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K. Reich, M. Schecter, B.I. Shklovskii, University of Minnesota

Part 1: Two-dimensional electron gas in STO. K. Reich, M. Schecter, B.I. Shklovskii, University of Minnesota. Dielectric constant of STO. The origin LAO-STO 2DEG. J. Mannhart et al, MRS Bull. 33 1027 (2008 ). Thomas-Fermi accumulation layer. Landau Hamiltonian.

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K. Reich, M. Schecter, B.I. Shklovskii, University of Minnesota

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  1. Part 1: Two-dimensional electron gas in STO K. Reich, M. Schecter, B.I. Shklovskii, University of Minnesota

  2. Dielectric constant of STO

  3. The origin LAO-STO 2DEG J. Mannhart et al, MRS Bull. 33 1027 (2008)

  4. Thomas-Fermi accumulation layer

  5. Landau Hamiltonian

  6. Thomas-Fermi accumulation layer. Linear dielectric response

  7. TF-Linear results: Ya. I. Frenkel, Ioffe Institute, 1928

  8. TF-Nonlinear results

  9. TF results for d combined

  10. Justification of TF approach

  11. Experimental density profile of electrons n(x) (Y. Yamada, H. K. Sato, Y. Hikita, H. Y. Hwang, and Y. Kanemitsu, Applied Physics Letters 104, 151907 (2014)) obtained by time-resolved photoluminescence. Fitting with our theory is shown by the solid line: d = 250b = 9 nm.

  12. Experimental density profile of electrons n(x) FIG. 2. Fitting by (x+d)^{-12/7} obtained by infrared ellipsometry in A. Dubroka, M. Rossle, K. W. Kim, V. K. Malik,L. Schultz, S. Thiel, C. W. Schneider, J. Mannhart, G. Herranz, O. Copie, M. Bibes, A. Barthelemy, and C. Bernhard, Phys. Rev. Lett. 104, 156807 (2010). The fitting parameter d =142b = 5 nm.

  13. Part 2: Spherical charge in STO Han Fu, K. Reich, B.I. Shklovskii University of Minnesota.

  14. Drawing on LAO/STO C. Cen, S. Thiel, G. Hammerl, C. W. Schneider, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, Nature Materials 7, 298 (2008)

  15. Thomas-Fermi "atom" in STO κ = 20000 At Z > Zc , collapse happens!

  16. Collapse of the "atom" and charge renormalization Electrons collapse to the center At large nuclear charge Z, the final net charge is renormalized to Z*

  17. Known collapse phenomena I. Pomeranchuk and Y. Smorodinsky (1945) Y. B. Zeldovich and V. S. Popov (1972) E. B. Kolomeisky, J. P. Straley, and H. Zaidi, (2013) M. M. Fogler, D. S. Novikov, and B. I. Shklovskii, (2007), Levitov (2007), M. F. Crommie, (2012) Supercritical nucleus Z > 1/α = 137 α = e2/ћc Narrow-band gap semiconductors, Weyl semimetals, and graphene αeff= e2/ћvκ, ε=pv

  18. Ek = pc ≈ ћc/r, U = -Ze2/r |U/Ek| = Zα, Z > 1/α → collapse happens, Relativistic origin A. B. Migdal, V. S. Popov, D. N. Voskresenskii (1977). E. B. Kolomeisky, J. P. Straley, H. Zaidi (2013). S Zn

  19. A different origin in STO:nonlinear dielectric response

  20. A different origin in STO:nonlinear dielectric response

  21. As Z increases, collapse strengthens Degenerate gas Collapse and charge renormalizaton

  22. Collapse and charge renormalization in STO at Z >> Z* S Zn Zc ≈R/a Z* ≈(R/a)9/7

  23. Redistribution of electron density nonlinear linear uncollapsed aB Collapsed, Saturn-like

  24. Double-layer structure Potential profile Fermi level Fermi sea Similar to supercharged nuclei border studied by A. B. Migdal, V. S. Popov, D. Voskresenskii (1977).

  25. Thermal ionization at finite T s = kB ln (n / n0), n0=2 / λ3, λ ~ T-1/2, n=Zi N I = Zie2/κri = Zi2e2/κ2ab, ri=κab/Zi I=sT Zi > Z*at T > 8K, Inner tail ionized at T > 450 K Finite temperature

  26. Temperature-induced metal-insulator crossover d T > 10 K T < 10 K

  27. Thank you

  28. Electron layer width d from accumulation to inversion

  29. Role of dispersion term

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