Session N15: Electronic Structure of Superconductors: Theory

Relation between the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments

The one-band and three-band Hubbard models which describe the electronic structure of cuprate superconductors are known to provide very different values of effective electronic parameters, such as the on-site Coulomb energy and the hybridization strength. In contrast, electronic parameters of several cuprates obtained from the three-band model are quite similar to corresponding values from cluster model calculations used to simulate experimental spectroscopy and scattering results. In this work, the Heisenberg exchange coupling J obtained by a downfolding method in terms of the three band parameters is used to carry out an optimization analysis consistent with J from neutron scattering experiments for a series of cuprates. In addition, the effective one-band parameters U' and t' can be described using the three band parameters, thus revealing the hidden equivalence of the one-band and three-band models. The ground-state singlet weights obtained from an exact diagonalization elucidates the role of Zhang-Rice singlets in the equivalence. The results provide a consistent method to connect electronic parameters obtained from spectroscopy and the three-band model with values of J obtained from scattering experiments, band dispersion measurements and the effective one-band Hubbard model [1].

[1] K. Sheshadri, D. Malterre, A. Fujimori, and A. Chainani, Connecting the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments, Phys. Rev. B 107, 085125 (2023).   

Ab-Initio Calculation of Quasiparticle Interference in Sr2RuO4

Quasiparticle interference (QPI) imaging of multiband materials with a two-dimensional electronic structure has been instrumental in the study of low-energy states and in capturing details of multiband ordering in these systems. Unbiased ab-initio calculation of quasiparticle interference from a microscopic model enables the study of parameters such as band structure, spin-orbit coupling (SOC) and Hund’s interaction on the superconducting order and allows comparison to the experimental QPI observed in the Ruthenates. To this end we utilize the functional renormalization group (fRG) to construct an unbiased self-energy for a three band model of the Ruthenates with a broken pseudospin symmetry. We find the interplay between the SOC and Hund’s coupling to be the primary driver of patterns in the measured QPI of the Ruthernates. Further, by varying the level of doping in the model, the fRG allows for an accounting of the role played by the Van Hove singularity in the superconducting state observed in Sr₂RuO₄.      

Interlayer couplings in cuprates: mechanisms and structure-based estimators

The cuprates superconductors are layered materials with one or more adjacent copper-oxygen (CuO₂) planes.  While the superconductivity is directly related to the in-plane electronic bands, the critical temperature varies with the number of adjacent CuO₂ planes [1], highlighting the importance of interlayer couplings.  However, multi-layer cuprates are more difficult to study due to the increased complexity of their unit cells.  Without a clear ab initio microscopic picture, interlayer couplings in cuprates are usually obtained empirically by tight-binding fits to the experimental photoemission spectra [2-3] which limits the understanding of microscopic mechanisms or engineering the materials.

Based on first-principles calculations, we identify multiple coexisting interlayer coupling mechanisms in cuprates and directly relate each to relevant structural properties.  We focus on the prototypical bilayer cuprates Bi₂Sr₂CaCu₂O_8+x (Bi-2212) and Pr_x+yY_1-xBa_2-yCu₃O₇ (Pr-YBCO) and demonstrate a method of estimating interlayer couplings, including their k-space dispersion, directly from the measured/computed crystal structure.  These mechanisms can hopefully lead to further design and engineering of these fascinating materials.

References

[1] Shimizu et al., J. Phys. Soc. Jpn. 78, 064705 (2009)

[2] Luo et al., Nat. Phys. https://doi.org/10.1038/s41567-023-02206-0 (2023)

[3] Kunisada et al., Science 369, 6505 (2020)   

Candidate High-Tc Superconductors in a Class of Quaternary Hydrides

Based on our previous work on Lu-H-N ternary hydride structures [arXiv:2305.18196], we propose a class of quaternary structures as potential very high temperature superconductors. In these structures, metallic hydrogen states are dominant at the Fermi energy (E_F) near ambient pressure by chemically preserving a core MH₁₁ (e.g., M=Lu). The computed electronic structure for different compositions within this class also exhibit hydrogen-dominant states near E_F. The networking-value critical temperature (T_c) estimator predicts all of these compounds have T_c around or above 200 K, with some compounds plausibly being room temperature superconductors near ambient pressures. We explore the stability and electronic properties of the structures in terms of local chemical bonding interactions, which give rise to metallic hydrogen sublattices common to very high T_c hydride superconductors. This is naturally realized in the proposed parent structure, which can be viewed as a semiconductor-metal-semiconductor heterostructure. These theoretically predicted structures can provide templates for the continued search for superconductors at ambient conditions.   

Frustrated Altermagnetism and Charge Density Wave in Kagome Superconductor CsCr3Sb5

Using the first-principles density-functional calculations, we investigate the electronic structure and magnetism of the kagome superconductor CsCr₃Sb₅. At the ambient pressure, its ground state is found to be 4×2 altermagnetic spin-density-wave (SDW) pattern, with an averaged effective moment of ∼1.7μB per chromium atom. The magnetic long range order is coupled to the lattice structure, generating 4a₀ structural modulation. However, multiple competing SDW phases are present and energetically very close, suggesting strong magnetic fluctuation and frustration. The electronic states near the Fermi level are dominated by Cr-3d orbitals, and flat band or van Hove singularities are away from the Fermi level. When external pressure is applied, the structural modulations and the energy differences between competing orders are suppressed by external pressure. The magnetic fluctuation remains present and important at high pressure because the non-magnetic phase is unstable up to 30 GPa. In addition, a bonding state between Cr-3d_xz and Sb^II-p_z quickly acquires dispersion and eventually becomes metallic around 5 GPa, leading to a Lifshitz transition. Our findings strongly support unconventional superconductivity in the CsCr₃Sb₅ compound above 5 GPa, and suggest the crucial role of magnetic fluctuations in the pairing mechanism.   

