The course aims at providing the theoretical basis necessary to understand and describe the physics of condensed matter. The student will learn how to apply the laws of quantum mechanics to study the functioning mechanism of solid-state quantum devices, with applications in the area of quantum sensing, quantum communication and quantum computing. During the first part of the course, the basics of solid-state physics are presented, while the second part deals with the physics of low-dimensional nanostructures such as quantum wells, multi-quantum wells, quantum wires and quantum dots. Finally, the course addresses quantum phenomena such as superconductivity, the Hall effect and others, that are currently exploited for the realization of qubits and quantum devices.

The students are expected to learn how to apply the principles of quantum physics to study, describe and predict the physical properties of condensed matter both at the micro and nanoscale. Main anticipated achievements are: - Knowledge of solid-state structure - Knowledge of electronic and optical properties of solids and nanostructures - In-depth knowledge of quantum charge conduction in nanostructures - Knowledge of the effects related to quantum coherence and ballistic regime of electrons in nanostructures - Knowledge of superconductivity - Ability to evaluate the effect of confinements on the electronic motion in nanostructures - Ability to evaluate band structures in low-dimensional systems - Ability to apply quantum condensed matter physics for the realization of solid-state qubits and quantum sensors - Ability to use physics-based models for the prediction of materials and nanostructures properties.

Classical Physics. Basic knowledge of quantum mechanics.

- Condensed matter structure: crystalline and amorphous materials. Direct and reciprocal lattice. Point defects in crystals (F-centers). (6 hours) - Electrons in solids: the Sommerfeld model, Bloch theorem, bands and Fermi surfaces. Semiconductors and doping. (9 hours) - Phonons in condensed matter. Electron-phonon interaction. (6 hours) - 2-dimensional electron gas (2DEG). Quantum devices based on 2DEG. Quantum Transport in two dimensions. Quantum Hall Effects and Quantum Spin Hall Effect. (10.5 hours) - Quantum wells and multi-quantum wells, quantum wires and quantum dots, with application as qbits. Quantized conductance, tunnelling transport, the Aharonov-Bohm effect, and the Coulomb blockade effect. (12 hours) - Topological insulators. (3 hours) - Introduction single photon sources and quantum sensors. (3 hours) - Superconductivity: the macroscopic quantum state (MQM, macroscopic quantum model), flux quantization, Josephson effect and junctions, SQUID RF and DC (10.5 hours)

The course consists of theoretical lectures and class practices. The latter include simple problem-solving activities and small computer program coding, with strict connections to theoretical lectures.

H. Ibach and Hans Lüth, Solid-State Physics: An Introduction to Principles of Materials Science, Springer 2009. T. Ihn, Semiconductor Nanostructures: Quantum States and Electronic Transport, Oxford Unix. Press, 2012. J. Davies, The physics of low-dimensional semiconductors, Cambridge Univ. Press, 2012. M. Tinkham, Introduction to superconductivity, McGraw-Hill, 2° edition, 1996. T. P. Orlando and K. A. Delin, Foundations of applied superconductivity, Addison-Wesley, 1991. Lectures notes produced by the teacher will be available on-line at the course web page.

Slides; Dispense; Libro di testo;

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... The Quantum Condensed Matter Physics exam consists of a written test aiming at addressing the degree of understanding achieved by the students on the subjects explained during the lectures (see expected learning outcome above). No supporting material is allowed during the exam. The exam aims at assessing the comprehension of the quantum condensed matter and nanophysics phenomema and to discuss the application of these concepts to quantum devices. When writing the exam sheet the student has to show that he/she is able to rigorously discuss and present the physical models introduced during the lectures, highlighting the approximations behind each model. The written test includes multiple-answer questions, statements (to be assessed as true or false) and two open questions covering all the course’s subjects. The maximum mark of questions/statements is 12/30, that of open questions is 18/30. The total allotted time is 90 min. The written test is passed with a score of at least 18/30. The final score will be obtained by averaging with the score obtained for the Electrons Devices part of the course.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.