Academic Year 2020/2021 - 2° Year - CONDENSED MATTER PHYSICS Curriculum

FIS/01 - 6 CFU - 1° Semester

The basic training aim is to acquire extended and in-depth knowledge concerning properties, preparation and stability of nanostructured materials and transport mechanisms in nanostructures.

By the end of the course the student will be able to understand, within a general scientific and technological framework, the most recent developments concerning nanotechnologies, optical properties of nanostructures, transport processes in nanostructured materials, and applications of nanostructures interdisciplinary fields. The student will be able to apply the scientific method to complex physical situations and will be able to estimate orders of magnitude and the approximations necessary for the description of advanced phenomena related to the physics of nanostructures. The student will acquire independent deepening skills and will be able to find specialized literature for the specific insights. The student will acquire the ability to present a current research topic to an audience of specialists.

Furthermore, with reference to the so-called Dublin Descriptors, this course helps to acquire the following transversal skills:

**Knowledge and understanding abilities**

- Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects
- Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics

**Applying knowledge and understanding ability**

- 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)
- Ability to plan and apply experimental and theoretical procedures to solve problems in academic or applied research, or to improve existing results

**Ability of making judgements**

- Ability to convey own interpretations of physical phenomena, when discussing within a research team

**Communication skills**

- Ability to discuss about advanced physical concepts, both in Italian and in English
- Ability to present one's own research activity or a review topic both to an expert and to an non-expert audience

**Learning skills**

- 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

**Teaching**

Lectures (remote teaching may be adopted, if restriction apply following University’s guidances).

During each lesson, students will always be given time for questions and comments. The lecturer-student interaction will be one of the fundamental element during lectures.

**Prerequisites**

Extensive and in-depth knowledge of: Thermodynamics, Electromagnetism, Quantum Mechanics, Structure of matter, Physics of the solid state, Physics of semiconductors are fundamental.

**Attendance to lectures**

Mandatory

Should the circumstances require full or partial online teaching, appropriate modifications to what is hereby stated may be introduced in order to achieve the main objectives of the course.

**Exams**

Exams may take place online, depending on circumstances.

1) Introduction: Mescoscopic physics and nanotechnology

Trends in nanoelectronics-Characteristic lengths in mesoscopic systems-Quantum coherence- Quantum wells, wires, dots-Density of states and dimensionality-Semiconductor heterostructures.

2) Overview of some concepts of solid state physics

Wave-particle dualism and Heisenberg principle-Schrödinger equation and elementary applications-Fermi-Dirac distribution-Free electron model for a solid-Density function of states-Bloch theorem-Electrons in a crystalline solid-Dynamics of electrons in bands energetic (motion equation, effective mass, gaps) -Lattice vibrations and phonons

3) Overview of some concepts of semiconductor physics.

Energy bands in semiconductors - Intrinsic and extrinsic semiconductors - Concentrations of electrons and semiconductor gaps - Elementary transport properties in semiconductors (Transport in an electric field, mobility; Conduction by diffusion; Continuity equation, life span of carriers and length of diffusion) -Degenerate semiconductors.

4) Physics of low-dimensional semiconductors

Fundamental properties of two-dimensional semiconductor nanostructures-Quantum well-Quantum wires-Quantum dots- Band diagram for quantum wells.

5) Semiconductor nanostructures and heterostructures

MOSFET-Heterojunctions-Quantum well multiple-Heterostructures structures (the concept of heterostructure and the Kronig-Penney model).

6) Transport by electric field in nanostructures

Parallel transport (electronic scattering mechanisms, some experimental observations) -Perpendicular transport (resonant tunneling, electric field effects in heterostructures) -Quantum transport in nanostructures (Quantized conductance; Landauer formula; Landauer-Büttiker formula; Coulomb blockade).

7) Transport by magnetic field in nanostructures and quantum Hall effect

Effect of a magnetic field on a crystal - Low-dimensional systems in a magnetic field - Density of the states of a two-dimensional system in a magnetic field - The Aharonov-Bohm effect - The Shubnikov-de Haas effect - The whole quantum Hall effect ( experimental facts and elementary theory; boundary states, extended states and localized states) -The fractional quantum Hall effect

8) Electronic devices based on nanostructures

MODFET-Bipolar heterojunction transistor-Resonant tunneling transistor- Esaki diode-Single electron transistor.

9) An introduction to graphene and 2D materials: from 3D Van der Waals materials to 2D materials. The example of graphene.

10) The electronic structure of graphene and the electrical and optical properties: transport in graphene. Nanostructured films of graphene. Quantum phenomena in 2D materials (quantum Hall effect and Faraday rotation).

11) Visible and NIR optical properties of 2D materials. Culomb drag and exciton condensation in graphene.

12) Synthesis of 2D materials: Mechanical exfoliation, Chemical vapour deposition, Solution Processing (Liquid phase, chemical routes), Nano-composites.

13) Nanostructured devices of 2D materials: Heterojuctions, 1D-2D hybrid devices and quantum-dots/graphenene. Field-effect transistor with 2D materials.

14) Transparent conducgint films of 2D materials: comparison with TCOs and application for printed and flexible electronics.

1) “Nanotechnology for Microelectronics and Optoelectronics”, J. M. Martinez-Duart, R. J. Martin-Palma, F.

Agullo-Rueda, Elsevier 2006

2) “Quantum Transport-Atom to transistor”, S. Datta, Cambridge University Press 2005

3) “Transport in Nanostructures”, D. K. Ferry, S. M. Goodnick, J. Bird, Cambridge University Press 2009

4) “The Physics of low-dimensional semiconductors-an introduction”, J. H. Davies, Cambridge University

5) “The Physics of graphene”, M. I. Katsnelshon, Cambridge University Press.