arXiv subjects

Rudi Hackl

Publications and source records attributed to Rudi Hackl.

At least 19 recordsLinked to original sources

arXiv2026

Fluctuation-enhanced electron-phonon coupling in FeSe

The interactions among lattice, charge, and spin degrees of freedom fundamentally shape material properties. In FeSe, symmetry-breaking perturbations serve as highly sensitive probes of these couplings. Previous work has shown that defects and isoelectronic substitution can substantially alter these interactions, giving rise to additional phonon modes. In this study, uniaxial strain is employed as a tunable symmetry-breaking control parameter to probe the intrinsic lattice response in the absence of disorder. The temperature evolution of phonon excitations was examined with fine temperature resolution in the vicinity of the nemato-structural transition temperature $T_s$, under strain applied along the $\langle 110 \rangle$ and $\langle 100 \rangle$ crystallographic directions. A subtle asymmetry of the $A_{1g}^{ph}$ mode appears in the unstrained crystal within a narrow temperature window around $T_s$, originating from the emergence of an additional mode in the fully symmetric channel. With applied strain, this feature becomes more distinctly resolved. The anomaly is attributed to modifications of the coupling between lattice and electronic degrees of freedom driven by the ordering fluctuations right above the nematic transition. These fluctuations enhance susceptibility for phonon-electron-phonon coupling in the vicinity of the X and R points of the Brillouin zone and promote two-phonon scattering close to the $A_{1g}^{ph}$ mode. The presence of this two-phonon scattering depends on both the strength and the direction of the applied strain, indicating a high sensitivity of FeSe to local symmetry breaking.

cond-mat.supr-con↗

arXiv2026

Phonon frequency comb close to an isolated Einstein mode in InSiTe3

The emergence of phonon frequency combs exemplifies a rare and intriguing phenomenon in quantum solids. Materials with distinctive phonon band structures are especially promising for hosting such states, as their vibrational dispersion landscape across the Brillouin zone can facilitate the formation of long-lived, collective lattice excitations. In the layered Van der Waals compound InSiTe$_3$, polarization-resolved Raman spectroscopy reveals a pronounced anharmonicity in symmetry-predicted modes and the formation of a self-organized frequency domain structure (coherent-like state), in the range of a localized highenergy A$_{1g}$ phonon mode near 500 cm$^{-1}$. This strong phonon-phonon coupling manifests itself as an anomalous temperature dependence around 200 K, coinciding with the appearance of higher-order excitations within the phonon density of states gap. These findings position InSiTe$_3$ as an unconventional platform where intrinsic highly structured phonon spectral correlations and unusually strong anharmonic effects coexist, opening new avenues for exploring emergent vibrational phenomena in low-dimensional materials.

cond-mat.mtrl-sci↗

arXiv2025

Detection of chiral spin fluctuations driven by frustration in Mott insulators

Topologically ordered states, such as chiral spin liquids, have been proposed as candidates that host fractionalized excitations. However, detecting chiral character or proximity to these non-trivial states remains a challenge. Resonant Raman scattering can be a powerful tool for detecting chiral fluctuations, as the $A_{2g}$ channel probes excitations with broken time-reversal symmetry and local chiral order. Here, we use exact diagonalization to characterize the resonant $A_{2g}$ channel, alongside two-magnon scattering in $B_{1g}$ and $E_g$ channels, for the Hubbard model on lattices with increasing levels of geometric spin frustration, where tuning the incident energy near the Mott gap reveals strong chiral spin excitation intensity. Increased spin frustration in the Mott insulator results in an overall softening of the Raman $A_{2g}$ response, indicating a tendency toward low energy chiral-chiral fluctuations in Mott insulators with magnetic frustration and proximity to chiral spin liquid states that can potentially be tuned by external perturbations.

cond-mat.str-el↗

arXiv2023

Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV$_3$Sb$_5$

The formation of charge density waves (CDW) is a long-standing open problem particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently, such as the missing Kohn anomaly in the acoustic phonons or the latent heat at the transition $T_{\rm CDW}$ = 95 K , further underpin this notion. Here, we study the Kagome metal CsV$_3$Sb$_5$ using polarized inelastic light scattering. The electronic energy gap $2\Delta$ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for $2\Delta/k_{\rm B}T_{\rm CDW}$. The A$_{1g}$ phonon has a discontinuity at $T_{\rm CDW}$ and a precursor starting 20 K above $T_{\rm CDW}$. Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures. The linewidths of all A$_{1g}$ and E$_{2g}$ phonon lines including those emerging below $T_{\rm CDW}$ were analyzed in terms of anharmonic symmetric decay revealing strong phonon-phonon coupling. In addition, we observe two CDW amplitude modes (AMs): one in A$_{1g}$ symmetry and one in E$_{2g}$ symmetry. The temperature dependence of both modes deviates from the prediction of mean-field theory. The A$_{1g}$ AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling. The asymmetric A$_{1g}$ AM, along with the discontinuity of the A$_{1g}$ phonon, the large phonon-phonon coupling parameters and the large gap ratio, indicate the importance of anharmonic strong phonon-phonon and electron-phonon coupling for the CDW formation in CsV$_3$Sb$_5$.

