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  1. Science
  2. Master Degree
  3. Fisica [F1703Q - F1701Q]
  4. Courses
  5. A.A. 2023-2024
  6. 1st year
  1. Quantum Materials
  2. Summary
Insegnamento Course full name
Quantum Materials
Course ID number
2324-1-F1701Q151
Course summary SYLLABUS

Course Syllabus

  • Italiano ‎(it)‎
  • English ‎(en)‎
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Obiettivi

Un materiale quantistico è un materiale le cui proprietà elettroniche o magnetiche sono originate da effetti quantomeccanici non banali, per i quali approssimazioni semi-classiche, che non considerano il carattere completo del sistema, non offrono una descrizione soddisfacente delle peculiarità osservate.

Il corso presenta i principi fisici alla base delle proprietà dei materiali quantistici, consentendo così di comprendere questi materiali in dettaglio. Verranno trattati in dettaglio diversi sistemi di materiali: dai superconduttori, il prototipo di materiale quantistico, all'effetto hall quantistico intero e agli isolanti topologici, che mostrano una stretta connessione delle loro proprietà elettroniche con invarianti derivati dalla topologia. Per ciascuna classe di materiali verranno brevemente discusse alcune applicazioni tecnologiche.

Obiettivi
• Conoscenza dettagliata dei concetti e degli approcci di base nella ricerca sui materiali quantistici.
• Comprendere i fenomeni emergenti nei materiali quantistici
• Comprendere gli effetti della topologia e delle simmetrie sulle proprietà elettroniche quantistiche dei materiali
• Acquisizione di capacità comunicative verbali e scritte in concetti avanzati di fisica quantistica.

Contenuti sintetici

• Introduzione: Materiali quantistici per tecnologie quantistiche.
• Teoria dei Superconduttori di Ginzburg Landau e BCS
• Effetto Hall quantistico intero
• Topologia e fase Berry
• Invarianti topologici e proprietà fisiche

Programma esteso

1) Introduzione:
• i materiali quantistici come strumento per le moderne tecnologie quantistiche.
• Panoramica dei prerequisiti del corso, dei contenuti delle lezioni, dei libri di testo/letteratura e dei metodi di valutazione.
2) Superconduttori:
• Interazione elettrone-fonone e coppie di Cooper
• Teoria di Ginzburg-Landau
• Teoria BCS della superconduttività
• Effetto Josephson e SQUIDS
• Q-Bit quantistici superconduttori
3) Effetto Hall quantistico intero:
• Livelli Landau
• Teoria di Laughlin dell'effetto Hall quantistico
• Perché 2D, disordine e localizzazione sono importanti
• Teoria della percolazione semiclassica
• Stati del bordo IQHE
4) Topologia:
• Fase di Berry, connessione e curvatura
• Fase di Berry per gli elettroni nei cristalli
• Applicazioni della fase di Berry: effetto Aharonov-Bohm, polarizzazione dei cristalli, elettroni cristallini in campo elettrico uniforme
• Numeri Chern
• Simmetrie di inversione temporale e di inversione: simmetria spezzata in Honeycomb Lattice
• IQHE senza livelli Landau
• Invarianti topologiche
• Superconduttori topologici

Prerequisiti

Concetti di meccanica quantistica e fisica dello stato solido.

Modalità didattica

Lezioni frontali ed esercitazioni alla lavagna e/o slides.

Materiale didattico

Le diapositive saranno messe a disposizione degli studenti attraverso la presente piattaforma e-learning.
Testi:
• Girvin, S., & Yang, K. (2019). Modern Condensed Matter Physics. Cambridge University Press. doi:10.1017/9781316480649
• Efthimios Kaxiras & John D. Joannopoulos (2019) Quantum Theory of Materials, Cambridge University Press. doi 10.1017/9781139030809:
• A.Bernevig with T. L. Hughes, Topological Insulators and Topological Superconductors, Princeton University Press (2013).
• Raffaele Resta, Geometry and Topology in Electronic Structure Theory, Notes, http://www-dft.ts.infn.it/~resta/gtse/draft.pdf
• P. G. De Gennes (1999) Superconductivity of Metals and Alloys, Westview Press, ISBN 0-7382-0101-4
• János K. Asbóth, László Oroszlány, András Pályi (2016). A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions. Springer

Articoli scientifici
Diversi argomenti del corso sono anche ben presentati in articoli scientifici, come ad esempio:
• Von Klitzing K (1986) The quantized Hall effect, Reviews of Modern Physics 58, 519
• R. B. Laughlin (1981) Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632
• Feliciano Giustino et al (2020) The 2021 quantum materials roadmap. J. Phys. Mater. 3 042006.
• B. Keimer & J. E. Moore (2017) The physics of quantum materials. Nature Physics 13, 1045–1055.
• Hasan MZ, Kane CL (2010) Colloquium: Topological insulators. Reviews of Modern Physics, 82(4):3045–3067.
• Haldane FDM (1988) Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly", Phys Rev. Lett. 61, 2015

Periodo di erogazione dell'insegnamento

Secondo semetre

Modalità di verifica del profitto e valutazione

Le conoscenze degli studenti saranno valutate attraverso una prova orale incentrata sugli argomenti trattati durante il corso.

