arXiv subjects

Fabian Schrodi

Publications and source records attributed to Fabian Schrodi.

16 recordsLinked to original sources

arXiv2024

Doping dependence and multichannel mediators of superconductivity: Calculations for a cuprate model

We study two aspects of the superconductivity in a cuprate model system, its doping dependence and the influence of competing pairing mediators. We first include electron-phonon interactions beyond Migdal's approximation and solve self-consistently, as a function of doping and for an isotropic electron-phonon coupling, the full-bandwidth, anisotropic vertex-corrected Eliashberg equations under a non-interacting state approximation for the vertex correction. Our results show that such pairing interaction supports the experimentally observed $d_{x^2-y^2}$-wave symmetry of the superconducting gap, but only in a narrow doping interval of the hole-doped system. Depending on the coupling strength, we obtain realistic values for the gap magnitude and superconducting critical temperature $T_c$ close to optimal doping, rendering the electron-phonon mechanism an important candidate for mediating superconductivity in this model system. Second, for a doping near optimal hole doping, we study multichannel superconductivity, by including both vertex-corrected electron-phonon interaction and spin and charge fluctuations as pairing mechanisms. We find that both mechanisms cooperate to support an unconventional $d$-wave symmetry of the order parameter, yet the electron-phonon interaction is mainly responsible for the Cooper pairing and high critical temperature $T_c$. Spin fluctuations are found to have a suppressing effect on the gap magnitude and critical temperature due to their repulsive interaction at small coupling wave vectors.

cond-mat.supr-con↗

arXiv2021

Selfconsistent investigation of multichannel superconductivity in a cuprate model system

The origin of high-temperature superconductivity in cuprates is still an unresolved issue. Among the most likely candidates for mediating the Cooper pair condensate are spin fluctuations and the electron-phonon interaction. While the former have long been proposed to be responsible for various observables in the superconducting state, the latter has recently been shown to produce unconventional gap symmetries when vertex corrections are self-consistently taken into account. Here, we develop multichannel Eliashberg theory to incorporate both pairing mechanisms. Solving self-consistently the full-bandwidth, anisotropic Eliashberg equations for a cuprate model system we find the characteristic $d_{x^2 -y^2}$ symmetry of the superconducting gap and a reasonable order of magnitude for $T_c$ ($50-120$ K). We further find that both mechanisms support an unconventional $d$-wave symmetry of the order parameter, yet the electron-phonon interaction is chiefly responsible for the Cooper pairing and high $T_c$, whereas the spin fluctuations have a suppressing effect on the gap magnitude and critical temperature.

cond-mat.supr-con↗

arXiv2021

Induced odd-frequency superconducting state in vertex-corrected Eliashberg theory

We show that vertex corrections to Migdal's theorem in general induce an odd-frequency spin-triplet superconducting order parameter, which coexists with its more commonly known even-frequency spin-singlet counterpart. Fully self-consistent vertex-corrected Eliashberg theory calculations for a two dimensional cuprate model, isotropically coupled to an Einstein phonon, confirm that both superconducting gaps are finite over a wide range of temperatures. The subordinate $d$-wave odd-frequency superconducting gap is found to be one order of magnitude smaller than the primary even-frequency $d$-wave gap. Our study provides a direct proof of concept for a previously unknown generation mechanism of odd-frequency superconductivity as well as for the generic coexistence of both superconducting states in bulk materials.

cond-mat.supr-con↗

arXiv2021

Prediction of an unusual trigonal phase of superconducting LaH$_{\bf 10}$ stable from 250 to 425 GPa pressure

