Johnston Research Group

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

P. Mai et al., Nature Communications 14, 2889 (2023) — Intertwined unidirectional spin- and charge modulations (e.g., stripes) are ubiquitous features of both the high-temperature superconducting cuprates. Here, we studied the spin and charge correlations of the electron-doped two-dimensional Hubbard model and contrasted them with the hole-doped case using the dynamical cluster approximation with a quantum Monte Carlo cluster solver. We found evidence for robust two-component charge correlations on the electron-doped side, consisting of superimposed checkerboard and stripe-like components. These charge correlations are further decoupled from any stripe-like modulations of the spins and instead coexist with short-range antiferromagnetic correlations, in contrast to the hole-doped case. Our results also agree well with observed the doping dependence of charge modulations.

Evidence for chiral d-wave superconductivity in a third of a monolayer of Tin

F. Ming et al., Nature Physics 19, 500 (2023) — Tin adatoms on a Si(111) substrate with a one-third monolayer coverage form a two-dimensional triangular lattice with one unpaired electron per site. These electrons order into an antiferromagnetic Mott-insulating state, but doping the Sn layer with holes creates a two-dimensional conductor that becomes superconducting at low temperatures. Although the pairing symmetry of the superconducting state is currently unknown, the combination of repulsive interactions and frustration inherent in the triangular adatom lattice opens up the possibility of a chiral order parameter. Collaborating with Prof. Weitering's group, we studied the superconducting state of Sn/Si(111) using scanning tunnelling microscopy, scanning tunnelling spectroscopy and quasiparticle interference imaging. We found evidence for a doping-dependent superconducting critical temperature with a fully gapped order parameter, the presence of time-reversal symmetry breaking, and a strong enhancement in zero-bias conductance near the edges of the superconducting domains. Our combined results suggest the superconduting state in Sn/Si(111) has an unconventional chiral d-wave superconductor.

Hybrid Monte Carlo study of charge order in BaBiO₃

B. Cohen-Stead et al., npj Computational Materials 9, 40 (2023) — The barium family of superconductors Ba_1-xK_xBiO₃ (BKBO) and Ba_1-xBi_xPbO₃ exhibit high-temperature superconductivity in proximity to a charge-density-wave (CDW) insulating phase, with a reported critical temperature of T_c = 32 K at x = 0.35 in BKBO. The underlying pairing mechanism in the superconducting phase, and its proximity to a charge ordered phase, remains unsettled. However, experimental results indicate the electron-phonon (e-ph) interactions may play an important role in explaing the low-energy physics. Here we study the CDW transition in BaBiO₃, the parent compound of the bismuthate superconductors. We simulate an effective electron-phonon model using a recently introduced hybrid quantum Monte Carlo method. Our multi-orbital model includes the Bi 6s and O 2p orbitals and a coupling to the Bi-O bond-stretching branch of optical phonons via the Su-Schrieffer–Heeger (SSH)-like modulation of the Bi-O hopping integral. Our results demonstrate that an SSH coupling mechanism to the bond-stretching optical oxygen modes accounts for all aspects of the CDW phase in this compound. Our work provides for a similar computationally rigorous solution of a model appropriate to the CDW phase of the bismuthates and may provide valuable insight into the origin of the superconducting phase in the barium family of superconductors.

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

Y. Shen et al., Phys. Rev. X 12, 011055 (2022); Y. Shen et al., Phys. Rev. X 13, 011021 (2023) We have recently identified a minimal model for the recently discovered low-valence superconducting nickelates. The Ni atoms in these materials have a smaller nuclear charge than Cu in cuprates, which would tend to increase the charge transfer energy. This expectation motivated extensive interest in determining the Mott-Hubbard versus charge-transfer nature of square-planar nickelates, with some researchers categorizing them as Mott-Hubbard systems, and others regarding them as cuprate analogs. We answered this question in a set of combined experimental and theoretical studies. First, we performed O K-edge RIXS measurements of La₄Ni₃O₈ alongside a cuprate La_2−xSr_xCuO₄ with equivalent effective doping (x = 1/3). The results established that low-valence nickelates are of mixed charge-transfer/Mott-Hubbard character with Coulomb repulsion being compatible to the charge-transfer energy. This endows these materials with partly (but not completely) cuprate-like properties and explains the moderate magnetic superexchange observed previously in these materials. Charge order is a ubiquitous feature in both the cuprate and nickelates, but the electronic character of this symmetry breaking is controversial. Therefore, we also studied La₄Ni₃O8’s charge ordered phase using Ni L₂-edge RIXS measurements and calculations. This work extended our model by introducing charge order via the application of a site-dependent potential difference and identified intertwined involvements of Ni 3d, 3d, and O 2p orbitals in the charge order. The Ni 3d x²−y² orbitals, strongly hybridized with planar O 2p orbitals, largely shape the spatial charge distribution and lead to a Ni site-centered charge order.

