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

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

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

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

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

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

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

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

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, …..

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

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)

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)

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

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)

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)

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.

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

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

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)

Can we do gap engineering with Mott gap???

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

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, 075106 (2006)

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, 075106 (2006)

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?

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, 204 - 209 (2006)

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.

Polar catastrophe in mott insulator heterostructure Z 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, 075339 (2007)

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……

A Wild guess Thermoelectrical power changes sign around QCP T x Phys. Rev. B vol. 82, 214503 (2010) Thermoelectrical power changes sign around QCP T x Is there a QCP in cuprate phase diagram?

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, 115101 (2011)