FG Computational Physics
We investigate order parameter fluctuations in the Hubbard model within a time-dependent Gutzwiller approach. While in the weak coupling limit we find that the amplitude fluctuations are short-lived due to a degeneracy with the energy of the edge of the quasiparticle continua (and in agreement with Hartree-Fock+RPA theory), these are shifted below the edge upon increasing the interaction. Our calculations therefore predict undamped amplitude (Higgs) oscillations of the order parameter in strongly coupled superconductors, cold atomic fermion condensates, and strongly interacting charge- and spin-density wave systems. We propose an experimental realization for the detection of the spin-type Higgs mode in undoped cuprates and related materials where, due to the Dzyaloshinsky-Moriya interaction, it can couple to an out-of-plane ferromagnetic excitation that is visible via the Faraday effect.
The Shrinking Fermi Liquid Scenario for Strange-Metal Behavior from Overdamped Optical Phonons
(2024)
We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.
We discuss a formalism that allows for the calculation of a higher-harmonic-current response to a strong applied electric field for disordered superconducting systems described on the basis of tight-binding models with on- and/or intersite interactions. The theory is based on an expansion of the density matrix in powers of the field amplitudes, where we solve the equation of motion for the individual components. This allows the evaluation of higher-order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In the case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.
Electronic inhomogeneities are nowadays a well established feature of high-temperature superconductors, most prominently exemplified by the observation of charge-ordered states in a large number of cuprate materials. In this contribution we review the particular contribution of the Stuttgart-Tartu-Cottbus group to this field, which has been largely stimulated by intense discussion with K. Alex Müller. The original scenario, which was based on the formation of a percolative electronic network, is substantiated by a microscopic analysis of the clustering of magnetic polarons within the one-band Hubbard model.
We present a detailed theoretical investigation of the linear and nonlinear optical response in a model system for a disordered d-wave superconductor. By evaluating the quasiparticle contribution (BCS response) we show that for both quantities the gap symmetry considerably changes the paradigm of the optical response as compared to the conventional s-wave case. For what concerns the linear response our findings agree with previous work showing that in strongly disordered d-wave superconductors a large fraction of uncondensed spectral weight survives below Tc, making the optical absorption around the gap-frequency scale almost unchanged with respect to the normal state. Our numerical results are in excellent quantitative agreement with experiments in overdoped cuprates. In the nonlinear regime we focus on the third-harmonic generation (THG), finding that, as already established for the s-wave case, in general a large THG is triggered by disorder-activated paramagnetic processes. However, in the d-wave case the BCS response is monotonously increasing in frequency, losing any signature of THG enhancement when the THz pump frequency ω matches the gap maximum Δ, a hallmark of previous experiments in conventional s-wave superconductors. Our findings, along with the mild polarization dependence of the response, provide an explanation for recent THG measurements in cuprates, setting the framework for the theoretical understanding of nonlinear effects in unconventional cuprates.
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.
We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. We show that, depending on the order of the thermodynamic limit and large times, a situation can arise in which the Fermi liquid keeps a memory of the parent BCS state. Furthermore, a time inversion of the interaction, supplemented by a manipulation analogous to a spin-/photon-echo experiment, allows us to recover the parent BCS state. Moreover, we study the evolution of the order parameter phase ϕ in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density, we explicitly show how to use the dynamics of ϕ together with gauge invariance to build up the noninteracting chemical potential away from particle-hole symmetry. We further analyze the role of ϕ in restoring the gauge-invariant current response when the noninteracting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field.
Anomalous metallic properties are often observed in the proximity of quantum critical points, with violation of the Fermi Liquid paradigm. We propose a scenario where, near the quantum critical point, dynamical fluctuations of the order parameter with finite correlation length mediate a nearly isotropic scattering among the quasiparticles over the entire Fermi surface. This scattering produces a strange metallic behavior, which is extended to the lowest temperatures by an increase of the damping of the fluctuations. We phenomenologically identify one single parameter ruling this increasing damping when the temperature decreases, accounting for both the linear-in-temperature resistivity and the seemingly divergent specific heat observed, e.g., in high-temperature superconducting cuprates and some heavy-fermion metals.
Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.
THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode
(2022)
Recent experiments with strong THz fields in unconventional cuprate superconductors have clearly evidenced an increase of the non-linear optical response below the superconducting critical temperature Tc. As in the case of conventional superconductors, a theoretical estimate of the various effects contributing to the non-linear response is needed in order to interpret the experimental findings. Here, we report a detailed quantitative analysis of the non-linear THz optical kernel in cuprates within a realistic model, accounting for the band structure and disorder level appropriate for these systems. We show that the BCS quasiparticle response is the dominant contribution for cuprates, and its polarization dependence accounts very well for the third-harmonic generation measurements. On the other hand, the polarization dependence of the THz Kerr effect is only partly captured by our calculations, suggesting the presence of additional effects when the system is probed using light pulses with different central frequencies.