Stripe correlations in the Hubbard-Holstein model

S. Karakuzu et al., Communications Physics 5, 311 (2022) — Over the last decade, several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, but it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters.

The dynamical properties of doped corner-shared Cuprate spin chains

S. Li et al., Communications Physics 4, 217 (2021) — Although many experiments imply that oxygen orbitals play an essential role in the high-temperature superconducting cuprates, their precise role in collective spin and charge excitations and superconductivity is not yet fully understood. Here, we study the doping-dependent dynamical spin and charge structure factors of single and multi-orbital (pd) models for doped one-dimensional corner-shared spin-chain cuprates using determinant quantum Monte Carlo, Density Matrix Renormalization group, and exact diagonalization. In doing so, we provided detailed predictions for the electronic structure and dynamical spin and charge correlation functions of doped cuprate spin chains. We observe a particle-hole asymmetry in the orbital-resolved charge excitations, which is directly relevant to resonant inelastic x-ray scattering experiments and not captured by the single-band Hubbard model.

The structure of a Cooper pair in the cuprates

P. Mai et al., npj Quantum Materials 6, 26 (2021) — We performed the state-of-the-art dynamic cluster approximation (DCA) quantum Monte Carlo (QMC) calculations of the three-band Hubbard model. We then determined the structure of the Cooper pairs and thus obtained a non-perturbative picture of the pairing interaction from solving the Bethe-Salpeter equation. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. This rich orbital structure simplifies once we frame it in terms of the molecular orbitals of the Zhang-Rice Singlet (ZRS), and then is well compared with that from an effective single-band Hubbard model. Our results strongly support that, even when the oxygen orbitals contribute significantly to the low-energy electronic degrees of freedom, a single-band Hubbard model provides an adequate frame-work to understand the pairing in the cuprates.

Dynamical Mean-field theory on a quantum computer

T. Keen et al., Quantum Science and Technology 5, 035001 (2020) — We implemented a quantum-classical scheme for two-site dynamical mean-field theory (DMFT) applied to the single-band Hubbard model. These types of quantum-classical approaches can circumvent the exponential scaling inherent to classical algorithms, e.g. in storage requirements or computation time. The quantum part of the algorithm (i.e. the calculation of the impurity Green’s function in the time domain) was solved on one of IBM’s superconducting qubit chips. As a test case, we considered the Hubbard model. We found that the Trotter error introduced by approximating the time evolution operator produces unreliable updates in the impurity-bath hybridization parameter when calculated using methods proposed in the literature. This inaccuracy resulted in erroneous convergence in the DMFT loop, an issue that was compounded by noise in the quantum device. These results prompted us to employ a different method for updating the hybridization parameters, which allowed us to obtain convergence in the Mott insulating regime.

Accelerating lattice quantum Monte Carlo simulations using artificial neural networks

S. Li et al., Phys. Rev. B 100, 020302(R) (2019) — We designed artificial neural networks (ANNs) that predict with near-perfect accuracy state change probabilities in quantum Monte Carlo (QMC) simulations of many-body Hamiltonians and obtain an order of magnitude reduction in run time. This demonstration that machines can learn to perform efficient QMC simulations— without being provided with an underlying physics model and given only limited information about the configuration space—means the method can be easily generalized even to other challenging models, such as the Fermi-Hubbard model. The utility of this approach was demonstrated by integrating it into QMC simulations of the two-dimensional Holstein model describing interactions between electrons and lattice vibrations in materials. After training ANNs with data generated on small, inexpensive systems, researchers applied these ANNs to larger systems and achieved an order of magnitude speed-up in the QMC simulation. This capability allowed researchers using the model to access the Ising critical behavior of the metal-to-charge density wave (CDW) insulator transition, elucidating the universality class of this important phase transition.

Phase Diagram of the Holstein Model

P. M. Dee et al., Phys. Rev. B 99, 024514 (2019) — The Holstein model has long been used to study superconductivity, charge-density waves (CDW), and polarons. Much is known about the possible phases this model yields, yet there are very few studies reporting the full temperature-doping phase diagram. Within the weak coupling regime, we studied the temperature-filling phase diagram of the two-dimensional single-band Holstein model under the self-consistent Migdal approximation using our state-of-the-art numerical algorithm. Among our many findings is a superconducting T_c-dome away from half-filling. We show that this non-monotonicity stems from several competing factors related to the quasiparticle renormalization.

