arXiv subjects

Karsten Held

Publications and source records attributed to Karsten Held.

At least 19 recordsLinked to original sources

arXiv2026

Two distinct gap structures in the mid-infrared optical conductivity of the Hubbard model

Mid-infrared (MIR) optical conductivities in cuprate superconductors show universal features. In this study, we demonstrate that these originate from two distinct gaps: the pseudogap mediated by antiferromagnetic spin fluctuations and the Mott-Hubbard gap. The MIR spectra from these two gaps show a characteristic and distinct shape and doping dependence, and can thus be distinguished. Specifically, the Mott-Hubbard correlations, while rendering a peak in the visible spectrum for small dopings, yield a broad optical response starting in the MIR when a ``waterfall'' develops in the one-particle spectrum at larger dopings. The numerically and analytically determined doping-dependence of both gaps consistently reproduce experiments, and provide a unified microscopic understanding of the cuprate MIR optical conductivity.

cond-mat.str-el↗

arXiv2026

Tuning crystal-fields by He-irradiation and orbital Widom line in SrVO$_3$ films

Helium-ion irradiation of epitaxial SrVO$_3$/SrTiO$_3$ films causes a metal-insulator transition, so far attributed to a Mott localization driven by a reduced kinetic energy. Using density-functional theory plus dynamical mean-field theory, we show that the driving mechanism is instead the crystal-field splitting generated by the irradiation-induced tetragonal expansion, not the interaction-to-bandwidth ratio. The resulting $c$-axis vs. temperature phase diagram mirrors that of the one-band Hubbard model, but its critical end-point spawns an orbital Widom line, rooted in an anomalous compressibility of orbital, rather than charge occupation. At an effectively quarter filling, superexchange-like processes favor orbital over magnetic long-range order. Our results semi-quantitatively reproduce the fluence-dependent spectral gaps and transition thresholds reported experimentally, establishing ion implantation as a route to chemically expand correlated materials.

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arXiv2026

Heterostructuring as Gateway to Electron Doping of Nickelate Superconductors

Despite enormous expenditures in the research field, the electron-doped side of nickelate superconductors remains uncharted territory. Substituting the trivalent rare-earth cations by a tetravalent one hitherto failed. Here, we demonstrate by first-principles calculations a disorder-free route to electron dope Ruddlesden-Popper nickelates. When intercalating wide-band-gap insulating layers such as La$X$O$_3$ ($X$=Al, Ga, Sc) into La$_2$NiO$_4$, the extra (LaO)$^+$ layers act as electron donors, releasing carriers into the Ni-3$d$ orbitals. This electron doping puts La$_2$NiO$_4$:La$_2$AlO$_4$ naturally in the optimal region for $d_{x^2-y^2}$-wave superconductivity with T$_c$ exceeding 50 K. The same concept also allows us to electron dope La$_3$Ni$_2$O$_7$, the superconductor in the limelight.

cond-mat.supr-con↗

arXiv2026

Nodal superconductivity with spin-triplet component in a noncentrosymmetric weakly-correlated metal

Although Cooper pairs in superconductors generally condense into a spin-singlet state, spin-triplet superconductivity has attracted sustained interest for dissipationless spin transport and topological quantum technologies. Noncentrosymmetric superconductors provide a promising route to triplet pairing because antisymmetric spin-orbit coupling (ASOC) can mix spin-singlet and spin-triplet states. To date, the strongest evidence for such mixed-parity superconductivity has been reported in heavy-fermion systems, where strong electronic correlations obscure the role of ASOC. Whether ASOC alone can support a substantial spin-triplet component therefore remains unresolved. Here we show that the weakly-correlated noncentrosymmetric superconductor Nb$_{18}$Re$_{82}$ (Nb-Re) hosts a mixed-parity superconducting state with a substantial spin-triplet contribution. Low-temperature scanning tunnelling spectroscopy on single crystals with different crystallographic orientations reveals distinct superconducting spectra. A symmetry-constrained analysis shows that the spectroscopic dataset is explained by an order parameter combining a nodal spin-singlet component with a spin-triplet contribution reaching up to half of the singlet amplitude. These findings resolve the debated pairing symmetry of Nb-Re and demonstrate that ASOC alone can foster triplet pairing. More broadly, they establish orientation-resolved tunnelling spectroscopy as a route to identifying mixed-parity superconducting states and suggest that triplet superconductivity may be more widespread among noncentrosymmetric materials than previously recognized.

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arXiv2026

Emergence of spin entanglement with the pseudogap onset in the Fermi-Hubbard model

Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

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arXiv2026

Beyond the conventional Emery model: crucial role of long-range hopping for cuprate superconductivity

The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter.

