## Lecture Topics and Background References

**Prof. Marco Grilli (2-6 October)**

**Title:**"

*Inhomogeneity, criticality, and topology of the LaXO3/SrTiO3 (X=Al,Ti) interfaces*"

**Plan of the lectures:**

1. Crystal and electronic structure of LXO/STO interface. Phenomenology: XAS, photoemission, ARPES, magnetic susceptibility, transport, Rashba spin-orbit coupling (RSOC).

2. Inhomogeneity of LXO/STO interfaces: experimental evidences. The percolative Superconductor-Metal-transition. Theoretical treatment: Effective Medium Theory and RRN modelling.

3. A primer on quantum critical points, scaling, dynamical critical index and so on. Superconductor-Metal-Transition: an example of quantum critical point.

4. Interplay between charge-density and Cooper-pair fluctuations: a road to new anomalous criticality. Rashba spin-orbit coupling, a road to spintronic applications: Spin-Hall effect, Edelstein effect, Inverse Edelstein effect (I).

5. Rashba spin-orbit coupling, a road to spintronic applications: Spin-Hall effect, Edelstein effect, Inverse Edelstein effect (II). Topological state and Majorana fermions in LXO/STO.

**References:**

[1] Research Update: Conductivity and beyond at the LaAlO3/ SrTiO3 interface S. Gariglio, M. Gabay, and J.-M. Triscone APL MATERIALS 4, 060701 (2016).

[2] Emergent phenomena at oxide interfaces H. Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, and Y. Tokura.

[3] Density inhomogeneities and Rashba spin-orbit coupling interplay in oxide interfaces N. Bovenzi, S. Caprara, M. Grilli, R. Raimondi, N. Scopigno, G. Seibold
arxiv:1704.01852 (J. Phys. Chem. of Sol. to appear).

[4] Metal–superconductor transition in low-dimensional superconducting clusters embedded in two-dimensional electron systems D Bucheli, S Caprara, C Castellani, and M GrilliNew J. Phys. 15, 023014 (2013).

[5] Multiband superconductivity and nanoscale inhomogeneity at oxide interfaces S. Caprara, et al.Phys. Rev. B 88, 020504(R) (2013).

[6] Inhomogeneous multi carrier superconductivity at LaXO3/SrTiO3 (X = Al or Ti) oxide interfaces S Caprara, et al. Supercond. Sci. Technol. 28. 014002 (2015).

[7] S. L. Sondhi, M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997).

[8] Interplay between density and superconducting quantum critical uctuations S Caprara, N Bergeal, J Lesueur and M Grilli J. Phys.: Condens. Matter 27, 425701 (2015).

[9] Intrinsic spin Hall effect in systems with striped spin-orbit coupling G. Seibold, S. Caprara, M. Grilli and R. Raimondi EPL, 112 (2015) 17004.

[10] Theory of the spin galvanic effect at oxide interfaces G. Seibold, S. Caprara, M. Grilli, R. Raimondi arXiv:1706.07243.

[11] New directions in the pursuit of Majorana fermions in solid state systems Jason Alicea Rep. Prog. Phys. 75, 076501 (2012).

[12] Unpaired Majorana fermions in quantum wires Kitaev A Y Phys.–Usp. 44, 131 (2001).

**Dr. George Jackeli (9-13 October)**

**Title:**"

*Spin-orbital interplay in bulk and reduced dimensional correlated oxides*"

**Plan of the lectures:**

1. Introduction: Mott insulators, Orbital degeneracy, Spin-orbital exchange interactions. [1,2,3]

2. Spin-orbital frustration: Geometrical frustration, Order-by-disorder, Unusual ordered/disorder states. [3,4,5]

3. Spin-orbit coupled Mott insulators: Local electronic structure and spin-orbital entanglement, Exchange interactions in pseudo-spin bases. [6,7]

4. Effective models and experimental implications: Layered Iridates, Ruthenates, and Vanadates, Molybdates and Osmates on frustrated lattices. [8,9]

5. Emergent novel states at the oxide interfaces: Polar catastrophe, collective electronic reconstructions, Spin-orbital interplay at the interfaces and superlattices. [10,11]

**References:**

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

[2] K.I. Kugel and D.I. Khomskii, Sov. Phys. Usp. 25, 231 (1982).