Electron-phonon coupling and polarons in the parent cuprate La2CuO4 from first-principles calculations

In the parent (undoped) phases of high-Tc cuprate superconductors, there is abundant experimental evidence for strong electron-phonon (e-ph) interactions, which result in broad photoemission spectra. The microscopic origin of these strong e-ph interactions in cuprates is not fully understood and their quantitative modeling remains challenging. In this talk, we will present first-principles e-ph calculations in the parent-compound lanthanum cuprate (La₂CuO₄, LCO) based on Hubbard-corrected density functional theory. Our calculations identify two classes of longitudinal optical (LO) phonons strongly coupled with hole states in LCO. Their energies (50-80 meV) are consistent with spectral signatures in photoemission experiments on doped cuprates. The associated electronic spectral functions in the valence band, obtained with a finite-temperature cumulant approach to describe high-order e-ph interactions, exhibit a significant broadening as well as satellite peaks due to polaron effects. The main features of the electron self-energy measured in angle-resolved photoemission spectroscopy (ARPES) are well reproduced in our calculations. Our results provide a quantitative evidence for strong e-ph interactions in parent cuprates and refine existing models by showing the importance of nonbonding orbitals and coupling with apical oxygen lattice vibrations.   

Electronic structure and magnetic properties of La3Ni2O7 under pressure

Following the recent report of superconductivity in the bilayer nickelate La₃Ni₂O₇ under pressure, in this talk we will present an analysis of the electronic and magnetic properties of the compound as a function of pressure using density functional theory-based methods. At the bare DFT level, the electronic structure of the ambient and high-pressure phase of La₃Ni₂O₇  is qualitatively similar. Upon including local correlation effects within DFT+U and allowing for magnetic ordering, we find a delicate interplay between pressure and electronic correlations. Within the pressure-correlations phase space, we identify a region (at U values consistent with constrained RPA calculations) characterized by a spin-state transition with increasing pressure, where the ground state of the material changes from a high-spin A-type antiferromagnet to a low-spin G-type antiferromagnet with contrasting electronic structures. While the energy landscape of this material is rich, with many competing magnetic states, we find a common thread to be that all of these different states are driven by the Ni d_x2-y2 orbitals. The electronic structure of pressurized La₃Ni₂O₇ will be compared with that of other members of the family of superconducting layered nickelates, focusing on the similarities and differences with cuprate physics.   

Nickelate superconductivity without doping at 100 GPa in PrNiO2

The discovery of superconductivity in infinite layer nickelates [1] has raised the hope for a better understanding of superconductivity in strongly correlated systems. Dynamical vertex approximation (DΓA) successfully predicted [2] the experimental phase diagram [3]. When applying a pressure of 12 GP, the superconducting critical temperature (T_c) of PrNiO₂ further increases to over 30 K [4]. 

Here we show in DΓA calculations [5] that even higher T_c's are possible if the ratio bandwidth-to-interaction is increased [5]. One way to achieve this is pressure, were we find (i) good agreement with [4], (ii) a further increase of T_c at higher pressures, and (iii) that superconductivity is possible even without doping in PrNiO₂ at a pressure slightly above 100 GPa. The last is due to the self-doping effect of the electron pockets. Another promising route we [5] identified to increase the bandwidth and T_c is to move from 3d nickelates to 4d palladates.

[1]  D. Li et al., Nature 573, 624 (2019).

[2] M. Kitatani et al., npj Quantum Materials 5, 59 (2020).

[3]  K. Lee et al. arXiv:2203.02580

[4] N. N. Wang et al, Nature Communications 13, 4367 (2022).

[5] M. Kitatani et al., Phys. Rev. Lett. 130, 166002 (2023).   

Towards predictive ab initio methods for unconventional superconductivity: a study of multilayer cuprates.

High-temperature n-layer cuprate superconductors have the remarkable universal feature that the maximum transition temperature T_C is always obtained for the tri-layer compound. It remains unclear how the recent breakthroughs [1,2], highlighting the relation of the charge transfer gap (CTG) and the spin-exchange J with the pairing density, can be related to this universality. By integrating an exact diagonalization solver to a density functional theory plus cluster dynamical mean-field theory framework [3], we carry unprecedented charge self-consistent calculations for n=1-5 multilayer cuprates. Remarkably, the undoped compounds already host a peculiar behavior as a function of n: the CTG first decreases until reaching a minimum at n=3, and then stabilizes. The CTG is smaller in the inner CuO₂ planes, and consequently the spin exchange J is larger as compared to the outer planes, which corroborates the experimental evidence of stronger antiferromagnetic spin fluctuations in the inner planes. Most importantly, our work paves the way towards ab initio material-specific predictions of the superconducting order parameter.

[1] N. Kowalski et al., PNAS 118 (2021)

[2] S. M. O’Mahony et al., PNAS 119 (2022)

[3] K. Haule et al., PRB 81 (2010)