Based on evolutionary crystal structure searches in combination with ab initio calculations, we predict an unusual structural phase of the superconducting LaH$_{10}$ that is stable from about 250 GPa to 425 GPa pressure. This new phase belongs to a trigonal $R\bar{3}m$ crystal lattice with an atypical cell angle, $α_{rhom}$ $\sim$ 24.56$^{\circ}$. We find that the new structure contains three units of LaH$_{10}$ in its primitive cell, unlike the previously known trigonal phase, where primitive cell contains only one LaH$_{10}$ unit. In this phase, a 32-H atoms cage encapsulates La atoms, analogous to the lower pressure face centred cubic phase. However, the hydrogen cages of the trigonal phase consist of quadrilaterals and hexagons, in contrast to the cubic phase, that exhibits squares and regular hexagons. Surprisingly, the shortest H-H distance in the new phase is shorter than that of the lower pressure cubic phase and of atomic hydrogen metal. We find a structural phase transition from trigonal to hexagonal at 425 GPa, where the hexagonal crystal lattice coincides with earlier predictions. Solving the anisotropic Migdal-Eliashberg equations we obtain that the predicted trigonal phase (for standard values of the Coulomb pseudopotential) is expected to become superconducting at a critical temperature of about 175 K, which is less than $T_c \sim$250 K measured for cubic LaH$_{10}$.

cond-mat.supr-con↗

arXiv2021

Unconventional superconductivity mediated solely by isotropic electron-phonon interaction

Unconventional superconductivity is commonly linked to electronic pairing mechanisms, since it is believed that the conventional electron-phonon interaction (EPI) cannot cause sign-changing superconducting gap symmetries. Here, we show that this common understanding needs to be revised when one considers a more elaborate theory of electron-phonon superconductivity beyond standard approximations. We selfconsistently solve the full-bandwidth, anisotropic Eliashberg equations including vertex corrections beyond Migdal's approximation assuming the usual isotropic EPI for cuprate, Fe-based and heavy-fermion superconductors with nested Fermi surfaces. In case of the high-$T_c$ cuprates we find a $d$-wave order parameter, as well as a nematic state upon increased doping. For Fe-based superconductors, we obtain $s_{\pm}$ gap symmetry, while for heavy-fermion CeCoIn$_5$ we find unconventional $d$-wave pairing. These results provide a proof-of-concept that EPI cannot be excluded as a mediator of unconventional and of high-$T_c$ superconductivity.

cond-mat.supr-con↗

arXiv2021

Cascade of replica bands in flat band systems: predictions for twisted bilayer graphene

We investigate the effect of electron-phonon interactions (EPI) in systems exhibiting one or more flat electron bands close to the Fermi level and a comparatively large phonon energy scale. After solving the self-consistent full-bandwidth Eliashberg equations, we compute Angular Resolved Photo Emission Spectroscopy and Scanning Tunneling Spectroscopy/Microscopy spectra. We obtain a sequence of quasiparticle replica bands in both the normal and superconducting states that originate from frequency dependent features of the electron mass renormalization function. We show that these replica bands can be used to extract the relevant phonon energy scale from experiments. Focusing in particular on twisted bilayer graphene, we predict replica-band formation which, when observed, will shed light on the role of EPI in this archetypal flat-band system.

cond-mat.supr-con↗

arXiv2021

Exploring multichannel superconductivity in ThFeAsN

We investigate theoretically the superconducting state of the undoped Fe-based superconductor ThFeAsN. Using input from $ab~initio$ calculations, we solve the Fermi-surface based, multichannel Eliashberg equations for Cooper-pair formation mediated by spin and charge fluctuations, and by the electron-phonon interaction (EPI). Our results reveal that spin fluctuations alone, when coupling only hole-like with electron-like energy bands, can account for a critical temperature $T_c$ up to $\sim7.5\,\mathrm{K}$ with an $s_{\pm}$-wave superconducting gap symmetry, which is a comparatively low $T_c$ with respect to the experimental value $T_c^{\mathrm{exp}}=30\,\mathrm{K}$. Other combinations of interaction kernels (spin, charge, electron-phonon) lead to a suppression of $T_c$ due to phase frustration of the superconducting gap. We qualitatively argue that the missing ingredient to explain the gap magnitude and $T_c$ in this material is the first-order correction to the EPI vertex. In the noninteracting state this correction adopts a form supporting the $s_{\pm}$ gap symmetry, in contrast to EPI within Migdal's approximation, i.e., EPI without vertex correction, and therefore it enhances tendencies arising from spin fluctuations.

