arXiv subjects

Thomas A. Maier

Publications and source records attributed to Thomas A. Maier.

At least 37 records · Page 2Linked to original sources

arXiv2023

Trends in electronic structures and $s_{\pm}$-wave pairing for the rare-earth series in bilayer nickelate superconductor $R_ 3$Ni$_2$O$_7$

The recent discovery of pressure-induced superconductivity in the bilayer La$_3$Ni$_2$O$_7$ (LNO) has opened a new platform for the study of unconventional superconductors. In this publication, we investigate theoretically the whole family of bilayer 327-type nickelates $R_3$Ni$_2$O$_7$ ($R$ = Rare-earth elements) under pressure. From La to Lu, the lattice constants and volume decrease, leading to enhanced in-plane and out-of-plane hoppings, resulting in an effectively reduced electronic correlation $U/W$. Furthermore, the Ni's $t_{2g}$ states shift away from the $e_g$ states, while the crystal-field splitting between $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ is almost unchanged. In addition, six candidates were found to become stable in the Fmmm phase, with increasing values of critical pressure as the atomic number increased. Similar to the case of LNO, the $s_{\pm}$-wave pairing tendency dominates in all candidates, due to the nesting between the {\bf M}=$(π,π)$ and the {\bf X}=$(π,0)$ and {\bf Y}=$(0,π)$ points in the Brillouin zone. Then, $T_c$ is expected to decrease as the radius of rare-earth (RE) ions decreases. Our results suggest that LNO is already the "optimal" candidate, with Ce a close competitor, among the whole RE bilayer nickelates, and to increase $T_c$ we suggest to grow on special substrates with larger in-plane lattice spacings.

cond-mat.supr-con↗

arXiv2023

Electronic structure, magnetic correlations, and superconducting pairing in the reduced Ruddlesden-Popper bilayer La$_3$Ni$_2$O$_6$ under pressure: different role of $d_{3z^2-r^2}$ orbital compared with La$_3$Ni$_2$O$_7$

The recent discovery of superconductivity in bilayer La$_3$Ni$_2$O$_7$ (327-LNO) under pressure stimulated much interest in layered nickelates. However, superconductivity was not found in another bilayer nickelate system, La$_3$Ni$_2$O$_6$ (326-LNO), even under pressure. Using density functional theory and the random phase approximation (RPA), we systematically investigate 326-LNO under pressure. The large crystal-field splitting between the $e_g$ orbitals caused by the missing apical oxygen moves the $d_{3z^2-r^2}$ orbital farther away from the Fermi level, implying that the $d_{3z^2-r^2}$ orbital plays a less important role in 326-LNO than in 327-LNO. This also results in a smaller bandwidth for the $d_{x^2-y^2}$ orbital and a reduced energy gap for the bonding-antibonding splitting of the $d_{3z^2-r^2}$ orbital in 326-LNO, as compared to 327-LNO. Moreover, the in-plane hybridization between the $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals is found to be small in 326-LNO, while it is much stronger in 327-LNO. The weak inter-layer coupling suggests that $s_{\pm}$-wave pairing is unlikely in 326-LNO. The robust in-plane ferromagnetic coupling also suggests that d-wave superconductivity, which is usually caused by antiferromagnetic fluctuations of the $d_{x^2-y^2}$ orbital, is also unlikely in 326-LNO. These conclusions are supported by our many-body RPA calculations of the pairing behavior. Contrasting with the cuprates, for the bilayer cuprate HgBa$_2$CaCu$_2$O$_6$, we find a strong "self-doping effect" of the $d_{x^2-y^2}$ orbital under pressure, with the charge of Cu being reduced by approximately 0.13 electrons from 0 GPa to 25 GPa. In contrast, we do not observe such a change in the electronic density in 326-LNO under pressure, establishing another important difference between the nickelates and the cuprates.

cond-mat.supr-con↗

arXiv2023

Weak-Coupling Theory of Neutron Scattering as a Probe of Altermagnetism

Inelastic neutron scattering provides a powerful probe of the magnetic excitations of quantum magnets. Altermagnets have recently emerged as a new class of magnets with vanishing net magnetization characteristic of antiferromagnets and with a spin-split electronic structure typical of ferromagnets. Here we introduce a minimal Hubbard model with two-sublattice orthorhombic anisotropy as a framework to study altermagnetism. Using unrestricted Hartree-Fock calculations, we find an altermagnetic state for this model that evolves from a metallic state to an insulating state with increasing Hubbard-$U$ Coulomb repulsion. We then examine the inelastic neutron scattering response in these states using random-phase approximation calculations of the dynamic spin susceptibility $χ''({\bf q}, ω)$. We find that the magnetic excitation spectrum depends on its chirality for ${\bf q}$ along certain directions in reciprocal space, an observation that may be used in inelastic neutron scattering experiments as a probe of altermagnetism.

