Phases of Mott-Hubbard Bilayers Ref: Ribeiro et al, cond-mat/0605284 Jung Hoon Han Sung Kyun Kwan U. 成均館大 Ref: Ribeiro et al, cond-mat/0605284 Han & Jia, cond-mat/0605426

Sharp Interface of Band Insulator and Mott Insulator H.Y.Hwang, Nature (2002) La Sr SrTi(d0)O3 and LaTi(d1)O3 interfacial layer with atomic precision was successfully fabricated.

Millis-Okamoto Theory N-layers of Mott insulators are sandwiched between band insulators Ti t2g orbital states are studied within Hartree-Fock theory Okamoto & Millis, Nature (2004)

Millis-Okamoto Theory Electron leakage occurs; Spectral function shows metallic behavior

Can we do something similar with interface of two doped Mott insulators? After all physics of doped Mott insulators is much richer than that of doped band insulator, e.g. spin liquid, d-wave superconductivity, and antiferromagnetism

Sharp Interface of two Mott Insulators Bozovic, Nature (2003)

Layers are oppositely doped with density x of holes(doublons) Our Model Ramesh, Science (2004) Layers are oppositely doped with density x of holes(doublons) Short-range Coulomb coupling across the layers Each layer modeled as large-U Hubbard or tJ

In this talk we try to answer a naïve question: What are the possible phases of coupled doped Mott insulators?

Phase Diagram of Hubbard Model – Recent Efforts Senechal et al, PRL (2005)

Single-layer tJ Model – slave boson meanfield theory Han, Wang, Lee IJMPB (2001)

Lessons from 1D Coupled Chains (A. Seidel) 1D constrained hopping model has (wavefunction) = (charge w.f.) X (spin w.f.) Inter-layer interaction for the charge sector has effective Hamiltonian given by 1D attractive Hubbard model Ribeiro et al, cond-mat/0605284

Lessons from 1D Coupled Chains (A. Seidel) 1D analog of paired superfluid phase emerges as the ground state; In the original picture this is the holon-doublon exciton Existence of exciton instability is rigorously established in coupled 1D chains Ribeiro et al, cond-mat/0605284

Phases of Mott-Hubbard Bilayers at T=0 DOPING INTERLAYER INTERACTION Han & Jia, cond-mat/0605426

Spin Liquid Insulator – a new phase for bilayers Exciton pairing acts like a pairing gap for quasiparticles. Single charge excitation has a gap due to excitons: Insulator It emerges after magnetic order has melted: Spin Liquid

Dichotomy of one-particle vs. two-particle responses In the SLI phase, one-particle Green’s function has a charge gap Two-particle response function such as conductivity is that of a superfluid due to transport by excitons

Other Phases of Bilayer Mott-Hubbard Model DOPING INTERLAYER INTERACTION AFI: Antiferromagnetic insulator with (,) ordering; Charge gap due both to AFM and exciton gaps; Evolves into SLI when magnetism vanishes; Transport still superfluid-like m-dSC: Magnetic d-wave Superconductor; Exciton gap has vanished; d-wave pairing of electrons; Evolves into non-magnetic d-wave superconductor upon doping

Phases of Mott-Hubbard Bilayers from Berkeley group Ribeiro et al, cond-mat/0605284 Calculation based on doped carrier formulation Results are consistent with slave boson theory

New Features of Bilayers Exciton binding is responsible for incoherent quasiparticles and charge gap for small doping Exciton binding is responsible for in-plane superfluid transport Easy realization of spin liquid without lattice frustration