[3] D.I. Khomskii “Transition Metal Compounds”, Cambridge University Press (2014).

[4] G. Jackeli, and D.A. Ivanov, Phys. Rev. B 76, 132407 (2007).

[5] G. Jackeli and D. I. Khomskii, Phys. Rev. Lett. 100, 147203 (2008).

[6] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

[7] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 103, 067205 (2009).

[8] J.G. Rau, E.K.-H. Lee, and H.-Y. Kee, Annual Review of Condensed Matter Physics 7, 195 (2016).

[9] J. Romhányi, L. Balents, and G. Jackeli, Phys. Rev. Lett. 118, 217202 (2017).

[10] H. Boschker and J. Mannhart, Annual Review of Condensed Matter Physics 8, 145 (2017).

[11] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 101, 216804 (2008).

**Dr. Fabio Miletto Granozio and Dr. Marco Salluzzo (2-6 October)**

**Title:**

**"**X-ray spectroscopy on oxides heterostructures - Growth of epitaxial thin films and heterostructures - Road to spintronic applications"

Plan of the lectures:

1. Growth of epitaxial thin films and heterostructures: physical mechanisms, deposition techniques, in-situ monitoring and strain effects.

2. Two-Dimensional electron gases at oxide interfaces. What do we know about the carriers origin and the mechanisms that determine their density, mobility and spatial extension?

3. Oxide Technology Roadmap. Discussion on the possible applications of oxide films and heterostructures: which ones can potentially have a technological impact within a decade?

4. X-ray Absorption Spectroscopy on Oxides and Oxide heterostructures.

5. The physics of the LaAlO3/SrTiO3 2DEG: orbital reconstruction; magnetism, in-gap states and Nanoscale inhomogeneities; structural relaxation in LAO/STO investigated by grazing incidence x-ray Diffraction.

**References:**

**1. Growth of epitaxial thin films and heterostructures: physical mechanisms, deposition techniques, in-situ monitoring and strain effects. **

I suggest to have a look at* Sections I to IV *of this review:

http://www.mmm.psu.edu/DGSchlom2008_JACS_Athinfilmapproach.pdf

During the lecture I will briefly describe several technique described in the paper aboves, but then focus on one, i.e. PLD.

Interested students can have a look at this dedicated paper

http://iopscience.iop.org/article/10.1088/0953-8984/20/26/264005/meta**2. Two-Dimensional electron gases at oxide interfaces. What do we know about the carriers origin and the mechanisms that determine their density, mobility and spatial extension?**I suggest that the students only have a look to this very general introductory paper

http://phys.columbia.edu/~millis/oxideheterostructures/mrsrevew.pdf

although it is today outdated in several aspects.

**3. Oxide Technology Roadmap. Discussion on the possible applications of oxide films and heterostructures: which ones can potentially have a technological impact within a decade?**

I will be hopefully able to provide some unpublished material that I am currently editing, at the time of the lectures.

**For the moment I can only report on the existence of this recently published review**

http://iopscience.iop.org/article/10.1088/0022-3727/49/43/433001/pdf

**but I would only recommend to only have a general look at it.**

**References:**

[1] Zaanen, J., G. A. Sawatzky, and J.W. Allen Phys. Rev. Lett. 55, 418 (1985).

[2] Book : core level spectroscopy of solids, Frank De Groot, Akio Kotani CRC Press 2008: https://doi.org/10.1201/9781420008425.ch1; https://doi.org/10.1201/9781420008425.ch4; https://doi.org/10.1201/9781420008425.ch6; https://doi.org/10.1201/9781420008425.ch6

[3] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Rev. Mod. Phys. 83, 705 (2011).

[4] Book: Oxide Thin Films, Multilayers, and Nanocomposites, a cura di Paolo Mele,Tamio Endo,Shunichi Arisawa,Chaoyang Li,Tetsuo Tsuchiya; Chapter 10.

[5] M. Salluzzo,et al. Phys. Rev. Lett. 102, 166804 (2009).

[6] J. Chackalian et al. Nature Physics Letters, 2, 244 (2006).

[7] J. Chakhalian, et al., Science 318, 1114 (2007).