cond-mat.str-el↗

arXiv2023

Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

cond-mat.str-el↗

arXiv2022

Spin singlet topological superconductivity in the attractive Rashba Hubbard model

Fully gapped, spin singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. We generally find that the Rashba coupling has a beneficial effect towards s-wave superconductivity. In the presence of a finite Zeeman field, when superconductivity is suppressed by Pauli pair-breaking, the Rashba coupling counteracts the spin imbalance created by the Zeeman field by mixing the spins, and thus restores superconductivity at finite temperatures. We show that this favorable effect of the spin-orbit coupling is traced to a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. Moreover, by inspecting the Fermi surface of the interacting model, we show that for sufficiently large Rashba coupling and Zeeman field, the superconducting state is expected to be topologically non-trivial.

cond-mat.supr-con↗

arXiv2022

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

There is growing evidence that the hole-doped single-band Hubbard and $t$-$J$ models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

cond-mat.str-el↗

arXiv2022

Stripe correlations in the two-dimensional Hubbard-Holstein model

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, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband 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 like the next-nearest-neighbor hopping $t^\prime$ or phonon energy $Ω$. Our results help elucidate how the $e$-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-$T_\mathrm{c}$ cuprates.

cond-mat.str-el↗

arXiv2022

Strongly anisotropic electronic and magnetic structures in oxide dichlorides RuOCl$_2$ and OsOCl$_2$

Here, using density functional theory and density matrix renormalization group methods, we investigate the electronic and magnetic properties of RuOCl$_2$ and OsOCl$_2$ with $d^4$ electronic configurations. Different from a previous study using VOI$_2$ with $d^1$ configuration, these systems with $4d^4$ or $5d^4$ do not exhibit a ferroelectric instability along the $a$-axis. Due to the fully-occupied $d_{xy}$ orbital in RuOCl$_2$ and OsOCl$_2$, the Peierls instability distortion disappears along the $b$-axis, leading to an undistorted I${\rm mmm}$ phase (No. 71). Furthermore, we observe strongly anisotropic electronic and magnetic structures along the $a$-axis. The large crystal-field splitting energy (between $d_{xz/yz}$ and $d_{xy}$ orbitals) and large hopping between nearest-neighbor Ru and Os atoms suppresses the spin-orbital effect in $M$OCl$_2$ ($M$ = Ru or Os) with electronic density $n = 4$, resulting in a spin-1 system instead of a $J = 0$ singlet ground state. Moreover, we find staggered antiferromagnetic order with $π$ wavevector along the $M$-O chain direction ($a$-axis) while the magnetic coupling along the $b$-axis is weak. Based on Wannier functions from first-principles calculations, we calculated the relevant hopping amplitudes and crystal-field splitting energies of the $t_{2g}$ orbitals for the Os atoms to construct a multi-orbital Hubbard model for the $M$-O chains. Staggered AFM with $\uparrow$-$\downarrow$-$\uparrow$-$\downarrow$ spin structure dominates in our DMRG calculations, in agreement with DFT calculations.

cond-mat.str-el↗

arXiv2022

Fluctuating intertwined stripes in the strange metal regime of the Hubbard model

Strongly correlated electron systems host a variety of poorly understood correlations in their high temperature normal state. Unlike ordered phases defined by order parameters, these normal state phases are often defined through unconventional properties such as strange metallic transport or spectroscopic pseudogaps. Characterizing the microscopic correlations in the normal state is necessary to elucidate mechanisms that lead to these properties and their connection to ground state orders. Here we establish the presence of intertwined charge and spin stripes in the strange metal normal state of the Hubbard model using determinant quantum Monte Carlo calculations. The charge and spin density waves constituting the stripes are fluctuating and short-ranged, yet they obey a mutual commensurability relation and remain microscopically interlocked, as evidenced through measurements of three-point spin-spin-hole correlation functions. Our findings demonstrate the ability of many-body numerical simulations to unravel the microscopic correlations that define quantum states of matter.

cond-mat.str-el↗

arXiv2022

Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit

The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper-oxygen layers in these materials. Finite cluster methods typically find that spin and charge stripe order dominates, while embedded quantum cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calculation for the Hubbard model. This discovery demonstrates that striped states survive in the thermodynamic limit and allows us to study their influence on the model's superconducting properties, where we find evidence for pair-density-wave correlations intertwined with the stripe correlations.

cond-mat.str-el↗

arXiv2021

Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wave like structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interacting due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave-vectors in the limit of weakly coupled ladders.

cond-mat.supr-con↗

arXiv2021

Superconductivity in the bilayer Hubbard model: Are two Fermi surfaces better than one?

