Academic Year 2022/2023 - Teacher: FELICE TORRISI

Expected Learning Outcomes

The fundamental training objective consists in the acquisition of in-depth knowledge relating to the properties, preparation and stability of two-dimensional materials (semimetals, semiconductors and metals) and the transport mechanisms in disordered low-dimensional materials.

At the end of the course the student will be able to understand and frame in a general context the most recent developments relating to synthesis, optical and transport properties in two-dimensional materials (giant Faraday rotation, anomalous Berry phase, Klein tunneling), focusing on the example of graphene and transition metal dichalcogenides. In a second part, the course will focus on the study of transport in disordered and granular two-dimensional materials, addressing the theory of localisation (localised and extended states, Anderson localization, finite temperatures and inelastic scattering effects), transport between localized states at finite temperatures and transport by hopping (VRH, NNH, ES-VRH), strong and weak localization concepts for disordered metallic materials and for low-dimensional structures.

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

Course Structure


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.


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

Attendance to lectures


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 may take place online, depending on circumstances.

Required Prerequisites

Solid understanding of: thermodynamics, Electromagnetism, Quantum mechanics, Condensed matter Physics and Solid State Physics

Attendance of Lessons

Normally, lecture attendance is mandatory (further details on the Regolamento Didattico del Corso di Studi).

Detailed Course Content

1) Introduction to graphene and two-dimensional materials: from 3D materials with Van der Waals bonds to two-dimensional materials. The example of graphene.
2) The electronic structure and the electrical and optical properties: transport of charge carriers in graphene. Graphene nanostructured films. Quantum phenomena originating in two-dimensional structures (quantum Hall effect and Faraday rotation).
3) Optical properties of 2D materials in the visible and near infrared.
4) Synthesis of two-dimensional materials: Mechanical exfoliation, Chemical vapor deposition, Solution Processing (Liquid phase, chemical routes), Nano-composites.
5) Nanostructured devices: junctions of 2D materials. Hybrid junctions and 1D-2D hybrid devices or quantum-dots / graphene. Field-effect transistor with 2D materials.
6) Transparent and conductive thin films: Comparison with TCO, applications in flexible and printed electronics.
7) Transport in disordered and granular materials.
8) Concepts of strong and weak localization for disordered metal materials and for low-dimensional structures.
9) Theory of localization (localized and extended states, Anderson localization, finite temperatures and inelastic scattering effects).
10) Transport between localized states at finite temperatures and transport via hopping (VRH, NNH, ES-VRH).

Textbook Information

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.

Course Planning

 SubjectsText References
11) Introduzione a graphene e materiali bidimensionali: dai materiali 3D con legami di Van der Waals a materiali bidimensionali. L’esempio del grafene.3,4
22) La struttura elettonica e le proprieta' elettriche e ottiche: trasporto di portatori in grafene. Film nanostrutturati di grafene. Effetti quantistici dovuti alla struttura bidimensionale (quantum Hall effect and Faraday rotation).2,4
33) Proprieta' ottiche dei materiali 2D nel visibile e nel vicino infrarosso.4
44) Sintesi di materiali bidimensionali: Mechanical exfoliation, Chemical vapour deposition, Solution Processing (Liquid phase, chemical routes), Nano-compositi.4,6
55) Dispositivi nanostrutturati: giunzioni di materiali 2D. Giunzioni ibride e disporitivi ibridi 1D-2D o quantum-dots/grafene. Field-effect transistor con materiali 2D.1,2,3,4
66) Film sottili trasparenti e conduttori: Confronto con TCO, applicazioni in elettronica flessibile e stampata.
77) Trasporto in materiali disordinati e granulari.2,5
88) Concetti di localizzazione forte e debole per materiali metallici disordinati e per strutture a bassa dimensionalita’.3,4,5
99) Teoria della localizzazione (stati localizzati ed estesi, localizzazione di Anderson, finite temperatures ed effetti di scattering inelastico).3,5
1010) Trasporto tra stati localizzati a temperature finite e trasporto mediante hopping (VRH, NNH, ES-VRH).1,2,5


Learning Assessment Procedures


The exam consists of a presentation / essay developed by the student on a topic relating to the course program and agreed with the lecturer. 
Taking a start from the presentation / essay developed by the student, questions will follow on the remaining part of the program. The evaluation will take into account the level of depth of the topic, the knowledge of the basic topics, the property of language, the clarity of presentation, the ability to identify applications, including interdisciplinary ones. The typical duration of the oral exam ranges from 30 to 45 minutes. Verification of learning can also be carried out electronically, should the conditions require it. EXAMINATION APPEALS For the oral exam there are 2 exam sessions in the first exam session period, 2 exam sessions in the second exam session period and 2 exam sessions in the third exam session period. There are also 2 sessions reserved for students who are out of course and laggards (paragraphs 5 and 5 bis of the university teaching regulations) during the suspension of teaching activities, generally in the period April / May or November / December. There are no further exams beyond those approved by the teaching secretariat.Consult the Exam Calendar at the website:

Examples of frequently asked questions and / or exercises


Some topics typically questioned during the oral exam are the following:

    - Density of electronic states in zero-, one-dimensional, two-dimensional nanostructures
    - Techniques of production and synthesis of two-dimensional materials
    - Klein Tunneling, Faraday rotation
    - Optical properties of two-dimensional materials
    - Landauer and Kubo formulae with application to the case of graphene.
    - Quantization of conductance
    - Quantization of the magnetic field flux
    - Quantum Hall effect in graphene
    - Metal-graphene junction
    - Graphene Field effect transistor
    - Applications of graphene for transparent electrodes and conductors
    - Graphene-based printed electronic devices