Electron-hole Bose liquid is a novel phase in strongly correlated 3d systems

A.S. Moskvin

Department of Theoretical Physics, Institute of Natural Sciences UFUXIX Ural International Winter School on the Physics of SemiconductorsFebruary 20- 25, 2012 Ekaterinburg, Russia

Concept of electron-hole Bose liquid in strongly correlated 3d systems is based on many earlier model approaches suggested for strongly correlated systems: Shafroth composite bosons Disproportionation scenario (chemical route) Negative-U model Bipolarons

Some referencesP.W. Anderson, Phys. Rev. Lett. 34, 953 (1975)S. P. Ionov, G. V. Ionova, V. S. Lubimov, and E. F. Makarov, Phys.Status Solidi B 71, 11 (1975).I.O. Kulik, A.G. Pedan, JETP, 1980, Vol. 52, No. 4, p. 742J.E. Hirsch and D.J. Scalapino, PRB, 32, 5639 (1985)C.M. Varma, PRL, 61, 2713 (1988)John A Wilson, J. Phys.: Condens. Matter 12 (2000) R517R547T.H. Geballe and B.Y. Moyzhes, Physica C 341-348, 1821-1824 (2000);Low Temperature Physics 27, 777 (2001)K.V. Mitsen and O.M. Ivanenko, Phys. Usp. 47, 493 (2004)K.D. Tsendin, B.P. Popov, and D.V. Denisov, Supercond. Sci. Technol. 19, 313 (2006)S. Larsson, Int. J. Quantum Chem., 90, 1457 (2002); Physica C, 460-462, 1063 (2007)Hiroshi Katayama-Yoshida, Koichi Kusakabe, Hidetoshi Kizaki, and Akitaka Nakanishi, arXiv:0807.3770v1).

OutlineDisproportionation and local bosonsElectron-hole (EH) dimersEH Bose liquid: singlet local bosonsEH Bose liquid: triplet local bosonsEH Bose liquid in cupratesEH Bose liquid in manganites Key words: + mixed valence, electron-hole excitations, charge transfer excitons, exciton self-trapping, cuprates, manganites, pnictides, high-Tc superconductivity, colossal magnetoresistance,

Disproportionation as a way to electron-hole Bose liquid

Disproportionation in 3d oxidesAt present, a charge transfer (CT) instability with regard to disproportionation is believed to be a rather typical property for a number of perovskite 3d transition-metal oxides such as CaFeO3, SrFeO3, LaCuO3, RNiO3, moreover, in solid state chemistry one consider tens of disproportionated systems

Simple algebra for disproportionationOne-particle charge transfer and formation of EH-dimer (charge transfer exciton)

Two-particle charge transfer in EH-dimer

Composite local boson in EH-dimer

However,To introduce a local composite boson we need:1. No configurational mixing for the both and configurations, and a simple genealogy

Thenis a two-particle, or boson transfer integral:

To provide the boson mobility we need (eg2)1A1g or (eg2)1A2g composite boson structureTo minimize the reduction effects of orbital overlap and draw the strongest -bond into boson transfer we need the eg2-type configuration for composite boson.To minimize reduction effects of local electron-lattice coupling we need S-type bosons with the A1g or A2g symmetry.To minimize the reduction effects of spin degrees of freedom we need spin singlet 1A1g or 1A2g boson.

There are only several specific 3dn configurations that meet these requirements. For high-symmetry crystal fields these are shown in Figure. Yet, all these point to spin triplet local bosons!

However, for low-symmetry crystal fields there are configurations that permit formation of spin singlet composite local bosons, e.g. Cu2+(3d9) in strong tetragonal crystal field

Singlet local bosons in tetragonal Cu2+ cupratesCu2+(3d9) in strong tetragonal crystal field corresponds to b1g(dx2-y2)-hole. Than the Cu1+(3d10) electron center can be considered as hole center Cu3+(3d8), or b1g2:1A1g (Zhang-Rice singlet) with localized two-electron composite spin singlet boson b1g2:1A1g

Spin and orbital singlet local bosons(quantum charges)

Minimal model of the EHBL:quantum chargesThe minimal model of the EHBL is described by a Hamiltonian of local, or hardcore bosons on a lattice

Equivalent s=1/2 pseudospin Hamiltonian Anisotropic Heisenberg model in external field

Typical T-n phase diagram of 2D local boson systemG. Schmid et al., Phys. Rev. Lett. 88,167208 (2002).n is the deviation from half-filling

Spin triplet but orbital singlet local bosons

Effective Hamiltonian for triplet s=1 local bosons on a spin-S latticeA.S. Moskvin, Phys. Rev. B 79, 115102 (2009)

These Hamiltonians imply the preformed EH Bose liquid. However, in the most part of 3d systems under study the ground state is related with the bare 3dn ions. Formation of the EHBL needs in some transformations of the system, in particular, the nonisovalent substitution, photoexcitation, or mechanic pressure. In any case the EHBL evolves from EH-dimers.

Formation of the EHBL starts with EH-dimersLet address EH-dimers in several hottest 3d systems.

S- and P-type EH-dimers in cupratestB~1000 K !

(theoretical estimations and different optical data, see A.S. Moskvin, Phys. Rev. B 84, 075116 (2011))

S- and P-type EH-dimers can be termed as bonding and antibonding ones, respectively

Energy of EH-dimer, or d-d CT exciton = d-d CT gap

Two types of CT gap: Franck-Condon and non-Franck-Condon CT gaps

What is the energy of EH-dimer in cuprates?

