comments from the students are highly appreciated. The presence in the classroon is not mandatory but strongly recommended. The course is in English. Copy of the slides and notes are deposited on the moodle.unimore.it platform. The students are invited to subscribe on the platform.
. The working students who cannot participate in the class must notify the professor of the situation so as to receive the necessary information and copy of the lecture notes.
(*) because of the COVID19 pandemic the lectures may take place on-line in streaming or they may be registered and made available on moodle.unimore.it
Testi di riferimento
- F. Wooten, "Optical Properties of Solids", Academic Press
- F. Bassani e U. Grassano: "Fisica dello Stato Solido", Boringhieri.
- Copy of the teacher slides on Dolly
Verifica dell'apprendimento
The evaluation of the student preparation and learning of the course contents will be made through an oral exam comprising of a set of questions on the topics of the course as listed in "Contenuti del corso" and a power point presentation on a topic of choice of the student, where some aspects or applications are treated in depth. The duration of the exam will be approximately of 40 minutes (25 minute of power point presentation plus 15 minutes of answering questions). The mark will be assigned at the end of the exam.
The oral test aims at verifying the degree of knowledge and understanding of the concepts, the ability to apply what has been learnt, and the ability to express it correctly and properly.
The exams may take place on-line depending on the evolution of the COVID19 emergency.
Risultati attesi
Knowledge and understanding
The course focuses on the theoretical methods for the description of the optical properties of condensed matter phases. At the end of the course the student is expected to:
- have correctly understood the link between theoretical and experimental methodologies used to optically characterize the materials.
- to correctly interpret the results of the experimental measurements in terms of material properties.
- to understand critically the limits of the theoretical models presented in the course.
- have a good knowledge of the description of the interaction between electromagnetic waves and matter and the effects such interaction has on the material properties.
- have a good knowledge of the description of the interaction between electrons and a material and the effects provoked in the material.
- to derive response functions and optical coefficients through application of quantum-mechanics principles.
Applying knowledge and understanding
At the end of the course the students are expected to be able to analyze and interpret optical and particle energy loss experiments on the basis of the fundamental properties of the materials.
Autonomy of judgment
Students are expected to acquire the ability to evaluate critically the outcomes of basic experiments of condensed matter physics. They are also required to assess critically the limits of validity of the hypotheses used in the various theoretical treatments.
Communication skills
Students should acquire the capability of discussing the topics presented in the course exhaustively and using the appropriate terminology.
Learning skills
Students will be able to learn easily the developments resulting from the theory and experiments of condensed matter physics.