cond-mat.supr-con↗

arXiv2020

Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems

Eliashberg's foundational theory of superconductivity is based on the application of Migdal's approximation, which states that vertex corrections to first order electron-phonon scattering are negligible if the ratio between phonon and electron energy scales is small. The resulting theory incorporates the first Feynman diagrams for electron and phonon self-energies. However, the latter is most commonly neglected in numerical analyses. Here we provide an extensive study of full-bandwidth Eliashberg theory in two and three dimensions, where we include the full back reaction of electrons onto the phonon spectrum. We unravel the complex interplay between nesting properties, Fermi surface density of states, renormalized electron-phonon coupling, phonon softening, and superconductivity. We propose furthermore a scaling law for the maximally possible critical temperature $T_c^{\textrm{max}}\proptoλ(Ω) \sqrt{Ω_0^2-Ω^2}$ in 2D and 3D systems, which embodies both the renormalized electron-phonon coupling strength $λ(Ω)$ and softened phonon spectrum $Ω$. Also, we analyze for which electronic structure properties a maximal $T_c$ enhancement can be achieved.

cond-mat.supr-con↗

arXiv2020

Phonon-mode specific contributions to room-temperature superconductivity in atomic hydrogen at high pressures

We investigate the role of specific phonon mode symmetries for the room temperature superconductivity in atomic hydrogen under large pressure. Using anisotropic Migdal-Eliashberg theory with ab initio input from density functional theory, we show that the $E_u$ phonon modes are the dominant driving force for obtaining such high critical temperatures. When going from 400 to 600 GPa, we find an increased transition temperature, however, the total electron-phonon coupling strength is counterintuitively reduced. Our analysis reveals that this is due to an enhanced contribution to the coupling strength by the $E_u$ phonon mode.

cond-mat.supr-con↗

arXiv2020

Multichannel superconductivity of monolayer FeSe on SrTiO$_3$: Interplay of spin fluctuations and electron-phonon interaction

We investigate the effects of electron-phonon coupling, as well as of spin and charge fluctuations on the superconducting state in a single layer of FeSe on SrTiO$_3$ substrate. These three bosonic mediators of Cooper pairing are treated on equal footing in a multichannel, full-bandwidth, multiband, and anisotropic Eliashberg theory of the interacting state. Our self-consistent calculations show that an s-wave symmetry of the superconducting gap is compatible only with a complete absence of spin fluctuations. When spin fluctuations are present, the sign-changing nodeless d-wave pairing symmetry is always obtained, yet the essential ingredient for explaining the gap magnitude and critical temperature is still the interfacial electron-phonon interaction.

cond-mat.supr-con↗

arXiv2020

Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation

We solve the anisotropic, full-bandwidth and non-adiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The non-adiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface restricted Eliashberg-theory calculations. We find that non-adiabatic contributions to the superconducting gap can be positive, negative or negligible, depending on the dimensionality of the considered system, the degree of non-adiabaticity, and the coupling strength. We further examine non-adiabatic effects on the transition temperature and the electron-phonon coupling constant. Our treatment emphasizes the importance of overcoming previously employed approximations in estimating the impact of vertex corrections on superconductivity and opens a pathway to systematically study vertex correction effects in systems such as high-$T_c$, flat band and low-carrier density superconductors.

cond-mat.supr-con↗

arXiv2020

Eliashberg theory for spin-fluctuations mediated superconductivity -- Application to bulk and monolayer FeSe