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping $t_\perp$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Liftshiz transition and even when it becomes incipient. Here, we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust $s_\pm$ pairing correlations in the large $t_\perp$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased $T_c$. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.

cond-mat.str-el↗

arXiv2021

Pairing correlations in the cuprates: a numerical study of the three-band Hubbard model

We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an "optimal" value of the charge-transfer energy for the model where $T_c$ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.

cond-mat.supr-con↗

arXiv2020

Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates

The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO$_2$ planes. Here, we use a dynamic cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.

cond-mat.supr-con↗

arXiv2020

Effects of momentum-dependent quasiparticle renormalization on the gap structure of iron-based superconductors

We discuss the influence of momentum-dependent correlations on the superconducting gap structure in iron-based superconductors. Within the weak coupling approach including self-energy effects at the one-loop spin-fluctuation level, we construct a dimensionless pairing strength functional which includes the effects of quasiparticle renormalization. The stationary solution of this equation determines the gap function at $T_c$. The resulting equations represent the simplest generalization of spin fluctuation pairing theory to include the effects of an anisotropic quasiparticle weight. We obtain good agreement with experimentally observed anisotropic gap structures in LiFeAs, indicating that the inclusion of quasiparticle renormalization effects in the existing weak-coupling theories can account for the observed anomalies in the gap structure of Fe-based superconductors.

cond-mat.supr-con↗

arXiv2020

The overdoped end of the cuprate phase diagram

Studying the disappearance of superconductivity at the end of the overdoped region of the cuprate phase diagram offers a different approach for investigating the interaction which is responsible for pairing in these materials. In the underdoped region this question is complicated by the presence of charge and stripe ordered phases as well as the pseudogap. In the overdoped region the situation appears simpler with only a normal phase, a superconducting phase and impurity scattering. Here, for the overdoped region, we report the results of a combined dynamic cluster approximation (DCA) and a weak Born impurity scattering calculation for a $t-t'-U$ Hubbard model. We find that a decrease in the $d$-wave pairing strength of the two-particle scattering vertex is closely coupled to changes in the momentum and frequency structure of the magnetic spin fluctuations as the system is overdoped. Treating the impurity scattering within a disordered BCS $d$-wave approximation, we see how the combined effects of the decreasing $d$-wave pairing strength and weak impurity scattering lead to the end of the $T_c$ dome.

cond-mat.supr-con↗

arXiv2020

Continuous momentum dependence in the dynamical cluster approximation

The dynamical cluster approximation (DCA) is a quantum cluster extension to the single-site dynamical mean-field theory that incorporates spatially nonlocal dynamic correlations systematically and nonperturbatively. The DCA$^+$ algorithm addresses the cluster shape dependence of the DCA and improves the convergence with cluster size by introducing a lattice self-energy with continuous momentum dependence. However, we show that the DCA$^+$ algorithm is plagued by a fundamental problem when its self-consistency equations are formulated using the bare Green's function of the cluster. This problem is most severe in the strongly correlated regime at low doping, where the DCA$^+$ self-energy becomes overly metallic and local, and persists to cluster sizes where the standard DCA has long converged. In view of the failure of the DCA$^+$ algorithm, we propose to complement DCA simulations with a post-interpolation procedure for single-particle and two-particle correlation functions to preserve continuous momentum dependence and the associated benefits in the DCA. We demonstrate the effectiveness of this practical approach with results for the half-filled and hole-doped two-dimensional Hubbard model.

cond-mat.str-el↗

arXiv2019

DCA++: A software framework to solve correlated electron problems with modern quantum cluster methods

We present the first open release of the DCA++ project, a high-performance research software framework to solve quantum many-body problems with cutting edge quantum cluster algorithms. DCA++ implements the dynamical cluster approximation (DCA) and its DCA$^+$ extension with a continuous self-energy. The algorithms capture nonlocal correlations in strongly correlated electron systems, thereby giving insight into high-$T_c$ superconductivity. The code's scalability allows efficient usage of systems at all scales, from workstations to leadership computers. With regard to the increasing heterogeneity of modern computing machines, DCA++ provides portable performance on conventional and emerging new architectures, such as hybrid CPU-GPU, sustaining multiple petaflops on ORNL's Titan and CSCS' Piz Daint supercomputers. Moreover, we show how sustainable and scalable development of the code base has been achieved by adopting standard techniques of the software industry. These include employing a distributed version control system, applying test-driven development and following continuous integration.

physics.comp-ph↗