Syllabus

Syllabus-PHZ7097, “Unconventional Superconductivity”

    University of Florida Dept. of Physics Fall 2025

Prof. Peter Hirschfeld

• Office hours: W3pm, F3pm, but open if I have time

• Prerequisites: Solid State I and II.

•    Unconventional Superconductivity

Most of the current excitement in the field of superconductivity is centered on materials which exhibit high critical temperatures Tc.  With the exception of high-pressure hydrides, which we will not cover,  in these systems, the interaction leading to the phenomenon of Cooper pairing is thought to be essentially electronic in nature, in contrast to the classic electron-phonon superconductors.  This leads to a natural tendency for pairs to condense in a state of higher orbital angular momentum, e.g. p,d,.., thereby breaking the point group symmetry of the normal state for T>Tc.  I will review the theory of superconductivity briefly,  generalize it to unconventional states, and discuss the properties of several classes of materials in their superconducting state, including cuprates, Fe-based superconductors, and heavy fermion systems.  A substantial amount of time will be devoted to experimental methods and to discussion of classic experiments that were used to deduce the nature of the superconductivity.

• Schedule: 

  • 22 August: Intro to course -- history & phenomenology of superconductors

  • 25 August: Intro continued, phenomenology of SC, restrictions of Pauli principle 

  • 27 August: Electron-phonon interaction & Cooper problem

  • 29 August: BCS Theory 1: BCS Hamiltonian and mean field theory 

  • 1 September: Labor Day Holiday

  • 3 September BCS Theory 2: Gauge invariance & non-BCS pairing possibilities; Bogoliubov transformation

  • 5 September BCS Theory 3: Quasiparticle excitations and Thermodynamics

  • 8 September: BCS Theory 4: Electrodynamics  

  • 10 September: BCS Theory 5: Real space pairing & Effect of Magnetic Field

  • 12 September:  PH TRAVEL (Georgetown U.)

  • 15 September:  BCS Theory 6: Multiband superconductivity

  • 17 September: Ginzburg-Landau Theory 1: Intro

  • 19 September:  Ginzburg-Landau Theory 2: Fluctuations and collective modes

  • 22 September:   Ginzburg-Landau Theory 3: Type I and II superconductors PH TRAVEL (Oxford U.) Prof. Muttalib guest lecture

  • 24 September:  Ginzburg-Landau Theory 4: Vortex lattice & SC length scales PH TRAVEL (Oxford U.) Prof. Muttalib guest lecture

  • 26 September: Ginzburg-Landau Theory 5:  Single vortex 

  • 29 September:   Ginzburg-Landau Theory 6: Josephson Effect 

  •  1 October: Nontrivial pairing  

  • 3 October: Superconductivity in multiple pairing channels 

  • 6 October: Group theory for superconductors 

  • 8 October: Disorder in trivial and nontrivial superconductors 

  • 10 October: Properties of nodal superconductors

  • 13 October:  Symmetry and GL functional of nontrivial SC; mixing of irreps, strain, vortices 

  • 15 October Experimental probes: NMR, spin susceptibility 

  • 17 October: Homecoming

  • 20 October: Detection of low energy excitations (specific heat, thermal conductivity, ultrasound attenuation...)

  • 22 October: Spectroscopies: microwave, Raman, optics, ARPES, STM ...

  • 24 October: Phase-sensitive probes: novel Josephson phenomena, impurities, neutron spin resonance

  • 27 October: Detecting time reversal symmetry breaking

  • 29 October: Pairing by electronic excitations 1: SC from repulsive interactions

  • 31 October: Pairing by electronic excitations 2: Spin fluctuation theory

  • 3 November: Cuprates: overview

  • 5 November: Microscopic models of correlated Fermi systems:  Mott & CT insulators

  • 7 November: Pseudogap & strange metal phase

  • 10 November: SC state: d-wave phenomenology and experiments

  • 12 November: Fe-based SC 1: Electronic structure, correlations, nematic order

  • 14 November: Fe-based SC 2: Multiband SC in 2-band, 5 band models

  • 17 November: Fe-based SC 3: Interband pairs & incipient band pairing

  • 19 November: Fe-based SC 4: Spin fluctuation pairing models 

  • 21 November: Heavy fermion superconductors 

  • 24 November Topological superconductors 1: Superfluid 3He-A

  • 26,28 November: Thanksgiving holiday

  • 1 December: Topological superconductors 2: Kitaev model 

  • 3 December: Topological superconductors 3: 2D chiral p-wave states

•  Lecture notes: course is based on lecture notes developed for a book in preparation, see Notes page for latest version. Condensed versions will be prepared for each class and posted on Notes page by date. 

•     Homework: weekly problem set

• Other recommended texts: "Introduction to Superconductivity", M. Tinkham, Dover 2004; "Theory of Superconductivity", Advanced Books Classics 1999.  “Phenomenological theory of unconventional superconductivity”, M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991); “Introduction to Unconventional Superconductivity”, by V. P. Mineev  and K.V. Samokhin, Gordon and Breach, Amsterdam, 1999;  “Pairing symmetry in cuprate superconductors”,  C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 974 (2000); “The Superconducting Phases of UPt3 “,  R. Joynt and L. Taillefer, Rev. Mod. Phys. 74, 235 (2002). “Superconducting phases of f-electron compounds”, C. Pfleiderer, Rev. Mod. Phys. 81, 1551 (2009);  ``Gap symmetry and structure of Fe-based superconductors", P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin,  Rep.  Prog. Phys. 74,  124508 (2011); “Chiral p-wave order in Sr2RuO4”, C. Kallin, Rep. Prog. Phys. 75, 042501 (2012).