## Lecture Topics and Background References

**Bernd Büchner ****Title: **Fe based Superconductors: Materials, phase diagrams, and spectroscopy **Plan of the lectures**:

Lecture I

Overview on Materials and General Phase Diagrams of Fe based Superconductors

(in particular, differences between BaFe2As2, LaOFeAS families will be shown and discussed)

Lecture II

Low energy probes of the physical properties of Fe based superconductors

(including a short introduction of NMR and transport measurements); focus will lie on anomalous normal state properties, such as the temperature dependence of the magnetic susceptibility and evidence for “polarons”;

Lecture III

Electron spectroscopy on Fe based superconductors

(including a short introduction to ARPES and its use in superconductors); main focus will be the difference between band structure calculations and the real electronic structure seen in experiments, evidence for electronic correlations will be highlighted;

Lecture IV

Aspects of STM on Fe based superconductors

(including a short introduction to STM and quasi particle interference); main focus will be studies of the “unconventional” pnictide superconductor LiFeAs;

Lecture V

Experimental Studies of Nematic Order in Fe based SC

After a short survey on the findings in BaFe2Fe2 type systems the ongoing discussion on the properties of FeSe will presented and discussed;

**Background references:**

[1] Principles of Magnetic Resonance, (C.P. Slichter)

[2] Photoelectron spectroscopy (S. Hüfner),

[3] Scanning Probe Microscopy and Spectroscopy (R. Wiesendanger)

[4] More on the ArXIV

[5] Iron-Based Superconductivity, Peter D. Johnson, Gungyong Xu, Wei-Guo Yin (Editors), Springer 2015

[6] D.C. Johnston, Adv. Phys.,59, 803 (2010);

[7] J-P Paglione and R.L. Greene, Nature Phys.6,18645 (2010);

[8] G. R. Stewart Rev. Mod. Phys. 83, 1589 (2011);

[9] H.H. Wen and S. Li, Annu. Rev. Condens. Matter Phys.,2, 121 (2011)

[10] J. Hoffman, Rep. Prog. Phys., 74, 124513 (2011)

[11] A. Chubukov and P. Hirschfeld (arxiv 2015)

**Massimo Capone & Luca de' Medici****Title:** Modeling many-body physics in Fe-superconductors and other multi-orbital materials with the Slave-Spin mean-field: Mott and Hund's physics**Plan of the lectures:**

Lecture I

Interactions and correlations. Single-particle vs many-body physics. Chemistry of correlated materials. The Hubbard model.[1][2]

Lecture II

Introduction to the Slave-spin method. Auxiliary variables. Mean-field decoupling [3][4]

Lecture III

The Mott-Hubbard transition. Strongly Correlated Fermi-liquids [5][6][7]

Lecture IV

Multi-orbital Hubbard models. Hund’s coupling. Mott transition in a multi-orbital context. Mott vs Hund physics.[8]

Lecture V

Slave-spin mean-field for realistic correlated band structures. Mott and Hund’s physics in Fe-based pnictides. Comparison with experiments. [4][9]**Background references:**

[1] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)

[2] A. Georges, “Strongly Correlated Electron Materials: Dynamical Mean‐Field Theory and Electronic Structure”, AIP Conf. Proc. 715, 3 (2004)

[3] L. de’ Medici, S. Biermann and A. Georges, Phys. Rev. B 72, 205124 (2005), S. R. Hassan and L. de’ Medici, Phys. Rev. B 81,035106 (2010)

[4] L. de’ Medici, G. Giovannetti and M. Capone, Phys. Rev. Lett. 112, 177001 (2014)

[5] F. Gebhard, “The Mott metal-insulator transition”, Springer Tracts in Modern Physics, Vol 137 (1997)

[6] N. F. Mott, Proc. Phys. Soc. (London) A62, 416 (1949), N. F. Mott, Rev. Mod. Phys., 40, pp. 677–683

[7] D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984), A. Georges et al. Rev. Mod. Phys. 68, 13 (1996).

[8] A. Georges, L. de’ Medici and J. Mravlje, Ann. Rev. Cond. Mat. 4, 137 (2013)

[9] L. de’ Medici, “Strong AND Weak correlations in Fe superconductors”, pp.409-441 in “Iron-Based Superconductivity”, Springer Series in Material Science Vol 211, (2015).

**Ilya Eremin ****Title:** Cooper-pairing, magnetic frustration, and spin fluctuations in iron-based superconductors**Plan of the lectures:**

Lecture I

Leading instabilities in ferropnictides: weak-coupling analysis, RPA and renormalization group study, comparison to cuprates

Lecture II

Magnetic order: manifold of the ground states, C2 and C4 phases, selection of the magnetic states, role of spin orbit coupling

Lecture III

Spin excitations in the magnetic state within itinerant description: magnetic anisotropy of the excitations, coexistence with the superconducting state

Lecture IV

SC state: multiband effects beyond simple s - (nodal structure, role of additional hole pockets with difference orbital structure), role of 'simple' disorder on Tc, quasiparticle interference.

**Background references:**

Books on many-body physics in general (occupation number formalism, multiorbital Hubbard model, Green function, self-energy, finite temperature formalism, Fermi liquid theory) see, for example:

Chapters 6,7,8,9,10 of P. Coleman, "Many_Body Physics", G. Mahan "Many body physics", Bruus and Felnsberg "Many body quantum theory in condensed matter"

References for all lectures and lecture I

[1] R. Shankar, Rev. Mod. Phys. 66, 129 (1994).

