arXiv subjects

Karsten Held

Publications and source records attributed to Karsten Held.

At least 55 records · Page 3Linked to original sources

arXiv2023

No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an $\textit{ab initio}$ derived two-band model of the Cu $e_g$ orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin-singlet $d$-wave superconductivity at $T_{\mathrm{c}}\geq300$ K if the system is put close enough to a magnetic instability.

cond-mat.supr-con↗

arXiv2023

Electronic structure of the putative room-temperature superconductor Pb$_9$Cu(PO$_4$)$_6$O

A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf 33}, 61 (2023)] provides some experimental indications that Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with $x$ -- very similar to experiment. The DFT electronic structure shows Cu$^{2+}$ in a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This puts Pb$_{9}$Cu(PO$_4$)$_6$O in an ultra-correlated regime and suggests that, without doping, it is a Mott or charge transfer insulator. If doped such an electronic structure might support flat-band superconductivity or an correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.

cond-mat.supr-con↗

arXiv2023

A functional-analysis derivation of the parquet equation

The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger--Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green's functions potentially leading to a classification of these in terms of their (ir)reducible components.

cond-mat.str-el↗

arXiv2023

Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O: a Mott or charge transfer insulator in need of further doping for (super)conductivity

We briefly review the status quo of research on the putative superconductor Pb$_9$Cu(PO$_4$)$_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from substituting Pb by Cu and thus differs from LK-99) is required to make it metallic and potentially superconducting.

cond-mat.supr-con↗

arXiv2023

Chiral magnetism and ordering of oxygen vacancies in SrTiO$_{2.5}$

Oxygen vacancies in the perovskite insulator SrTiO$_3$ free electrons that couple with other physical degrees of freedom such as lattice, orbital, and spin. This leads to the emergence of exotic quantum states such as superconductivity and unusual ferromagnetism. We perform density-functional theory and dynamical mean-field theory calculations and demonstrate that the orientation and ordering of the TiO$_5$ pentahedra plays a crucial role. Specifically, for vacancy-rich SrTiO$_{3-δ}$ ($δ\sim$0.5), we find a chiral ordering of the TiO$_5$ pentahedra in a sixfold superlattice. This chiral structure is accompanied by a chiral magnetic state with a net moment in the (111) direction at room temperature, which can explain several experimental observations.

cond-mat.str-el↗

arXiv2023

Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering

The mechanism of the pseudogap observed in hole-doped cuprates remains one of the central puzzles in condensed matter physics. We analyze this phenomenon via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which would open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry trigger a very different mechanism: a large imaginary part of the spin-fermion vertex promotes damping of antinodal fermions and, at the same time, protects the nodal Fermi arcs (antidamping). Our analysis naturally explains puzzling features of the pseudogap observed in experiments, such as Fermi arcs being cut off at the antiferromagnetic zone boundary and the subordinate role of hot spots.

cond-mat.str-el↗

arXiv2023

Optimizing superconductivity: from cuprates via nickelates to palladates

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature $T_{\rm c}$ as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high $T_{\rm c}$ to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr$_2$PdO$_3$ and $A^{\prime}_2$PdO$_2$Cl$_2$ ($A^{\prime}$=Ba$_{0.5}$La$_{0.5}$), to be virtually optimal, while others, such as NdPdO$_2$, are too weakly correlated.

cond-mat.supr-con↗

arXiv2023

Transition from Diffusive to Superdiffusive Transport in Carbon Nanotube Networks via Nematic Order Control

The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy, but other types of behaviours are suppressed by disorder. Here, we compare the dynamics of quasiparticles under strong electric fields in aligned and random CNT networks using a combination of terahertz emission and photocurrent experiments and out-of-equilibrium numerical simulations. We find that the degree of alignment strongly influences the excited quasiparticles' dynamics, rerouting the thermalisation pathways. This is, in particular, evidenced in the high-energy, high-momentum electronic population (probed through the formation of low energy excitons via exciton impact ionization) and the transport regime evolving from diffusive to superdiffusive.

cond-mat.mtrl-sci↗

arXiv2023

Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model

Three-particle correlators are relevant for, among others, Raman, Hall and non-linear responses. They are also required for the next order of approximations extending dynamical mean-field theory diagrammatically. We present a general formalism on how to treat these three-particle correlators and susceptibilities, and calculate the local three-particle response of the Anderson impurity model numerically. We find that genuine three-particle vertex corrections are sizable. In particular, it is not sufficient to just take the bare bubble terms or corrections based on the two-particle vertex. The full three-particle vertex must be considered.

cond-mat.str-el↗

arXiv2023

Absence of electron-phonon-mediated superconductivity in hydrogen-intercalated nickelates

