Stripes and Nematicity in Hole-Doped Three-Orbital Spin-Fermion Model for Cuprates

1. Stripes and Nematicity in a Hole-Doped Three-Orbital Spin-Fermion Model for Superconducting Cuprates Adriana Moreo Dept. of Physics, University of Tennessee, and Materials Science and Technology Division, ORNL

2. Collaborators ElbioDagotto (UT/ORNL) Mostafa Hussein (Univ. of Tennessee) Maria Daghofer (Stuttgart)

3. High Tc Cuprates 1-orbital model t YBa2Cu3O7 (YBCO) J 3-orbital model

4. Mott versus Charge-Transfer Insulators • Single-orbital models are often used: • ARPES show one single band at the Fermi surface. • Zhang-Rice singlet transforms the three-orbital model to a t-J model. • However, cuprates are charge-transfer insulators. • Do oxygen pσ orbitals play an important role? • Role of O in half-filled stripes? • We need a three-orbital model that can be studied numerically in large lattices and at all temperatures. Single-Orbital models Multi-Orbital models

5. Spin-Fermion Model for the CuO2 planes: Spin-Fermion model Three-band Hubbard model HSF = HTB + Hd + Hp+ HHeis Prevents double occupancy in d orbitals. Introduces frustration. Si are phenomenological localized spins. Encourages AF order. Simplification: classical localized spins can be studied with Monte Carlo Pnictides: S. Liang et al., PRL 109, 047001 (2012); Cuprates: C. Buhler et al., PRL 84, 2690 (2000); Manganites: E. Dagotto et al., PRB 58, 6414 (1998).

6. Parameter Values Spin-Fermion model Three-band Hubbard model M. Hussein et al., PRB 98, 035124 (2018). Electron representation Hole representation TB Jd=0 Jd=8 Ud/t=8 Physical case 50/50 p-d in ZRB UHB LHB? ZRB Physical case 50/50 p-d in ZRB Jd=3 Jd=12 Ud/t=16 LHB UHB Variational Cluster Approach: E. Arrigoni et al., NJP 11, 055066 (2009). Jp=1, JHeis=0.1, 8x8 lattice, β=100 Parameter values: JNN=0.1eV, Jp=1eV,Jd=3eV

7. Spectral Functions A(k,w) M. Hussein et al., PRB 98, 035124 (2018). Undoped Case: 5 electrons per unit cell. B.O.Wells et al., PRL 74, 964 (1995) • The ZRB appears. • Its dispersion is ~ 0.5-0.8 eV, close to experimental result. • Dispersion symmetric about (π/2,π/2) not captured by t-J model. Points: experimental results Solid line: t-J model

8. Magnetic Structure Undoped Case: 5 electrons per unit cell. M. Hussein et al., PRB 98, 035124 (2018). Classical Spins Quantum d Spins X 5 • Tendency towards AF long-range order. • TN~300-500K. • Quantum Cu spins follow classical spins.

9. What happens upon hole doping? Experiment: half-filled stripes Single Band Models: filled stripes 4 lattice sites • t-J: ½-filled stripes with DMRG and external fields to stabilize AF. (White and Scalapino, PRL 80, 1272 (1998)). • t’ hopping leads to filled stripes in t-J. (Dodaro et al., PRB 95, 155116 (2017)). • t’ hopping produces ½ filled stripes in Hubbard. (Jiang and Devereaux, arXiv:1806.01465)). 8 lattice sites Single band Hubbard model: filled stripes (nh=1/8). Zheng et al., Science 358, 1155 (2017). 8 lattice sites Idealized stripes in LSCO from neutron scattering data:half-filled stripes (nh=1/8). Tranquada et al., Nature 375, 561 (1995). Single band spin-fermion model: filled stripes (nh=1/8). Buhler et al., PRL 84, 2690 (2000).

10. Half-filled Stripes M. Hussein et al., PRB 99, 115108 (2019). 16x4, β=800 eV-1, T~15K • AF uniform charge distribution in undoped case. • Added holes form half-filled stripes. • A π-shift is observed in the magnetic order across the stripes. • Holes occupy both the d and p orbitals due to the hybridization. • Without the p orbitals the stripes become filled. (Buhler et al., PRL84, 2690 (2000)).

11. Magnetic and Charge incommensurability • ksmax=(π-δ,π) and kcmax=(2δ,0). • δ=2πnh=2π(Nh/N)=2πδexp. • Good agreement with experiments for LSCO. Birgeneau et al., J. Phys. Soc. Jpn,75 111003 (2006) . M. Hussein et al., PRB 99, 115108 (2019).

12. Square Clusters M. Hussein et al., PRB 99, 115108 (2019). T~20K Spin-spin correlation functions Charge snapshot Spin-spin correlation functions Quantum Monte Carlo on 3 bands Hubbard model at high T (>1000K). E. Huang et al., Science 358, 1161 (2017).

13. Spin and Orbital Nematic Order Lawler et al., Nature 466, 347 (2010). Achkar et al., Science 351, 576 (2016). • STM: nematicity in O (BISCO). • Not clear if charge or magnetic origin • Resonant x-ray scattering experiments on LBCO indicate nematicity in Cu d orbitals. Zheng et al., Sci. Rep. 7, 8059 (2017).

14. Spin and Orbital Nematic Order M. Hussein et al., PRB 99, 115108 (2019). • No nematicity in undoped case. • Nematicity increases with doping. • It occurs also in the 8x8 cluster. • Asymmetric charge population in the oxygen. • Asymmetric spin correlations in the Cu.

15. Total versus local doping M. Hussein et al., PRB 99, 115108 (2019). • Does the distribution of the holes matter? • Yes. See Jurkutat et al., PRB90, 140504(R) (2014). • The distribution of the holes among the p and the d orbitals is material dependent. • Fine tuning of the parameters in the TB part of the Hamiltonian needed to improve agreement with experiments. • Single orbital models cannot study the hole distribution.

16. Conclusions Main Development: • A 3-orbital spin-fermion model for the CuO2 planes was presented. • The studied cluster sizes cannot be studied neither with DMRG, Lanczos nor Quantum Monte Carlo. Key question addressed: What role does the charge transfer insulator character of undopedcuprates play? • The presence of the O seems crucial to generate Zhang-Rice band and to estabilize ½ filled stripes. • Charge nematicity develops in the oxygens while spin nematicity in the Cu. • Charge and magnetic order develop at the same temperature. • The distribution of the holes among the d and p orbitals is material dependent. New Directions: Apply techniques such as TCA to reach larger clusters. Add disorder. Fine tune the parameters to reproduce different materials.