Academic Year 2021/2022 - 1° Year - Curriculum CONDENSED MATTER PHYSICS
Teaching Staff: Francesco M. D. PELLEGRINO
Credit Value: 6
Scientific field: FIS/02 - Theoretical physics, mathematical models and methods
Taught classes: 42 hours
Term / Semester:

Learning Objectives

The course aims to provide the student with the fundamentals of the physics of mesoscopic systems with reference to experiments and theory, with a particular focus on graphene and topological systems.

Knowledge and understanding. Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects. Adequate knowledge of advanced mathematical and numerical tools, currently used in both basic and applied research. Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics.

Applying knowledge and understanding. Ability to identify the essential elements in a phenomenon, in terms of orders of magnitude and approximation level, and being able to perform the required approximations. Ability to use analogy as a tool to apply known solutions to new problems (problem-solving).

Making judgments. Ability to convey own interpretations of physical phenomena, when discussing within a research team. Developing one's own sense of responsibility, through the choice of optional courses and of the final project.

Communication skills. Ability to discuss advanced physical concepts, both in Italian and in English.

Learning skills. Ability to acquire adequate tools for the continuous update of one's knowledge. Ability to access to specialized literature both in the specific field of one's expertise and in closely related fields. Ability to exploit databases and bibliographical and scientific resources to extract information and suggestions to better frame and develop one's study and research activity. Ability to acquire, through individual study, knowledge in new scientific fields.

Course Structure

Frontal lectures.+

Learning verification is an oral exam that consists of a discussion of three (3) distinct topics of the course contents, of which the first is chosen by the student.*

+Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.
*Learning assessment may also be carried out online, should the conditions require it.

Detailed Course Content

Semiclassical theory: Semiclassical Boltzmann equation, Relaxation time approximation, Elastic scattering, and diffusive limit, Inelastic scattering.
Scattering approach to quantum transport: Scattering region, leads, and reservoirs, Scattering matrix, Conductance from scattering, Resonant tunneling, Primer on the localization.
Fluctuations and correlations: Definition and main characteristics of noise, Scattering approach to noise, Boltzmann-Langevin approach, Primer on the effect of noise on quantum dynamics
Single-electron effects: Charging energy, Tunnel Hamiltonian and tunneling rates, Master equation, Cotunnelling.
Graphene: Electron dispersion relation in monolayer graphene, electrical doping, massive graphene, Landau levels in monolayer graphene.
Topological materials one and two dimensions: SSH model, Berry phase and polarization, Chern number, Edge states in the half-BHZ model (QWZ model). Edge states in the 2D Dirac equation, 2-dimensional time-reversal invariant topological insulators, Absence of backscattering, Electrical conduction of edge states.
Quantum dots: Electronic states in quantum dots, Weakly interacting limit, Weakly transmitting limit, and Coulomb blockade.

Textbook Information

[1] T. T. Heikkilä, The Physics of Nanoelectronics: Transport and Fluctuation Phenomena at Low Temperatures, Oxford Master Series in Physics (2013).

[2] M. I. Katsnelson, Graphene: Carbon in Two Dimensions, Cambridge University Press (2009).

[3] J.K. Asbóth, L. Oroszlány, A. Pályi, A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions, Springer (2016).

[4] S. M. Girvin, K. Yang, Modern Condensed Matter Physics, Cambridge University Press (2019).