A recent experiment [X. Ding et al., Nature 615, 50 (2023)] indicates that superconductivity in nickelates is restricted to a narrow window of hydrogen concentration: 0.22 < x < 0.28 in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$H$_{x}$. This reported necessity of hydrogen suggests that it plays a crucial role for superconductivity, as it does in the vast field of hydride superconductors. Using density-functional theory and its extensions, we explore the effect of topotactic hydrogen on the electronic structure and phonon-mediated superconductivity in nickelate superconductors. Our calculations show that the electron-phonon coupling in hydrogen-intercalated nickelates is not strong enough to drive the electron pairing, and thus cannot explain the reported superconductivity.

cond-mat.supr-con↗

arXiv2023

Topotactic-hydrogen forms chains in $AB$O$_2$ nickelate superconductors

Despite enormous experimental and theoretical efforts, obtaining generally accepted conclusions regarding the intrinsic magnetic and electronic properties of superconducting nickelates remains exceptionally challenging. Experiments show a significant degree of uncertainty, indicating hidden factors in the synthesized films, which call for further investigations. One of those "hidden factors" is the possibility of intercalating hydrogen during the chemical reduction process from Nd(La)NiO$_3$ to Nd(La)NiO$_2$ using CaH$_2$. While hydrogen has been detected in experimental samples, not much is known about its distribution through the crystal and its influence on the electronic environment. Here, we show the tendency toward the formation of one-dimensional hydrogen chains in infinite-layers LaNiO$_2$ superconductors using density-functional theory (DFT) supplemented by dynamical mean-field theory (DMFT). The formation of such hydrogen chains induces a coexistence of different oxidation states of Ni and competing magnetic phases, and possibly explains the recently observed charge order states in nickelate superconductors. Furthermore, it contributes to the difficulty of synthesizing homogeneous nickelates and determining their ground states. The smoking gun to detect excess hydrogen in nickelates are flat phonon modes, which are infrared active and quite insensitive to the exact arrangement of the H atoms.

cond-mat.mtrl-sci↗

arXiv2022

Aberration of the Green's function estimator in hybridization expansion continuous-time quantum Monte Carlo

We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuous-time quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implications as well as solutions. This issue does not occur when using worm sampling or in the presence of continuous baths. However certain energy spectra can be inherently close to a discrete limit, and we explain why autocorrelation times can become very large in these cases.

cond-mat.str-el↗

arXiv2022

Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters

We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show pronounced changes in the double occupation and spin energy. This analysis reveals that the loss of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections.

cond-mat.str-el↗

arXiv2022

Beyond DMFT: Spin Fluctuations, Pseudogaps and Superconductivity

This Chapter of the Jülich Summer School 2022 provides for a first reading on diagrammatic extensions of dynamical-mean-field theory and their application to spin fluctuations, pseudogap physics and supercondcutivtiy. The contents is as follows: 1 Introduction 2 Dynamical vertex approximation 3 Ladder dynamical vertex approximation 4 Hubbard model, cuprates and nickelates 5 Spin fluctuations 6 Pseudogap 7 Superconductivity 8 Conclusion and outlook

cond-mat.str-el↗

arXiv2022

Merging numerical renormalization group and intermediate representation to compactify two- and three-point correlators

The vanguard of many-body theory is nowadays dealing with the full frequency dynamics of n-point Green's functions for n higher than two. Numerically, these objects easily become a memory bottleneck, even when working with discrete imaginary-time Matsubara frequencies. Here, we use the intermediate representation (IR) to compactify the two-point Green's function and three-point Fermion-Bose vertex directly on the real frequency axis, on the basis of numerical renormalization group (NRG) data. We empirically observe an upper bound of the relative error when comparing the IR reconstructed signal with the original NRG data, and demonstrate that a IR compacification is possible.

cond-mat.str-el↗

arXiv2022

Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states

We derive the exact reduced density matrix for the electrons in an analytically solvable electron-phonon model. Here, the electrons are described as a Luttinger liquid that is coupled to Einstein phonons. We further derive analytical expressions for the electron-phonon entanglement, its spectrum and mutual information at finite and zero temperature as well as for excited states. The entanglement entropy is additive in momentum for the quasi-particle excited states, but not in the electron-phonon coupled eigenmodes of the system.

cond-mat.str-el↗

arXiv2022

Signatures of topotactic hydrogen in nickelate superconductors

Superconductivity has entered the nickel age marked by enormous experimental and theoretical efforts. Notwithstanding, synthesizing nickelate superconductors remains extremely challenging, not least due to incomplete oxygen reduction and topotactic hydrogen. Here, we present density-functional theory calculations, identify a phonon mode as a possible indication for topotactic hydrogen and discuss the charge redistribution patterns around oxygen and hydrogen impurities.

cond-mat.supr-con↗

arXiv2022

Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.

cond-mat.str-el↗