K. Reich, M. Schecter, B.I. Shklovskii,

University of Minnesota

Part 1: Two-dimensional electron gas in STO

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

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Landau Hamiltonian

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Thomas-Fermi accumulation layer. Linear dielectric response

7Ya. I. Frenkel, Ioffe Institute, 1928

TF-Linear results:

9

TF-Nonlinear results

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TF results for d combined

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Justification of TF approach

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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.

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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.

Experimental density profile of electrons n(x)

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Part 2:Spherical charge in STO

Han Fu, K. Reich,B.I. Shklovskii

University of Minnesota.

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)

Drawing on LAO/STO

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• κ = 20000

• At Z > Zc , collapse happens!

Thomas-Fermi "atom" in STO

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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*

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Known collapse phenomena • Supercritical nucleus Z > 1/α = 137

α = e2/ћc

• Narrow-band gap semiconductors, Weyl semimetals, and graphene αeff= e2/ћvκ, ε=pv

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)

Relativistic origin

• Ek = pc ≈ ћc/r, U = -Ze2/r |U/Ek| = Zα,

• Z > 1/α → collapse happens,

Zn

S

A. B. Migdal, V. S. Popov, D. N. Voskresenskii (1977).

E. B. Kolomeisky, J. P. Straley,

H. Zaidi (2013). SZZn

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A different origin in STO:nonlinear dielectric response

20000,4

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3

20

3

P

AP

P

APPE

PPED 44 3DE

62

1)(

1)(

rrE

rrE

5

1)(

1)(

rr

rr

21

A different origin in STO:nonlinear dielectric response

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Collapse and charge renormalizaton

• As Z increases, collapse strengthens

• Degenerate gas

2

2

5

243

)(,)(R

aeRE

R

eaZRe k

a

RZc

,/

)(1.0)(

2/3

3

bb ae

r

arn

2/92/7

*0

2 5.0)(4 ZZ

ZZrnrdrS

cZa

RZ

7/9*

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Collapse and charge renormalization in STO

Zc ≈ R/a Z* ≈ (R/a)9/7

Zn

S

*ZSZZn at Z >> Z*

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Redistribution of electron density

Collapsed, Saturn-like

uncollapsed

linearnonlinear

aB

Potential profile

• Double-layer structure

Fermi level

Fermi sea

Similar to supercharged nuclei border studied by A. B. Migdal, V. S. Popov, D. Voskresenskii (1977).

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Finite temperature

• 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 > 8 K, Inner tail ionized at T > 450 K

T < 10 K

d

T > 10 K

Temperature-induced metal-insulator crossover

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Thank you

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Electron layer width d from accumulation to inversion

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Role of dispersion term