1. New Possibilities in Transition-metal oxide Heterostructures
Wei-Cheng Lee
University of Illinois at Urbana-Champaign

2. What is a heterostructure?
Two different materials put together to form a clear interface

3. Semiconductor
One shouldn’t work on semiconductors, that is a filthy mess; who knows if they really exist?
Wolfgang Pauli, 1931

4. Semiconductor – Band Insulator with small band gap
Band structure of Si crystaline
electron doped (n-type)
hole doped (p-type)

5. Success of semiconductor heterostructure
Tunneling junction
Insulating layer
Modulation doping
(will be explained later)
Quantum Well
Another great platform for quantum Hall effect
P-N junction
Diode, transistor, LED, etc…
MOSFET, quantum Hall effect, topological insulator found in HgTe quantum well

6. Moore’s law
The number of transistors on integrated circuits doubles approximately every two years.
Gordon E. Moore

7. 14 nm-PC by Intel (2013),
Moore’s law is still not dead
From Wikipedia

8. What is next after the death of Moore’s Law?
New Devices?? Qubit, quantum dot, etc….
Alternatively, can we find new materials for known heterostructure?
Ideal candidate should be:
Gapped
Dopable
Layered
Transition Metal Oxides

9. Perovskite Transition metal oxides (AMO3)
Band Insulators, # of electrons on 3d orbital of M is even.
SrTiO3, LaAlO3
Mott Insulators, # of electrons on 3d orbital of M is odd.
LaTiO3, YTiO3, …..

10. Layer-by-layer growth
E. Dagotto, Science 318, 1076 (2007)

11. Insulator + Insulator = Metal !!!!!
First striking result
LaTiO3
SrTiO3
SrTiO3  Band Insulator
LaTiO3  Mott Instulator
Both are AMO3 perovskite.
Lattice constants are almost the same.
Insulator + Insulator = Metal !!!!!
A. Ohtomo, et. al., Nature 419, 378 (2002)

12. Theoretical Consideration
Oxygen bands are all lined up  Just need to consider d-electrons on Ti atoms
SrTi O 3 → Ti 4+ (3 𝑑 0 )
LaTi O 3 → Ti 3+ (3 𝑑 1 )
La 3+ , Sr 2+ → La 1+ , Sr 0
S. Okamoto and A.J. Millis, Nature (2004), PRB (2005)

13. Gap generation in hubbard model
𝐻 𝐻𝑢𝑏𝑏𝑎𝑟𝑑 = 𝑘,𝜎 𝜀 𝑘 −𝜇 𝑐 𝑘𝜎 + 𝑐 𝑘𝜎 +𝑈 𝑖 𝑛 𝑖↑ 𝑛 𝑖↓
1. In symmetry breaking phase  Gap generated by reduced Brillouin zone (BZ)
Ferromagnetic order
Real space
Antiferromagnetic order

14. Gap generation in hubbard model
𝐻 𝐻𝑢𝑏𝑏𝑎𝑟𝑑 = 𝑘,𝜎 𝜀 𝑘 −𝜇 𝑐 𝑘𝜎 + 𝑐 𝑘𝜎 +𝑈 𝑖 𝑛 𝑖↑ 𝑛 𝑖↓
1. In symmetry breaking phase  Gap generated by reduced Brillouin zone (BZ)
Ferromagnetic order
Antiferromagnetic order
Real space
k-space (BZ)

15. Gap generation in hubbard model
How can we obtain a gap without symmetry breaking??
Still a unresolved question, but we have a non-trivial method which becomes exact in a strange limit  Dynamical Mean Field Theory (DMFT)

16. Gap generation in hubbard model
How can we obtain a gap without symmetry breaking??
Still a unresolved question, but we have a non-trivial method which becomes exact in a strange limit  Dynamical Mean Field Theory (DMFT)
Electron self energy due to onsite interaction 𝑈, Σ(𝑘,𝜔)
Σ(𝑘,𝜔) DMFT Σ(𝜔)
All on-site correlations are included (non-perturbattive)
The inter-site correlations are sacrificed.
It becomes exact in the limit of the infinite dimension.

17. Dynamical Mean Field Theory (DMFT)
Self-consistent conditions:
Successes: Mott transition, spectral function.

18. We are ready Symmetry breaking phases: FM, AFM Normal State: DMFT
S. Okamoto and A.J. Millis, Nature (2004), PRB (2005)

19. Results Carrier concentration Spectral function obtained from DMFT
STO LTO STO
Spectral function obtained from DMFT
Carrier concentration
S. Okamoto and A.J. Millis, Nature (2004), PRB (2005)

20. Can we do gap engineering with Mott gap???

21. Modulation doping
Dopants + extra charges
2DES with high mobility!!!

22. Proposed modulation doping for Mott insulator heterostructure
Oxygen bands are all lined up  Just need to consider d-electrons on M atoms
AM O 3 →𝑀 (3 𝑑 1 )
A′M O 3 →𝑀 (3 𝑑 1 )
𝐴, 𝐴 ′ have the same valence charge → A 0 , A′ 0
For dopant → 𝐷 1+
Example: LaTiO3/YTiO3
W.-C. Lee and A. H. MacDonald, Phys. Rev. B 74, (2006)

23. results Paramagnetic state with DMFT
Layer-resolved spectral function for paramagnetic state with DMFT
Paramagnetic state without DMFT
W.-C. Lee and A. H. MacDonald, Phys. Rev. B 74, (2006)

24. What is unique about it?
Mott gap is necessary not adiabatically connected to any weak coupling systems.
Ideal doped 2D Mott insulator (less disorder)  cuprates?
Multi-orbital structure with spin-orbit coupling topological phases?

25. Polar catastrophe
SrTiO3/LaAlO3 : Band insulator + Band insulator = conducting interface!!!
All elements ( 𝑆𝑟 2+ , 𝑇𝑖 4+ , 𝐿𝑎 3+ , 𝐴𝑙 3+ , 𝑂 2− ) are in closed shell. No free charge at all
N. Nakagawa, H. Y. Hwang and D. A. Muller, Nature Materials 5, (2006)

26. Polar Catastrophe
This is never observed in semiconductor heterostructure!!!
Semiconductors: Conduction bands are strongly hybridized between s and p orbitals which are much more extended Polar discontinuity usually leads to a distorted interface
Transition metal oxide: Conduction bands are mostly d-orbitals which are much more localized Polar discontinuity can lead to the charge transfer.

27. Polar catastrophe in mott insulator heterostructureZ
HFT: Hartree-Fock Theory in normal state
DMFT: Normal state with DMFT
Np=2
Np=5
W.-C. Lee and A. H. MacDonald, Phys. Rev. B 76, (2007)

28. Final remarks
Semiconductor Heterostructures Transition Metal Oxide Heterostructures
Strongly hybrized s and p orbitals (extended states)
d orbitals (more local states)
Small band gap
Mott gap due to correlation
Weakly interacting  Allows a nice match between theory and experiments.
Strongly interacting
Very important for applications (transistors, etc.) and fundamental physics (2DES, quantum Hall effect)
Strongly correlated 2DES (doped Mott insulator?) a platform for understanding cuprates? Orbital degeneracy leading to topological phases? Many possibilities……

29. A Wild guess Thermoelectrical power changes sign around QCP T x
Phys. Rev. B vol. 82, (2010)
Thermoelectrical power changes sign around QCP T x
Is there a QCP in cuprate phase diagram?

30. A Wild guess T x
In a doped multiorbital Mott insulator, QCP will move to smaller doping concentration, which will produce a higher Tc superconductors.
W.-C. Lee and Philip Phillips, Phys. Rev. B 84, (2011)