Orario di ricevimento

Dal lunedì al venerdì a qualsiasi ora lavorativa (previo appuntamento con il docente via email).

Sustainable Development Goals

IMPRESE, INNOVAZIONE E INFRASTRUTTURE
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Aims

A quantum material is one whose electronic or magnetic properties are best described as having a nontrivial quantum mechanical origin, in other words materials where semi-classical approximations that do not consider the full character of the system are unable to capture the observed peculiarities.

The course presents the physical principles underlying the quantum materials properties, thus permitting to understand these materials from the basis. Several materials systems will be treated in detail: from superconductors, the prototypical example of a quantum material, to integer quantum hall effect and topological insulators, which show a strict connection of their electronic properties with topology derived invariants. For each class of materials we will briefly discuss some technological applications.

Learning Outcomes
• Detailed knowledge of the basic concepts and approaches in quantum materials research.
• Understanding emergent phenomena in quantum materials
• Understanding the effects of topology and symmetries on the quantum electronic properties of materials
• Acquisition of verbal and written communication skills in advanced concepts of quantum physics.

Contents

• Introduction: Quantum materials for quantum technologies.
• Ginzburg Landau theory of Superconductors and BCS
• Integer Quantum Hall Effect
• Topology and Berry phase
• Topological invariants and physical properties

Detailed program

1) Introduction:
• quantum materials as a tool for modern quantum technologies.
• Overview of course pre-requisite, lecture contents, textbooks/literature, and assessment methods.
2) Superconductors
• Electron-phonon interaction & Cooper pairs
• Ginzburg-Landau Theory
• BCS Theory of superconductivity
• Josephson effect & SQUIDS
• Superconducting quantum bits
3) Integer Quantum Hall Effect:
• Landau Levels
• Laughlin theory of the Quantum Hall Effect
• Why 2D, disorder and localization are important
• Semiclassical percolation theory
• IQHE edge states
4) Topology:
• Berry phase, Connection and curvature
• Berry’s Phase for Electrons in Crystals
• Applications of Berry’s Phase: Aharonov–Bohm Effect, Polarization of Crystals, Crystal Electrons in Uniform Electric Field
• Chern Numbers
• Time-reversal and inversion symmetries: Broken Symmetry in Honeycomb Lattice
• IQHE without Landau Levels
• Topological Invariants
• Topological superconductivity

Prerequisites

Quantum mechanics and solid-state physics concepts.

Teaching form

Frontal lectures and exercise sessions using blackboard and/or slides.

Textbook and teaching resource

Slides will be made available to the students through the present e-learning platform.
Textbooks:
• Girvin, S., & Yang, K. (2019). Modern Condensed Matter Physics. Cambridge University Press. doi:10.1017/9781316480649
• Efthimios Kaxiras & John D. Joannopoulos (2019) Quantum Theory of Materials, Cambridge University Press. doi 10.1017/9781139030809:
• A.Bernevig with T. L. Hughes, Topological Insulators and Topological Superconductors, Princeton University Press (2013).
• Raffaele Resta, Geometry and Topology in Electronic Structure Theory, Notes, http://www-dft.ts.infn.it/~resta/gtse/draft.pdf
• P. G. De Gennes (1999) Superconductivity of Metals and Alloys, Westview Press, ISBN 0-7382-0101-4
• János K. Asbóth, László Oroszlány, András Pályi (2016). A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions. Springer

Scientific articles:
Different topics of the course are also well presented in scientific articles, such as:

• Von Klitzing K (1986) The quantized Hall effect, Reviews of Modern Physics 58, 519
• R. B. Laughlin (1981) Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632
• Feliciano Giustino et al (2020) The 2021 quantum materials roadmap. J. Phys. Mater. 3 042006.
• B. Keimer & J. E. Moore (2017) The physics of quantum materials. Nature Physics 13, 1045–1055.
• Hasan MZ, Kane CL (2010) Colloquium: Topological insulators. Reviews of Modern Physics, 82(4):3045–3067.
• Haldane FDM (1988) Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly", Phys Rev. Lett. 61, 2015

Semester

Second semester

Assessment method

Students’ knowledge will be evaluated through an oral exam focusing on the topics discussed during the course.

Office hours

From Monday to Friday at any working hour (an appointment should be arranged with the teacher by email).

Sustainable Development Goals

INDUSTRY, INNOVATION AND INFRASTRUCTURE
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Key information

Field of research
FIS/03
ECTS
6
Term
Second semester
Activity type
Mandatory to be chosen
Course Length (Hours)
42
Degree Course Type
2-year Master Degreee
Language
English

Staff

    Teacher

  • DC
    Davide Campi

Students' opinion

View previous A.Y. opinion

Bibliography

Find the books for this course in the Library

Enrolment methods

Manual enrolments
Self enrolment (Student)

Sustainable Development Goals

INDUSTRY, INNOVATION AND INFRASTRUCTURE - Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation
INDUSTRY, INNOVATION AND INFRASTRUCTURE

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