[2] D. J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012)

[3] A. V. Chubukov, D. Efremov, and I. Eremin, Phys. Rev. B 78, 134512 (2008)

[4] P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin, Rep. Prog. Phys. 74, 124508 (2011)

[5] K. Suzuki, H. Usui, and K. Kuroki, Phys. Rev. B 84, 144514 (2011).

[6] S. Maiti, M. M.Korshunov, T. A. Maier, P. J. Hirschfeld, and A. V. Chubukov, Phys. Rev. B. 84, 224505 (2011)

[7] R. Thomale, C. Platt, W. Hanke, J-P Hu, and B. Andrei Bernevig,Phys. Rev. Lett. 107, 117001 (2011)

[8] T. A. Maier, S. Graser, P. J. Hirschfeld, and D. J.Scalapino, Phys. Rev.B 83, 100515(R) (2011)

[9] A.V. Chubukov Annul. Rev. Cond. Mat. Phys.3, 13.1 (2012)

Lecture II

[10] P. Chandra, P. Coleman and A.I. Larkin, Phys. Rev. Lett.64, 88 (1990)

[11] I. Eremin and A.V. Chubukov Phys. Rev. B 81, 024511 (2010)

[12] R. Fernandes, A. Chubukov and J. Schmalian, Nature Phys. 10, 97 (2014)

Lecture III

[13] J. R. Schrieffer, X. G. Wen, and S. C. Zhang, Phys. Rev. B 39 11663 (1989)

[14] J. Knolle, I. Eremin, A.V. Chubukov, R. Moessner Phys. Rev. B 81, 140506(R) (2010)

Lecture IV

[15] on the role of impurities in superconductors, see chapter by Theory of Superconducting Alloys by L.P.Gor'kov in Bennemann and Ketterson Physics of Superconductors

A.V. Chubukov, D. Efremov, and I. Eremin, Phys. Rev. B 78, 134512 (2008)

[16] J. E. Hoffman, Reports on Progress in Physics 74, 124513 (2011)

[17] P.J. Hirschfeld, D. Altenfeld, I. Eremin, I.I. Mazin, arXiv:1507.08317 (to appear in PRB)

further references will be given during the course

**Jörg Schmalian****Title:** Nematic order and fluctuations in iron based superconductors**Plan of the lectures:**

Lecture I

Summary of collective field theories of magnetism

a) Order-parameter field theory from a microscopic Hamiltonian[1,2]

b) Solution of the field theory (introduction to the large-N approach)[2,3]

Lecture II

Emergent nematic order in iron based systems

a) Order-parameter theory of stripe magnetic order[4]

b) Analysis of the large-N limit and Ising-nematicity[5,6,7]

Lecture III

Phase diagram and observables I

a) Analysis of the phase diagram[7]

b) Nematic susceptibility and elastic properties [8]

Lecture IV

Phase diagram and observables II

a) Anisotropy of the resistivity [9]

b) Raman scattering and nematic susceptibility [10]

Lecture V

Impact on superconductivity

a) Raman resonance mode in the superconducting state [11]

b) Nematic fluctuations and pairing [12,13]

**Background references:**

Books on many-body physics:

(i) Chapters 1-5 of J. W. Negele and H. Orland, "Quantum Many-Particle Systems" (Addison-Wesley, 1988), or

(ii) Chapters 1-5 of A. Altland and B. Simon “Condensed Matter Field Theory” Second Edition (Cambridge Univ. Press. 2010)

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[2] A. J. Millis, Phys. Rev. B 48, 7183 (1993) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.48.7183

[3] A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.11919

[4] R. M. Fernandes and J. Schmalian, Phys. Rev. B 82, 014521 (2010) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.014521

[5] C. Xu, M. Müller, and S. Sachdev, Phys. Rev. B 78, 020501(R) (2008) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.78.020501

[6] C. Fang, H. Yao, W.-F. Tsai, J.P. Hu, and S. A. Kivelson Phys. Rev. B 77, 224509 (2008) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.77.224509

[7] R. M. Fernandes, A. V. Chubukov, J. Knolle, I. Eremin, and J. Schmalian, Phys. Rev. B 85, 024534 (2012) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.024534

[8] R. M. Fernandes, L. H. VanBebber, S. Bhattacharya, P. Chandra, V. Keppens, D. Mandrus, M. A. McGuire, B. C. Sales, A. S. Sefat, and J. Schmalian, Phys. Rev. Lett. 105, 157003 (2010) http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.157003

[9] R. M. Fernandes, E. Abrahams, and J. Schmalian Phys. Rev. Lett. 107, 217002 (2011) http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.217002

[10] U. Karahasanovic, F. Kretzschmar, T. Böhm, R. Hackl, I. Paul, Y. Gallais, and J. Schmalian, Phys. Rev. B 92, 075134 (2015) http://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.075134

[11] Y. Gallais, I. Paul, L. Chauviere, J. Schmalian, preprint, arXiv:1504.04570 http://arxiv.org/abs/1504.04570

[12] R. M. Fernandes, A. V. Chubukov, and J. Schmalian, Nature Physics 10, 97–104 (2014) http://www.nature.com/nphys/journal/v10/n2/abs/nphys2877.html

[13] S. Lederer, Y. Schattner, E. Berg, and S. A. Kivelson Phys. Rev. Lett. 114, 097001 (2015) http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.097001