We present a novel method for embedding spin and charge fluctuations in an anisotropic, multi-band and full-bandwidth Eliashberg treatment of superconductivity. Our analytical framework, based on the random phase approximation, allows for a selfconsistent calculation of material specific characteristics in the interacting, and more specifically, the superconducting state. We apply this approach to bulk FeSe as representative for the iron-based superconductors and successfully solve for the superconducting transition temperature $T_c$, the gap symmetry and the gap magnitude. We obtain $T_c \approx 6$ K, consistent with experiment ($T_c \approx 8$ K), as well as other quantities in good agreement with experimental observations, thus supporting spin fluctuations mediated pairing in bulk FeSe. On the contrary, applying our approach to monolayer FeSe on SrTiO$_3$ we find that spin fluctuations within the full Eliashberg framework give a $d$-wave gap with $T_c\le 11$ K and therefore cannot provide an explanation for a critical temperature as high as observed experimentally ($T_c \approx 70$ K). Our results hence point towards interfacial electron-phonon coupling as the dominant Cooper pairing mediator in this system.

cond-mat.supr-con↗

arXiv2020

Prominent Cooper Pairing Away From the Fermi Level and its Spectroscopic Signature in Twisted Bilayer Graphene

We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in the superconducting state. We predict several such features in tunneling and angle resolved photoemission spectra for future experiments.

cond-mat.supr-con↗

arXiv2019

Increased Performance of Matsubara space calculations: A case study within Eliashberg theory

We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite summations involved, our scheme allows for the efficient calculation of such sums extended formally up to infinity. The method is first benchmarked with isotropic Migdal-Eliashberg theory calculations and subsequently applied to the solution of the full-bandwidth, multiband and anisotropic equations focusing on the FeSe/SrTiO$_3$ interface as a case study. Compared to the standard procedure, we reach similarly well converged results with less than one fifth of the number of frequencies for the anisotropic case, while for the isotropic set of equations we spare approximately ninety percent of the complexity. Since our proposed approximations are very general, our numerical scheme opens the possibility of studying the superconducting properties of a wide range of materials at ultra-low temperatures.

cond-mat.supr-con↗

arXiv2018

Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO$_3$

We study the temperature evolution of the quasiparticle bands of the FeSe monolayer on the SrTiO$_3$ (STO) substrate from 10 to 300 K by applying the anisotropic, multiband and full-bandwidth Eliashberg theory. To achieve this, we extend this theory by self-consistently coupling the chemical potential to the full set of Eliashberg equations. In this way, the electron filling can accurately be kept at a constant level at any temperature. Solving the coupled equations self-consistently, and with focus on the interfacial electron-phonon coupling, we compute a nearly constant Fermi surface with respect to temperature and predict a non-trivial temperature evolution of the global chemical potential. This evolution includes a total shift of 5 meV when increasing temperature from 10 to 300 K and a hump-like dependence followed by a kink at the critical temperature T$_c$. We argue that the latter behavior indicates that superconductivity in FeSe/SrTiO$_3$ is near to the BCS-BEC crossover regime. Calculating the temperature dependent Angle Resolved Photoemission Spectroscopy (ARPES) spectra, we suggest a new route to determine the energy scale of the interfacial phonon mode by measuring the energy position of second-order replica bands. Further, we re-examine the often used symmetrization procedure applied to such ARPES curves and demonstrate substantial asymmetric deviations. Lastly, our results reveal important aspects for the experimental determination of the momentum anisotropy of the superconducting gap.

cond-mat.supr-con↗

arXiv2017

Density-of-states of many-body quantum systems from tensor networks

We present a technique to compute the microcanonical thermodynamical properties of a manybody quantum system using tensor networks. The Density Of States (DOS), and more general spectral properties, are evaluated by means of a Hubbard-Stratonovich transformation performed on top of a real-time evolution, which is carried out via numerical methods based on tensor networks. As a consequence, the free energy and thermal averages can be also calculated. We test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using matrix product states, we show that the thermodynamical quantities as a function of temperature are in very good agreement with the exact results. This approach can be extended to higher-dimensional system by properly employing other types of tensor networks.

quant-ph↗