# CONDENSED MATTER PHYSICS

## Learning outcomes of the course unit

Condensed Matter Physics is the branch of physics that studies the microscopic physical properties of matter. In particular, it deals with the condensed phases, observable when the number of constituents of the system is large and interactions are strong. The most familiar examples of condensed phases are the solid phase and the liquid one, due to the electromagnetic interactions and bonds between atoms. Other more 'exotic' condensed phases are the superfluid phase, the Bose-Einstein condensate observed in some atomic systems at very low temperatures, the superconducting phase of conduction electrons in certain materials, and the ferromagnetic and antiferromagnetic phases of spins of certain atomic lattices.

The course aims at providing a general view of Condensed Matter Physics with focus on crystal systems. Structural and thermal properties of solids, electronic states and the main effects due to electron-electron interactions, namely magnetism and superconductivity, are described.

## Prerequisites

Statistical Mechanics

Basic Quantum Mechanics

Atomic And Molecular Physics

## Course contents summary

- Crystal Structure and Crystal Binding

- Crystal Dynamics and Thermal Properties

- Energy Bands

- Semiconductors

- Metals

- Insulators

- Surface and Interface Physics

- Magnetism

- Superconductivity

## Course contents

Crystalline Structures and interatomic forces.

Periodic atomic structures, classification of crystal lattices, diffraction techniques for crystallography: X-rays, electrons, neutrons, Bragg condition and Laue equation, reciprocal lattice and Brillouin zones, classification of Bravais lattices, Van der Waals forces, ionic bonding, covalent bonding, metallic bonding, hydrogen bonding, elastic constants.

Atomic dynamics in crystals and thermal properties.

Lattice vibrations in crystals, quantization of lattice vibrations, and phonon density of states, inelastic scattering by phonons and measurement of the dispersion curves, thermal properties: heat capacity, anharmonic effects, thermal conductivity.

Electronic states in solids

Beyond the free electron model, electronic levels in a periodic potential, Bloch theorem, electrons in a weak periodic potential, "tight-binding” model , classification of crystalline solids: metals, insulators and semiconductors.

Semiconductors

electrons and holes, donor and acceptor states, transport properties (Hall effect, cyclotron resonance), thermoelectric effects, optical properties.

Metals

energy bands in metals and Fermi surface, methods for the experimental determination of the Fermi surface

Insulators

dielectrics, ferroelectrics, soft-modes and structural transitions, optical processes, excitons.

Interfaces and low-dimensional systems

Surface electronic states, quantum Hall effect, pn junctions, heterostructures, semiconductor devices: LEDs, lasers, electronic structure of low dimensional systems.

Magnetism in solids

diamagnetism and paramagnetism, ferromagnetic order, antiferromagnetic, and ferrimagnetic, spin waves, magnetic domains, resonance techniques: EPR, NMR, NQR, Mössbauer, magnetic resonance imaging.

Superconductivity

phenomenology of superconductors, superconducting type I and II, the theory of superconuttività: London equations and BCS theory, Josephson effect.

## Recommended readings

- Introduction to Solid State Physics, 8th Edition - C. Kittel (2005 - John Wiley & Son)[Italian Edition: Editore: CEA 2800]

- Solid State Physics , - N.W. Ashcroft, N.D. Mermin (1987 - Mc Graw Hill)

- Solid State Physics - H. Ibach, H. Lüth (2003 - Springer

- Oxford Master Series in Condensed Matter Physics (Vols. 1 – 5),(Oxford University Press - ultima ristampa 2010)

## Teaching methods

Lectures (about 60% of the total time)

Class exercises (about 40% of the total time) carried out with the teacher supervision

## Assessment methods and criteria

During the semester three in-class exams will be given concerning:

Structural and thermal properties of solids

Electronic states of solids

Magnetism and superconductivity

Students with an average positive result (≥ 18/30) can have the final exam approved without further tests.

Alternatively the students have to pass a final exam (written + oral).