EH-dimers in parent cupratesSimple illustration of the electron-lattice polarization effects for the CT excitons: a) CT stable system; b) CT unstable system. Filling points to a continuum of unbounded electrons and holes. Right panel shows the experimentally deduced energy scheme for the CT states in La2CuO4

CT transitions in parent cuprates. Optical manifestation of EH dimersReconstruction of the whole NFC-FC CT band in Sr2CuO2Cl2. The scale of the respective absorption coecients diers by three orders of magnitude. Such an unconventional NFC-FC structure of the optical spectra is a typical one for all parent cuprates. Vertical arrow points to a hardly visible peak at 0.2 eV.J.D. Perkins, R.J. Birgeneau, J.M. Graybeal et al., Phys. Rev. B58, 9390 (1998).S.L. Cooper, D. Reznik, and A. Kotz et al., Phys. Rev. B 47, 8233 (1993).

Photoinduced absorption spectrum of La2CuO4J. M. Ginder et al., Phys. Rev. B 37, 75067509 (1988)Y. H. Kim et al., Phys. Rev. Lett. 67, 2227 (1991).

CT gap in parent cupratesEnergy gap over which the electron and hole charge carriers are optically activated in parent cuprate La2CuO4 (FC CT gap) to be CT(opt) 2.0 eV !!!.

(numerous optical measurements)

CT gap in parent cupratesEnergy gap over which the electron and hole charge carriers are thermally activated in parent cuprate La2CuO4 (non-FC CT gap) to be CT(free EH)=0.89 eV !!!.

Y. Ando, Y. Kurita, S. Komiya, S. Ono, and K. Segawa, Phys. Rev. Lett. 92, 197001 (2004)

CT gap in parent cupratesEnergy gap over which the electron-hole dimers are thermally activated in parent cuprate La2CuO4 (non-FC CT gap) to be CT(EH-dimer) 0.5 eV !!!.

A.S. Moskvin, Phys. Rev. B 84, 075116 (2011)

EH-dimer in nickellates (Ni2+)

EH-dimer in manganites (Mn3+)

EH-dimer=CT exciton=quantum of disproportionationTwo-electron transport with dynamical breathing modeOne-electron transport with anti-JT transition

Spin structure of the S- and P-type EH-dimers in LaMnO3 A. S. Moskvin, Phys. Rev. B 79, 115102 (2009).

EH-dimers in LaMn7O12 R. Cabassi, F. Bolzoni, E. Gilioli, F. Bissoli, A. Prodi, and A. Gauzzi, Phys. Rev. B 81, 214412 (2010)

55Mn NMR spectrum for EH dimers:local field

55Mn NMR spectrum for EH dimers 55Mn NMR frequencies for bare Mn4+,3+,2+ ions in LaMnO3 (Tomka,Allodi,Shimizu) and theoretical predictions for the EH-dimer in different spin states. Shown by filling is a 55Mn NMR signal for slightly nonstoichiometric LaMnO3 (Kapusta).

Formation of the EHBL phase in a model La1-xSrxCuO4 cuprate

Toy S=1 charge pseudospin model for mixed valence cuprate(Cu2+) M=0; (Cu1+) M=-1; (Cu3+) M=+1Effective pseudospin Hamiltonian

We made use of reasonable bare parameters as follows:=0.4, h=0, t=0.1, Vnn=0.35 eV. These agree with experimental ndings for La2CuO4: CT = 2 0.8-0.9 eV; EH = 2Vnn 0.4-0.5 eV; t Jnn 0.12 eV.The model impurity potential was produced by negative charges q = e randomly located at the positions of La3+ ions and forming an impurity zone with radius 4a and parameters = =-0.5, h=0.35, t=0.1, Vnn=0.25 eV which are considered to be constant all over the impurity zone. It means that throught the lattice covered by impurity potential the EHBL phase forms a stable ground state with the electron-hole recombination energy (or the energy of the inverse disproportionation reaction which denes an energy scale of a robustness of the EHBL phase) as large as CT (2 +Vnn) =1.25 eV. Model parameters

Quantum Monte-Carlo simulation

Phase pattern of the model CuO2 plane x=0 x=0.03 x=0.06

Phase pattern of the model CuO2 plane x=0.09 x=0.12 x=0.15

Phase pattern of the model CuO2 plane x=0.18 x=0.21 x=0.24

Inhomogeneous EHBL phaseT-x phase diagram of model cuprate

Signatures of the EHBL phase in manganites

Electronic phase separation andphysical properties of nominally stoichiometric LaMnO3S. Moskvin, Phys. Rev. B 79, 115102 (2009).

EHBL in YBaMn2O6?Susceptibility in manganites behaves in a fundamentally different way at high temperatures than is usually observed in magnetic materials with dominant superexchange interactions. Magnetic moment observed in YBaMn2O6 by ESR can be explained only, if to assume that all Mn ions are in a tetravalent state (!?). This points to EHBL phase with triplet local bosons eg2 moving in the lattice formed by Mn4+ centers. ESR contribution of the boson spin system cannot be detected when the hopping time becomes short compared to a Larmor period and prevents the occurrence of the precessional motion of the spin.D. V. Zakharov, J. Deisenhofer, H.-A. Krug von Nidda et al., PHYS. REV. B 78, 235105 (2008)

EHBL in YBaMn2O6?The linewidth for T>520 K appears to follow a classical Korringa-type behavior, typical for the localized spins coupled to the quasifree spin and charge carriers. * Dr. Joachim Deisenhofer (Uni-Augsburg), private communication

EHBL in manganitesThe very idea of using multiple-valence atoms as an active element electronically involved in the conduction mechanism namely, the Mn2+ and Mn4+ in manganites opens unexplored scenarios in the study of physical properties of CMR materials.

Thank you!