arXiv subjects

Karsten Held

Publications and source records attributed to Karsten Held.

At least 109 records · Page 6Linked to original sources

arXiv2019

Why the critical temperature of high-$T_{\rm c}$ cuprate superconductors is so low: The importance of the dynamical vertex structure

To fathom the mechanism of high-temperature ($T_{\rm c}$) superconductivity, the dynamical vertex approximation (D$Γ$A) is evoked for the two-dimensional repulsive Hubbard model. After showing that our results well reproduce the cuprate phase diagram with a reasonable $T_{\rm c}$ and dome structure, we keep track of the scattering processes that primarily affect $T_{\rm c}$. We find that local particle-particle diagrams significantly screen the bare interaction at low frequencies, which in turn suppresses antiferromagnetic spin fluctuations and hence the pairing interaction. Thus we identify dynamical vertex corrections as one of the main oppressors of $T_{\rm c}$, which may provide a hint toward higher $T_{\rm c}$'s.

cond-mat.supr-con↗

arXiv2018

Quantum Boltzmann equation for strongly correlated systems: comparison to dynamical mean field theory

We investigate the potential of a quantum Boltzmann equation without momentum conservation for description of strongly correlated electron systems out of equilibrium. In a spirit similar to dynamical mean field theory (DMFT), the momentum conservation of the electron-electron scattering is neglected, which yields a time-dependent occupation function for the equilibrium spectral function, even in cases where well-defined quasiparticles do not exist. The main assumption of this method is that the spectral function remains sufficiently rigid under the non-equilibrium evolution. We compare the result of the quantum Boltzmann equation to non-equilibrium DMFT simulations for the case of photo-carrier relaxation in Mott insulators, where processes on very different timescales emerge, i.e., impact ionization, intra-Hubbard-band thermalization, and full thermalization. Since quantum Boltzmann simulations without momentum conservation are computationally cheaper than non-equilibrium DMFT, this method allows the simulation of more complicated systems or devices, and to access much longer times.

cond-mat.str-el↗

arXiv2018

w2dynamics: Local one- and two-particle quantities from dynamical mean field theory

We describe the hybridization-expansion continuous-time quantum Monte Carlo code package "w2dynamics", developed in Wien and Würzburg. We discuss the main features of this multi-orbital quantum impurity solver for the Anderson impurity model, dynamical mean field theory as well as its coupling to density functional theory. The w2dynamics package allows for calculating one- and two-particle quantities; it includes worm and further novel sampling schemes. Details about its download, installation, functioning and the relevant parameters are provided.

cond-mat.str-el↗

arXiv2018

Impact of self-consistency in dual fermion calculations

The dual fermion (DF) method allows for calculating corrections due to non-local correlations relative to an effective impurity model. Choosing the impurity as that of a dynamical mean field theory (DMFT) solution at self-consistency is popular, and the corrections from dual fermion theory are physically meaningful. We investigate the effect of choosing the impurity instead in a self-consistent manner and find for the two dimensional Hubbard model an exponentially increase of the correlation length and susceptibility at low temperatures. There are pronounced differences for the two self-consistency schemes that are discussed in the literature; the self-consistent DF solution can even be more metallic than the DMFT solution.

cond-mat.str-el↗

arXiv2018

Importance of Schottky barriers for wide-bandgap thermoelectric devices

The development of thermoelectric devices faces not only the challenge of optimizing the Seebeck coefficient, the electrical and thermal conductivity of the active material, but also further bottlenecks when going from the thermoelectric material to an actual device, e.g., the dopant diffusion at the hot contact. We show that for large bandgap thermoelectrics another aspect can dramatically reduce the efficiency of the device: the formation of Schottky barriers. Understanding the effect, it can then be fixed rather cheaply by a two-metals contact solution.

cond-mat.mtrl-sci↗

arXiv2018

Impact ionization processes in the steady state of a driven Mott insulating layer coupled to metallic leads

We study a simple model of photovoltaic energy harvesting across a Mott insulating gap consisting of a correlated layer connected to two metallic leads held at different chemical potentials. Upon driving the layer with a time periodic electric field a particle current is induced from the low-energy to the high-energy lead. We address in particular the issue of impact ionization, whereby a particle photoexcited to the high-energy part of the upper Hubbard band uses its extra energy to produce a second particle-hole excitation. We find a drastic increase of the photocurrent upon entering the frequency regime where impact ionization is possible. At large values of the Mott gap, where impact ionization is energetically not allowed, we observe a suppression of the current and a piling up of charge in the high-energy part of the upper Hubbard band. Our study is based on a Floquet-DMFT treatment with the so-called auxiliary master equation approach as impurity solver. We verify that an approximation, whereby the self-energy is taken diagonal in the Floquet indices, is appropriate for the parameter range we are considering.