cond-mat.supr-con↗

arXiv2022

Polarized tip-enhanced Raman spectroscopy at liquid He temperature in ultrahigh vacuum using an off-axis parabolic mirror

Tip-enhanced Raman spectroscopy (TERS) combines inelastic light scattering well below the diffraction limit down to the nanometer range and scanning probe microscopy and, possibly, spectroscopy. In this way, topographic and spectroscopic as well as single- and two-particle information may simultaneously be collected. While single molecules can now be studied successfully, bulk solids are still not meaningfully accessible. It is the purpose of the work presented here to outline approaches toward this objective. We describe a home-built, liquid helium cooled, ultrahigh vacuum tip-enhanced Raman spectroscopy system (LHe-UHV-TERS). The setup is based on a scanning tunneling microscope and, as an innovation, an off-axis parabolic mirror having a high numerical aperture of approximately $0.85$ and a large working distance. The system is equipped with a fast load-lock chamber, a chamber for the \textit{in situ} preparation of tips, substrates, and samples, and a TERS chamber. Base pressure and temperature in the TERS chamber were approximately $3\times 10^{-11}$~mbar and 15~K, respectively. Polarization dependent tip-enhanced Raman spectra of the vibration modes of carbon nanotubes were successfully acquired at cryogenic temperature. Enhancement factors in the range of $10^7$ were observed. The new features described here including very low pressure and temperature and the external access to the light polarizations, thus the selection rules, may pave the way towards the investigation of bulk and surface materials.

cond-mat.supr-con↗

arXiv2021

Quantum critical fluctuations in an Fe-based superconductor

Quantum critical fluctuations may prove to play an instrumental role in the formation of unconventional superconductivity. Here, we show that the characteristic scaling of a marginal Fermi liquid is present in inelastic light scattering data of an Fe-based superconductor tuned through a quantum critical point (QCP) by chemical substitution or doping. From the doping dependence of the imaginary time dynamics we are able to distinguish regions dominated by quantum critical behavior from those having classical critical responses. This dichotomy reveals a connection between the marginal Fermi liquid behavior and quantum criticality. In particular, the overlap between regions of high superconducting transition temperatures and quantum critical scaling suggests a contribution from quantum fluctuations to the formation of superconductivity.

cond-mat.supr-con↗

arXiv2021

Phonon anomalies associated with spin reorientation in the Kagome ferromagnet Fe3Sn2

Polarization- and temperature-dependent Raman data along with theoretical simulations are presented for the Kagome ferromagnet Fe_3Sn_2. Eight out of nine expected phonon modes were identified. The experimental energies compare well with those from the simulations. The analysis of the line widths indicates relatively strong phonon-phonon coupling in the range 0.1 to 1. The temperature-dependent frequencies of three A_{1g} modes show weak anomalies at approximately 100 K. In contrast, the linewidths of all phonon modes follow the conventional exponential broadening up to room temperature except for the softest A_{1g} mode, whose width exhibits a kink close to 100 K and becomes nearly constant for T > 100 K. These features are indicative of a spin reorientation taking place in the temperature range above 100 K which might arise from spin-phonon coupling. The low-energy part of the electronic continuum in E_g symmetry depends strongly on temperature. The possible reasons include particle-hole excitation tracking the resistivity, a spin-dependent gap or spin fluctuations.

cond-mat.mtrl-sci↗

arXiv2021

Tendencies of enhanced electronic nematicity in the Hubbard model and a comparison with Raman scattering on high-temperature superconductors

The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbard model to experimental results from Raman spectroscopy in $\text{La}_{2-x}\text{Sr}_{x}\text{CuO}_{4}$, which show a prominent increase in the $B_{1g}$ response around 10% hole doping as the temperature decreases, indicative of a rise in nematic fluctuations at low energy. Our results support a picture of nematic fluctuations with $B_{1g}$ symmetry occurring in underdoped cuprates, which may arise from melted stripes at elevated temperatures.