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arXiv2026

Symmetric estimator for discrete self-energy of discrete many-body systems

We derive a discrete spectral representation of the single-particle self-energy using a discrete evaluation of Kugler's symmetric improved estimator. Our construction can be used on both the real and the complex (Matsubara) frequency axis. It is guaranteed to remain causal at the numerical level, in contrast to standard approaches that may generate unphysical negative spectral weight or require additional broadening. Our representation can be used for any Hamiltonian; here we apply it to quantum impurity models and in dynamical mean-field theory. The latter is formulated with a discrete hybridization function throughout its self-consistency loop. In both cases and across various numerical methods, we obtain significantly improved accuracy for a range of impurity properties.

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arXiv2026

Unconventional plasmon dynamics due to strong correlations in Sr$_2$RuO$_4$

Plasmon modes, their dispersion, and the onset of damping when approaching the electron-hole continuum are well understood when electron correlations are weak. However, we know little about how this picture is modified and what additional features emerge in strongly correlated materials. Here, we present a fully ab initio approach to plasmon excitations that combines density functional theory with dynamical mean-field theory, and we use it to reconcile controversial electron energy-loss spectroscopy results in Sr$_2$RuO$_4$. In particular, we show that electronic correlations reproduce the plasmon dispersion, while generating a large intrinsic width already below the electron-hole continuum. An additional high-energy peak reflecting transitions between incoherent features and a sharp increase of the plasmon's energy-momentum dispersion, akin to waterfalls in photoemission spectroscopy, are identified as genuine correlation effects.

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arXiv2025

Substrate and cation engineering for optimizing superconductivity in infinite-layer nickelates

In a recent experiment [Nature 642, 58 (2025)], a new record for the superconducting critical temperature $T_c$ among infinite-layer nickelates has been reported in doped SmNiO$_2$. Here, we use the cutting-edge dynamical vertex approximation (D$\Gamma$A), and qualitatively as well as quantitatively reproduce the $T_c$ vs. doping dome for this compound. Encouraged by this, we go further and identify a path towards realizing even higher $T_c$'s by changing the cation along the line Nd$\rightarrow$Sm$\rightarrow$Y$\rightarrow$Lu with matching substrates. The successively smaller cation radius allows for smaller lattice constants of the substrate. This in turn increases the in-plane hopping and thus eventually $T_c$.

cond-mat.supr-con↗

arXiv2025

Surfaces and interfaces of infinite-layer nickelates studied by dynamical mean-field theory

Infinite-layer nickelate superconductors are typically synthesized as thin films and thus include, besides the more bulk-like inner layers, distinct surface and interface layers in contact with the vacuum and substrate, respectively. Here, we employ density-functional theory and dynamical mean-field theory to investigate how electronic correlations influence these surface and interface regions. Our results show that electronic correlations can significantly modify the electronic structure, even driving surface layers into a Mott-insulating state with a 3$d^8$ electronic configuration. Moreover, surface termination effects induce a polar field that can shift the $\Gamma$ and $A$ pocket above the Fermi level, even for the undoped parent compound NdNiO$_2$. Finally, for an $n$-type interface, often synthesized experimentally, we find the Ti 3$d$ orbitals to become electron doped.

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arXiv2025

Lattice dynamics of the infinite-layer nickelate LaNiO$_2$

Infinite-layer (IL) nickelates have rapidly emerged as a new class of superconductors. However, due to the technical challenges of their topotactic synthesis, they have so far been realized primarily as thin films or polycrystalline powder samples, limiting comprehensive investigations of fundamental physical properties such as the lattice dynamics. Here, we present a time-of-flight inelastic neutron scattering study on a sample composed of a large number of co-aligned bulk crystals of the IL nickelate LaNiO$_2$. We observe several dispersive phonon branches, which are in good agreement with lattice dynamical calculations based on density-functional perturbation theory. In addition, we compare the characteristics of selected LaNiO$_2$ phonon modes to those of isostructural cuprate superconductors. Our findings provide a reference point for future experimental and theoretical efforts aimed at understanding the interplay between lattice dynamics and electronic properties in IL nickelates.

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arXiv2025

Entanglement across scales: Quantics tensor trains as a natural framework for renormalization

Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension, a measure of length scale entanglement, to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semi-analytical treatments. We present our results for the one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the 2n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function.