cond-mat.str-el↗

arXiv2017

The {\it victory} project v1.0: an efficient parquet equations solver

{\it Victory}, i.e. \underline{vi}enna \underline{c}omputational \underline{to}ol deposito\underline{ry}, is a collection of numerical tools for solving the parquet equations for the Hubbard model and similar many body problems. The parquet formalism is a self-consistent theory at both the single- and two-particle levels, and can thus describe individual fermions as well as their collective behavior on equal footing. This is essential for the understanding of various emergent phases and their transitions in many-body systems, in particular for cases in which a single-particle description fails. Our implementation of {\it victory} is in modern Fortran and it fully respects the structure of various vertex functions in both momentum and Matsubara frequency space. We found the latter to be crucial for the convergence of the parquet equations, as well as for the correct determination of various physical observables. In this release, we thoroughly explain the program structure and the controlled approximations to efficiently solve the parquet equations, i.e. the two-level kernel approximation and the high-frequency regulation.

cond-mat.str-el↗

arXiv2017

Quantum Anomalous Hall State in Ferromagnetic SrRuO$_3$ (111) Bilayers

SrRuO$_3$ heterostructures grown in the (111) direction are a rare example of thin film ferromagnets. By means of density functional theory plus dynamical mean field theory we show that the half-metallic ferromagnetic state with an ordered magnetic moment of 2$μ_{B}$/Ru survives the ultimate dimensional confinement down to a bilayer, even at elevated temperatures of 500$\,$K. In the minority channel, the spin-orbit coupling opens a gap at the linear band crossing corresponding to $\frac34$ filling of the $t_{2g}$ shell. We demonstrate that the respective state is Haldane's quantum anomalous Hall state with Chern number $C$=1, without an external magnetic field or magnetic impurities.

cond-mat.str-el↗

arXiv2017

Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three $t_{2g}$ orbitals of SrVO$_3$ within dynamical mean field theory (DMFT). We demonstrate how the knowledge of the high-frequency asymptotics reduces the statistical uncertainties of the vertex and further eliminates finite box size effects. The proposed method benefits the calculation of non-local susceptibilities in DMFT and diagrammatic extensions of DMFT.

cond-mat.str-el↗

arXiv2017

Local correlation functions of arbitrary order for the Falicov-Kimball model

Local n-particle vertex functions represent the crucial ingredient for all diagrammatic extensions of dynamical mean field theory (DMFT). Hitherto their application has been restricted -with a few exceptions- to the n=2-particle vertex while higher-order vertices have been neglected. In this paper we derive a general analytical expression for the n-particle (one-particle reducible) vertex of the Falicov-Kimball model (FKM). We observe that the magnitude of such vertex functions itself strongly increases with the particle-number n. On the other hand, their effect on generic Feynman diagrams remains rather moderate due to the damping effect of the Green's functions present in such diagrams. Nevertheless, they yield important contributions to the self-energy corrections calculated in diagrammatic extensions of DMFT as we explicitly demonstrate using the example of dual fermion (DF) calculations for the two-dimensional FKM at quarter filling of stationary f-electrons where corrections to the self-energy obtained from the three-particle vertex are indeed comparable in magnitude to corresponding corrections stemming from the two-particle vertex.

cond-mat.str-el↗

arXiv2017

Ab initio dynamical vertex approximation

Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (D$Γ$A) allow us to include non-local correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an AbinitioD$Γ$A approach for electronic structure calculations of materials. Starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare non-local Coulomb interaction and all local vertex corrections. From this we calculate the full non-local vertex and the non-local self-energy through the Bethe-Salpeter equation. The AbinitioD$Γ$A approach naturally generates all local DMFT correlations and all non-local $GW$ contributions, but also further non-local correlations beyond: mixed terms of the former two and non-local spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO$_3$.

cond-mat.str-el↗

arXiv2017

Thickness dependent properties in oxide heterostructures driven by structurally induced metal-oxygen hybridization variations

Thickness driven electronic phase transitions are broadly observed in different types of functional perovskite heterostructures. However, uncertainty remains whether these effects are solely due to spatial confinement, broken symmetry or rather to a change of structure with varying film thickness. Here, we present direct evidence for the relaxation of oxygen 2p and Mn 3d orbital (p-d) hybridization coupled to the layer dependent octahedral tilts within a La2/3Sr1/3MnO3 film driven by interfacial octahedral coupling. An enhanced Curie temperature is achieved by reducing the octahedral tilting via interface structure engineering. Atomically resolved lattice, electronic and magnetic structures together with X-ray absorption spectroscopy demonstrate the central role of thickness dependent p-d hybridization in the widely observed dimensionality effects present in correlated oxide heterostructures.