[8] D. Stornaiuolo, C. Cantoni, G. M. De Luca, R. Di Capua, E. Di Gennaro, G. Ghiringhelli, B. Jouault, D. Marrè, D. Massarotti, F. Miletto Granozio, I. Pallecchi, C. Piamonteze, S. Rusponi, F. Tafuri, and M. Salluzzo, Nature Materials 15, 278 (2016).

[9] M. Salluzzo, S. Gariglio, X. Torrelles, Z. Ristic, R. Di Capua, J. Drnec, M. M. Sala, G. Ghiringhelli, R. Felici, and N. B. Brookes, Adv. Mater. 25, 2333 (2013).

[10] M. Salluzzo, S. Gariglio, D. Stornaiuolo, V. Sessi, S. Rusponi, C. Piamonteze, G. M. De Luca, M. Minola, D. Marrè, A. Gadaleta, H. Brune, F. Nolting, N. B. Brookes, and G. Ghiringhelli, Phys. Rev. Lett. 111, 087204 (2013).

**Dr. Alexander Yaresko (9 – 13 October)**

**"Properties of transition metal oxides from band structure calculations"**

**Title:**** Plan of the lectures: **

1. Basics of band structure calculations Density functional theory; approximations to exchange correlation potential; methods

2. Strong correlations and band structure LDA+U approximation; DMFT.

3. Electronic structure of 5d transition metal oxides Spin-orbit coupling; non-collinear magnetism.

4. Calculations of effective magnetic interactions Spin-spiral calculations; magnetic force theorem.

5. Properties of multilayered structures Effects of reduced dimensionality; surface and interface states.

**References:**

[1] R. O. Jones and O. Gunnarsson, *The density functional formalism, its application and prospects.* Rev. Mod. Phys. 61, 689 (1989).

[2] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, *Restoring the density-gradient expansion for exchange in solids and surfaces.* Phys. Rev. Lett. 100, 136406 (2008).

[3] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density functional theory and strong interactions:* Orbital ordering in Mott-Hubbard insulators*. Phys. Rev. B 52, R5467 (1995).

[4] J. Kunes, I. Leonov, P. Augustinsky, V. Krapek, M. Kollar, and D. Vollhardt, *Lda plus Dmft approach to ordering **phenomena and the structural stability of correlated materials*. European Physical Journal-special Topics 226, 2641 (2017).

[5] A. N. Yaresko, G.-Q. Liu, V. N. Antonov, and O. K. Andersen, *Interplay between magnetic properties and Fermi surface nesting in iron pnictides*. Phys. Rev. B 79, 144421 (2009).

[6] I. Leonov, A. N. Yaresko, V. N. Antonov, M. A. Korotin, and V. I. Anisimov,* Charge and orbital order in Fe3O4*. Phys. Rev. Lett. 93, 146404 (2004).

[7] S. Leoni, A. N. Yaresko, N. Perkins, H. Rosner, and L. Craco, *Orbital-spin order and the origin of structural distortion in MgTi2O4.* Phys. Rev. B 78,125105 (2008).

[8] A. N. Yaresko, *Electronic band structure and exchange coupling constants in ACr2X4 spinels (A = Zn, Cd, Hg; X = O, S, Se).* Phys. Rev. B 77, 115106 (2008).

[9] A. V. Ushakov, D. A. Kukusta, A. N. Yaresko, and D. I. Khomskii,* Magnetism of layered chromium suldes MCrS2 (M = Li, Na, K, Ag, and Au): A rst-principles study*. Phys. Rev. B 87, 014418 (2013).

[10] Y. Matiks, A. N. Yaresko, K. Myung-Whun, A. Maljuk, P. Horsch, B. Keimer, and A. V. Boris, *Anisotropic optical response of the mixed-valent Mott-Hubbard insulator NaCu2O2*. Phys. Rev. B 84, 245116 (2011).

[11] T. Takayama, A. Yaresko, A. Matsumoto, J. Nuss, K. Ishii, M. Yoshida, J. Mizuki, and H. Takagi, *Spin-orbit coupling induced semi-metallic state in the 1/3 hole-doped hyper-kagome Na3Ir3O8*. Sci. Rep. 4, 6818 (2014).

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