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arXiv2025

Weyl nodes in CeRu$_4$Sn$_6$ studied by dynamical mean-field theory

The heavy fermion compound CeRu$_4$Sn$_6$ was recently shown to exhibit a spontaneous nonlinear Hall effect, indicating its topological nature. This is consistent with the lack of inversion symmetry that allows for the existence of Weyl nodes. Here, we employ density functional theory combined with dynamical mean-field theory, which is state-of-the-art for strongly correlated materials, and study the topology of CeRu$_4$Sn$_6$. We find five inequivalent Weyl nodes of either type I or II, each having either eight or sixteen symmetry-related replicas. These Weyl nodes bridge the Kondo insulating gap, which is a direct but not an indirect gap. The Weyl points closest to the Fermi level are situated only 0.5 meV below it, and have a very flat dispersion. Our ab initio results establish CeRu$_4$Sn$_6$ as a model system for investigating the interplay between strong electronic correlations and nontrivial topology. These findings provide a theoretical foundation for future studies of quantum transport and interaction-driven topological phases in heavy-fermion systems.

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arXiv2025

Diagnosing phase transitions through time-scale entanglement

Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is accessible through quantics tensor train diagnostics (QTTD), where the bond dimension of an $n$-particle correlator encodes the coupling between temporal scales. Our central result is that time-scale entanglement is generically enhanced in the vicinity of phase transitions and crossovers. At quantum critical points, it becomes scale-invariant. We demonstrate time-scale entanglement across a range of systems, including finite-size Hubbard rings, the transverse-field Ising model, the single-impurity Anderson model, and the Mott transition in the Hubbard model. Remarkably, the enhanced time-scale entanglement is largely independent of the specific observable, establishing QTTD as a universal and unbiased diagnostic of criticality.

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arXiv2025

Two-site entanglement in the two-dimensional Hubbard model

The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying distance, in the Hubbard model at weak coupling. This allows us to investigate the spatial structure of entanglement in dependence of interaction strength, electron filling, and temperature. We compare results from different entanglement measures, and benchmark against quantum Monte Carlo.

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arXiv2025

Topotactical Hydrogen Induced Single-Band $d$-wave Superconductivity in La$_2$NiO$_4$

La$_2$NiO$_4$ is an antiferromagnetic insulator with a structural resemblance to its cuprate counterpart, La$_2$CuO$_4$. However, La$_2$CuO$_4$ has a Cu$^{2+}$ or 3$d^9$ electronic configuration that needs to be hole or electron doped for superconductivity, whereas La$_2$NiO$_4$ is 3$d^8$ with divalent Ni$^{2+}$. Making a cuprate analog through conventional electron doping is impractical due to the rarity of tetravalent substituents for trivalent La. Here, we propose an alternative route: intercalating topotactical hydrogen, which is possible through electric-field-controlled protonation and transforms La$_2$NiO$_4$ into a 3$d_{x^2-y^2}$ single-band two-dimensional antiferromagnetic Mott insulator analogous to La$_2$CuO$_4$. This we find through density-functional theory and dynamical mean-field theory calculations. The furthergoing dynamical vertex approximation predicts that H-La$_2$NiO$_4$ can host $d$-wave superconductivity under 15\% hole doping with a critical temperature above 20\,K. Our findings not only suggest a new method for tuning the electronic structure of layered nickelates but also provide theoretical evidence for a new nickelate superconductor, awaiting experimental synthesis.

cond-mat.supr-con↗

arXiv2025

Entanglement in the pseudogap regime of cuprate superconductors

We find a strongly enhanced entanglement within the pseudogap regime of the Hubbard model. This entanglement is estimated from the quantum Fisher information and, avoiding the ill-conditioned analytical continuation, the quantum variance. Both are lower bounds for the actual entanglement that can be calculated from the (antiferromagnetic) susceptibility, obtained here with the dynamical vertex approximation. Our results qualitatively agree with experimental neutron scattering experiments for various cuprates. Theory predicts a $\ln(1/T)$ divergence of the entanglement for low temperatures $T$, which is however cut-off by the onset of superconductivity.

cond-mat.str-el↗

arXiv2025

Superconducting phase diagram of finite-layer nickelates Nd$_{n+1}$Ni$_n$O$_{2n+2}$

Following the successful prediction of the superconducting phase diagram for infinite-layer nickelates, here we calculate the superconducting $T_{\mathrm{c}}$ vs. the number of layers $n$ for finite-layer nickelates using the dynamical vertex approximation. To this end, we start with density functional theory, and include local correlations non-perturbatively by dynamical mean-field theory for $n=2$ to 7. For all $n$, the Ni $d_{x^2-y^2}$ orbital crosses the Fermi level, but for $n>4$ there are additional $(\pi, \pi)$ pockets or tubes that slightly enhance the layer-averaged hole doping of the $d_{x^2-y^2}$ orbitals beyond the leading $1/n$ contribution stemming from the valence electron count. We finally calculate $T_{\mathrm{c}}$ for the single-orbital $d_{x^2-y^2}$ Hubbard model by dynamical vertex approximation.

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