cond-mat.mtrl-sci↗

arXiv2016

Mott-Hubbard transition in the mass-imbalanced Hubbard model

The mass-imbalanced Hubbard model represents a continuous evolution from the Hubbard to the Falicov-Kimball model. We employ dynamical mean field theory and study the paramagnetic metal-insulator transition, which has a very different nature for the two limiting models. Our results indicate that the metal-insulator transition rather resembles that of the Hubbard model as soon as a tiny hopping between the more localized fermions is switched on. At low temperatures we observe a first-order metal-insulator transition and a three peak structure. The width of the central peak is the same for the more and less mobile fermions when approaching the phase transition, which agrees with our expectation of a common Kondo temperature and phase transition for the two species.

cond-mat.str-el↗

arXiv2016

Worm Improved Estimators in Continuous-time Quantum Monte Carlo

We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency behavior in irreducible quantities such as the one-particle self-energy or the irreducible two-particle vertex for non-density-density interactions. A good knowledge of the asymptotics of the two-particle vertex is essential for calculating non-local electronic correlations using diagrammatic extensions to the dynamical mean field theory as well as for calculating susceptibilities. We test our algorithm against analytic results for the multi-orbital atomic-limit and the Falicov-Kimball model.

cond-mat.str-el↗

arXiv2016

Magnetism in Sr$_{2}$CrMoO$_{6}$: A combined abinitio and model study

Using a combination of first-principles density functional theory (DFT) calculations and exact diagonalization studies of a first-principles derived model, we carry out a microscopic analysis of the magnetic properties of the half-metallic double perovskite compound, Sr$_2$CrMoO$_6$, a sister compound of the much discussed material Sr$_2$FeMoO$_6$. The electronic structure of Sr$_2$CrMoO$_6$, though appears similar to Sr$_2$FeMoO$_6$ at first glance, shows non trivial differences with that of Sr$_2$FeMoO$_6$ on closer examination. In this context, our study highlights the importance of charge transfer energy between the two transition metal sites. The change in charge transfer energy due to shift of Cr $d$ states in Sr$_2$CrMoO$_6$ compared to Fe $d$ in Sr$_2$FeMoO$_6$ suppresses the hybridization between Cr $t_{2g}$ and Mo $t_{2g}$. This strongly weakens the hybridization-driven mechanism of magnetism discussed for Sr$_2$FeMoO$_6$. Our study reveals that, nonetheless, the magnetic transition temperature of Sr$_2$CrMoO$_6$ remains high since additional superexchange contribution to magnetism arises with a finite intrinsic moment developed at the Mo site. We further discuss the situation in comparison to another related double perovskite compound, Sr$_2$CrWO$_6$. We also examine the effect of correlation beyond DFT, using dynamical mean field theory (DMFT).

cond-mat.mtrl-sci↗

arXiv2016

Real-space mapping of electronic orbitals

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the Ångström scale in bulk rutile (TiO2) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.

cond-mat.mtrl-sci↗

arXiv2016

Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model

We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum dependent, but it can be parametrized via the non-interacting energy-momentum dispersion $\varepsilon_{\mathbf{k}}$, except for pseudogap features right at the Fermi edge. That is, it can be written as $Σ(\varepsilon_{\mathbf{k}},ω)$, with two energy-like parameters ($\varepsilon$, $ω$) instead of three ($k_x$, $k_y$ and $ω$). The self-energy has two rather broad and weakly dispersing high energy features and a sharp $ω= \varepsilon_{\mathbf{k}}$ feature at high temperatures, which turns to $ω= -\varepsilon_{\mathbf{k}}$ at low temperatures. Altogether this yields a Z- and reversed-Z-like structure, respectively, for the imaginary part of $Σ(\varepsilon_{\mathbf{k}},ω)$. We attribute the change of the low energy structure to antiferromagnetic spin fluctuations.

cond-mat.str-el↗

arXiv2016

Screened moments and absence of ferromagnetism in FeAl

While the stoichiometric intermetallic compound FeAl is found to be paramagnetic in experiment, standard band-theory approaches predict the material to be ferromagnetic. We show that this discrepancy can be overcome by a better treatment of electronic correlations with density functional plus dynamical mean field theory. Our results show no ferromagnetism down to 100 K and since the susceptibility is decreasing at the lowest temperatures studied we also do not expect ferromagnetism at even lower temperatures. This behavior is found to originate from temporal quantum fluctuations that screen short-lived local magnetic moments of 1.6 $μ_B$ on Fe.

cond-mat.str-el↗