Ab initio effective Hamiltonians for cuprate superconductors

Abstract

Ab initio low-energy effective Hamiltonians of two typical high-temperature copper-oxide superconductors, whose mother compounds are La2CuO4 and HgBa2CuO4, are derived by utilizing the multi-scale ab initio scheme for correlated electrons (MACE). The effective Hamiltonians obtained in the present study serve as platforms of future studies to accurately solve the low-energy effective Hamiltonians beyond the density functional theory. It allows further study on the superconducting mechanism from the first principles and quantitative basis without adjustable parameters not only for the available cuprates but also for future design of higher Tc in general. More concretely, we derive effective Hamiltonians for three variations, 1) one-band Hamiltonian for the antibonding orbital generated from strongly hybridized Cu 3d x 2 −y 2 and O 2pσ orbitals 2) two-band Hamiltonian constructed from the antibonding orbital and Cu 3d 3z 2 −r 2 orbital hybridized mainly with the apex oxygen pz orbital 3) three-band Hamiltonian consisting mainly of Cu 3d x 2 −y 2 orbitals and two O 2pσ orbitals. Differences between the Hamiltonians for La2CuO4 and HgBa2CuO4, which have relatively low and high critical temperatures Tc, respectively, at optimally doped compounds, are elucidated. The main differences are summarized as i) the oxygen 2pσ orbitals are farther (∼ 3.7 eV) below from the Cu d x 2 −y 2 orbital in case of the La compound than the Hg compound (∼ 2.4 eV) in the three-band Hamiltonian. This causes a substantial difference in the character of the d x 2 −y 2 -2pσ antibonding band at the Fermi level and makes the effective onsite Coulomb interaction U larger for the La compound than the Hg compound for the two-and one-band Hamiltonians. ii) The ratio of the second-neighbor to the nearest transfer t ′ /t is also substantially different (0.26 for the Hg and 0.15 for the La compound) in the one-band Hamiltonian. Heavier entanglement of the two bands in the two-band Hamiltonian implies that the 2-band rather than the 1-band Hamiltonian is more appropriate for the La compound. The relevance of the three-band description is also discussed especially for the Hg compound.I.

Period 4 stripe in the extended two-dimensional Hubbard model

“…Thus from these results, we conclude that the W4 stripe is the ground state in a large region between 0.16(4) < −t /t < 0.423 (10), which includes realistic values predicted for cuprate materials [80,81].…”

“…In this paper, using state-of-the-art iPEPS simulations, we show that a period 4 stripe ground state is obtained in an extended Hubbard model including a realistic nextnearest neighbor (NNN) hopping at δ = 1/8 doping. Our systematic study demonstrates that: (i ) the groundstate stripe period decreases with the magnitude of the negative NNN hopping amplitude t ; (ii ) there exists a large region of t in which the period 4 stripe is stabilized, including realistic values for t predicted for the cuprates [80,81]; and finally that (iii ) the d-wave SC order does not coexist with the period 4 stripe at δ = 1/8 doping, but only at larger doping. Our observations of a decrease in the stripe period with negative t are also in agreement with recent works based on DMRG on width-4 cylinders [59] and VMC [58].…”

“…where t and t are nearest neighbor and NNN hopping amplitudes, U >0 is the on-site Coulomb repulsion, and c iσ (ĉ † iσ ) is the annihilation (creation) operator for an electron of spin σ on site i, andn iσ =ĉ † iσĉ iσ . We focus on U/t = 10, which has been predicted as a realistic value of the cuprates [80], and on δ=1/8 throughout this work, unless stated otherwise. Example stripe with a period 6 in the charge order and period 12 in the spin order obtained with iPEPS using a 12 × 2 supercell, for U/t = 10, t /t = 0, D = 12.…”

Materials design of dynamically stable d9 layered nickelates

“…• All the materials are in the strongly correlated regime: |U/t| is around 7-11. Correlation strength is comparable to that of the cuprates [8,[43][44][45][46][47][48].…”

Effective Hamiltonian for cuprate superconductors derived from multiscale ab initio scheme with level renormalization

“…To demonstrate the improvement, here, we take an example of the three-band Hamiltonian for the cuprates derived in Ref. 22, where the Wannier orbitals of d and p belong to different atoms, namely Cu and O, respectively. If the LRFB is applied, the level difference between the oxygen p σ and the copper d x 2 −y 2 orbital decreases in comparison to the GW results, as we show later.…”