cond-mat.supr-con↗

arXiv2020

Raman Study of Cooper Pairing Instabilities in (Li$_{1-x}$Fe$_x$)OHFeSe

We studied the electronic Raman spectra of (Li$_{1-x}$Fe$_x$)OHFeSe as a function of light polarization and temperature. In the B$_{1g}$ spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T$_c$. The nearly resolution-limited peak at 110 cm$^{-1}$ (13.6 meV) is identified as a collective mode. The peak at 190 cm$^{-1}$ (23.6 meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band structure of (Li$_{1-x}$Fe$_x$)OHFeSe, the most plausible explanations include conventional spin-fluctuation pairing between the electron bands and the incipient hole band and pairing between the hybridized electron bands. The absence of gap features in A$_{1g}$ and B$_{2g}$ symmetry favors the second case. Thus, in spite of various differences between the pnictides and chalcogenides, this Letter demonstrates the proximity of pairing states and the importance of band structure effects in the Fe-based compounds.

cond-mat.supr-con↗

arXiv2020

Suppression of Superconductivity and Nematic Order in Fe$_{1-y}$Se$_{1-x}$S$_x$ (0$\leq$$x$$\leq$1, $y$$\leq$0.1) Crystals by Anion Height Disorder

Connections between crystal chemistry and critical temperature $T_c$ have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that $T_c$ correlates with the average anion height above the Fe plane, i. e. with the geometry of the FeAs4 or FeCh4 (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe$_{1-y}$Se$_{1-x}$S$_x$ (0$\leq$$x$$\leq$1, $y$$\leq$0.1), we find that in alloyed crystals $T_c$ is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in $T_c$($x$) and tetragonal-to-orthorombic (nematic) transition $T_s$($x$) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)4 tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of $T_c$ and $T_s$ suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with Fe/S building blocks.

cond-mat.supr-con↗

arXiv2018

Frustrated Magnetism from Local Moments in FeSe

We investigate properties of a spin-1 Heisenberg model with extended and biquadratic interactions, which captures crucial aspects of the low energy physics in FeSe. While we show that the model exhibits a rich phase diagram with four different magnetic ordering tendencies, we identify a parameter regime with strong competition between N\`eel, staggered dimer, and stripe-like magnetic fluctuations, accounting for the physical properties of FeSe. Through the comparison of numerically evaluated spin and Raman response with experiments, we find evidence for enhanced magnetic frustration between N\`eel and co-linear stripe ordering tendencies, which increases with increasing temperature. The explanation of these spectral behaviors with this frustrated spin model supports the idea of local spin interactions in FeSe.

cond-mat.str-el↗

arXiv2018

Subdominant $d$-wave interaction in superconducting CaKFe$_4$As$_2$?

We report inelastic light scattering results on the stoichiometric and fully ordered superconductor CaKFe$_4$As$_2$ as a function of temperature and light polarization. In the energy range between 10 and 315 cm$^{-1}$ (1.24 and 39.1 meV) we observe the particle-hole continuum above and below the superconducting transition temperature $T_c$ and 7 of the 8 Raman active phonons. The main focus is placed on the analysis of the electronic excitations. Below $T_c$ all three symmetries projected with in-plane polarizations display a redistribution of spectral weight characteristic for superconductivity. The energies of the pair-breaking peaks in $A_{1g}$ and $B_{2g}$ symmetry are in approximate agreement with the results from photoemission studies. In $B_{1g}$ symmetry the difference between normal and superconducting state is most pronounced, and the feature is shifted downwards with respect to those in $A_{1g}$ and $B_{2g}$ symmetry. The maximum peaking at 134 cm$^{-1}$ (16.6 meV) has a substructure on the high-energy side. We interpret the peak at 134 cm$^{-1}$ in terms of a collective Bardasis-Schrieffer (BS) mode and the substructure as a remainder of the pair-breaking feature on the electron bands. There is a very weak peak at 50 cm$^{-1}$ (6.2 meV) which is tentatively assigned to another BS mode.

cond-mat.supr-con↗

arXiv2017

Frustrated spin order and stripe fluctuations in FeSe

The charge and spin dynamics of the structurally simplest iron-based superconductor, FeSe, may hold the key to understanding the physics of high temperature superconductors in general. Unlike the iron pnictides, FeSe lacks long range magnetic order in spite of a similar structural transition around 90\,K. Here, we report results of Raman scattering experiments as a function of temperature and polarization and simulations based on exact diagonalization of a frustrated spin model. Both experiment and theory find a persistent low energy peak close to 500cm$^{-1}$ in $B_{1g}$ symmetry, which softens slightly around 100\,K, that we assign to spin excitations. By comparing with results from neutron scattering, this study provides evidence for nearly frustrated stripe order in FeSe.