Probing multi-spinon excitations with RIXS

J. Schlappa et al., Nat. Commun. 9, 5394 (2018) — One-dimensional (1D) spin-1/2 magnetic insulators realize novel emergent quantum phenomena like quasiparticle fractionalization and quantum criticality. Their elementary magnetic excitations are spin-1/2 quasiparticles called spinons that typically are created in even numbers. While the continuum associated with two-spinon excitations is routinely observed, the study of higher multi-spinon states is ongoing. This study showed that four-spinon excitations can be accessed directly in a region of phase space clearly separated from the two-spinon continuum in Sr₂CuO₃ using RIXS. This observation is made possible by the nature of the correlation function probed by RIXS, and holds promise as a tool in the search for novel quantum states and quantum spin liquids.

Computing RIXS spectra using DMRG

Electron-lattice interactions in FeSe/STO interfaces

Theory of forward scattering in FeSe/STO interfaces

Using RIXS to probe electron-phonon interactions in quantum materials

S. Johnston et al., Nat. Commun. 7, 10563 (2016); W. S. Lee et al., Phys. Rev. Lett. 110, 265502 (2013) — Here, we exploited recent improvements in the resolution of RIXS experiments to examine electron-lattice interactions in the quasi-1D cuprate Li₂CuO₂ and Ca_2-xY_2+xCu₅O₁₀. we found that the dynamic electron-phonon (e-ph) coupling plays a key role in determining the fundamental electronic and magnetic properties of both of the materials. These studies highlight the power of RIXS for accessing and unraveling coupled collective excitations in quantum materials. In a recent collaboration [D. Meyers et al., PRL 121, 236802 (2018)] we extended this approach to measure e-ph interactions in ultrathin superlattices of SrIrO₃/SrTiO₃ (SIO/STO) Here, we identified a systematic evolution of the intensity of the phonon excitations with varying thicknesses of the SIO and STO layers. When combined with the observation of a negligible carrier doping into the STO layers, these results suggest that the e-ph coupling can be decoupled from doping. These results not only showcases RIXS's potential for probing interactions at buried interfaces, but also indicate a new method for engineering these interactions in superlattices.

Orbital-Selective Phases in multi-orbital Hubbard-Holstein models

S. Li et al., PRB 95, 121122(R) (2017); S. Li et al., PRB 97, 195116 (2017) — Researchers have recently begun focusing on electron-electron interactions in multiorbital systems like the Fe-based superconductors and discovered new phenomena like the orbital-selective Mott phase (OSMP). While these concepts have shaped our understanding of the enigmatic properties of these materials, little is known about how competition/cooperation with other factors like the electron-phonon (e-ph) interaction influences them. Here, we studied multi-orbital Hubbard-Holstein models using DMFT and DQMC. We found that the e-ph interaction, even at weak couplings, strongly modifies the phase diagrams of these models and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied OSMP.

Dynamics of quantum spin ladders

U. Kumar et al., PRB 99, 205130 (2019); A. Nocera et al., PRB 97, 195156 (2018) — Strongly correlated spin ladders are excellent platforms for studying quantum many-body phenomena such as high-T_c superconductivity. Recently, we have studied the dynamics of doped and undoped quantum spin ladders using multiple numerical and analytical methods. In doing so, we have provided detailed predictions for the spin and charge dynamical structure factors, as well as the resonant inelastic x-ray scattering intensity at the Cu L-edge. These studies provide a roadmap for future studies of the dynamical properties of spin ladders and their connection to unconventional superconductivity.

Non-linear electron-lattice interactions

S. Li et al. EPL 109, 27007 (2015) — Most models for electron-phonon interactions rely on linear models, where the electronic degrees of freedom couple to the linear lattice dispaclement. In this work, we examined nonlinear electron-phonon interactions, which are expected when the atomic displacments are large. We found additional nonlinear terms significantly alter the charge-density-wave and superconducting ordering tendencies predicted by the model. For example, the figure shows the CDW susceptibility for the half-filled Holstein model with linear and quadratic e-ph interactions. Here, we find that the CDW correlations predicted by the linear model are rapidly suppressed small quadratic interactions. Also see S. Li et al. PRB 92, 064301 (2015) and P. M. Dee et al Communications Physics, 3 45 (2022).