cond-mat.str-el↗

arXiv2017

Magnetic excitations and amplitude fluctuations in insulating cuprates

We present results from light scattering experiments on three insulating antiferromagnetic cuprates, YBa$_2$Cu$_3$O$_{6.05}$, Bi$_2$Sr$_2$YCu$_2$O$_{8+\delta}$, and La$_2$CuO$_4$ as a function of polarization and excitation energy {using samples of the latest generation. From the raw data we derive symmetry-resolved spectra.} The spectral shape in $B_{1g}$ symmetry is found to be nearly universal and independent of the excitation energy. The spectra agree quantitatively with predictions by field theory [\onlinecite{Weidinger:2015}] facilitating the precise extraction of the Heisenberg coupling $J$. {In addition, the asymmetric line shape on the high-energy side is found to be related to amplitude fluctuations of the magnetization. In La$_2$CuO$_4$ alone minor contributions from resonance effects may be identified.} The spectra in the other symmetries are not universal. The variations may be traced back to weak resonance effects and extrinsic contributions. For all three compounds we find support for the existence of chiral excitations appearing as a continuum in $A_{2g}$ symmetry having an onset slightly below $3J$. In La$_2$CuO$_4$ an additional isolated excitation appears on top of the $A_{2g}$ continuum.

cond-mat.str-el↗

arXiv2017

Microscopic pairing fingerprint of the iron-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$

Resolving the microscopic pairing mechanism and its experimental identification in unconventional superconductors is among the most vexing problems of contemporary condensed matter physics. We show that Raman spectroscopy provides an avenue for this quest by probing the structure of the pairing interaction at play in an unconventional superconductor. As we study the spectra of the prototypical Fe-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$ for $0.22\le x \le 0.70$ in all symmetry channels, Raman spectroscopy allows us to distill the leading $s$-wave state. In addition, the spectra collected in the $B_{1g}$ symmetry channel reveal the existence of two collective modes which are indicative of the presence of two competing, yet sub-dominant, pairing tendencies of $d_{x^2-y^2}$ symmetry type. A comprehensive functional Renormalization Group (fRG) and random-phase approximation (RPA) study on this compound confirms the presence of the two sub-leading channels, and consistently matches the experimental doping dependence of the related modes. The synopsis of experimental evidence and theoretical modelling supports a spin-fluctuation mediated superconducting pairing mechanism.

cond-mat.supr-con↗

arXiv2016

Charge density wave modulation and gap measurements in CeTe$_3$

We present a study of charge density wave (CDW) ordering in CeTe$_3$ at room temperature using a scanning tunneling microscope and Raman spectroscopy. Two characteristic CDW ordering wavevectors obtained from the Fourier analysis are assessed to be $|{\bf \textbf{c}}^\ast-{\bf q}|=4.19\,{\rm nm}^{-1}$ and $|{\bf q}|=10.26\,{\rm nm}^{-1}$ where $|{\bf c}^\ast| = 2\pi/c$ is the reciprocal lattice vector. The scanning tunneling spectroscopy measurements, along with inelastic light (Raman) scattering measurements, show a CDW gap $\Delta_{\rm max}$ of approximately 0.37 eV. In addition to the CDW modulation, we observe an organization of the Te sheet atoms in an array of alternating V- and N- groups along the CDW modulation, as predicted in the literature.

cond-mat.mtrl-sci↗

arXiv2015

Antiferromagnetic fluctuations in the quasi-two-dimensional organic superconductor detected by Raman spectroscopy

Using Raman scattering, the quasi-two dimensional organic superconductor k-(BEDT-TTF)2Cu[N(CN)2]Br (T_c=11.8 K) and the related antiferromagnet k-(BEDT-TTF)2Cu[N(CN)2]Cl are studied. Raman scattering provides unique spectroscopic information about magnetic degrees of freedom that has been otherwise unavailable on such organic conductors. Below T=200 K a broad band at about 500 cm-1 develops in both compounds. We identify this band with two-magnon excitation. The position and the temperature dependence of the spectral weight are similar in the antiferromagnet and in the metallic Fermi-liquid. We conclude that antiferromagnetic correlations are similarly present in the magnetic insulator and the Fermi-liquid state of the superconductor.

cond-mat.str-el↗

arXiv2015

Nematic fluctuations and the magneto-structural phase transition in ${\rm Ba(Fe_{1-x}Co_x)_2As_2}$

An inelastic light (Raman) scattering study of nematicity and critical fluctuations in ${\rm Ba(Fe_{1-x}Co_x)_2As_2}$ ($0\le x \le 0.051$) is presented. It is shown that the response from fluctuations appears only in $B_{1g}$ (${x^2-y^2}$) symmetry. The scattering amplitude increases towards the structural transition at $T_s$ but vanishes only below the magnetic ordering transition at $T_{\rm SDW} < T_s$, suggesting a magnetic origin of the fluctuations. The theoretical analysis explains the selection rules and the temperature dependence of the fluctuation response. These results make magnetism the favorite candidate for driving the series of transitions.%Below $T_{\rm SDW}$ the gap of the magnetically ordered phase opens up.

cond-mat.str-el↗