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Institute
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.
Particle-particle response function as a probe for electronic correlations in the p-d Hubbard model
(2010)
Domain wall structures in the two-dimensional Hubbard modelwith long-range Coulomb interaction
(2000)
In underdoped cuprates, both stripes and spiral states may account for the incommensurate spin response observed by elastic neutron scattering experiments. Here, we investigate the respective stability of both textures within the framework of the three-band Hubbard model which we treat within the unrestricted Gutzwiller approximation. Our calculations indicate that for parameter sets appropriate for lanthanum cuprates and small doping nor purely longitudinal stripes nor uniform spirals are stable but stripes with significant spin canting. Indeed at small doping uniform spirals are unstable toward nanoscale phase separation.
It is shown that the magnetic structure of high-T c superconductors is strongly influenced by the next-nearest neighbor hopping parameter t' which distinguishes different families of cuprates. Our investigations indicate that uniform spirals get favored by a large t'=t ratio but are unstable at small doping towards stripes with spin canting. For large /t'/t/ spirals can be stabilized under certain conditions in the overdoped regime which may explain the elastic incommensurate magnetic response recently observed in iron-co-doped Bi2201 materials.
Empirical evidence in heavy fermion, pnictide and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in ‘electronic polymers’. Within a Monte Carlo study, we find that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder blurs the positional order leaving a robust inversion symmetry breaking and a nematic order, accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, whose properties are reminiscent of soft-matter physics, produce charge and spin responses in good accord with experiments.
According to the Goldstone theorem the breaking of a continuous U(1) symmetry comes along with the existence of low-energy collective modes. In the context of superconductivity these excitations are related to the phase of the superconducting (SC) order parameter and for clean systems are optically inactive; that is, single-mode excitations do not directly couple to light. Here we show that for strongly disordered superconductors phase modes acquire a dipole moment and appear as a subgap spectral feature in the optical conductivity. This finding is obtained with both a gauge-invariant random-phase approximation scheme based on a fermionic Bogoliubov–de Gennes state and a prototypical bosonic model for disordered superconductors. In the strongly disordered regime, where the system displays an effective granularity of the SC properties, the optically active dipoles are linked to the isolated SC islands, offering a new perspective for realizing microwave optical devices.
We investigate the disorder dependence of the static density, amplitude, and current correlations within the attractive Hubbard model supplemented with onsite disorder. It is found that strong disorder favors a decoupling of density and amplitude correlations due to the formation of superconducting (SC) islands. This emergent granularity also induces an enhancement of the density correlations on the SC islands whereas amplitude fluctuations are most pronounced in the “insulating” regions. While density and amplitude correlations are short ranged at strong disorder, we show that current correlations have a long-range tail due to the formation of percolative current paths in agreement with the constant behavior expected from the analysis of one-dimensional models.
Pseudogap and (An)isotropic Scattering in the Fluctuating Charge-Density Wave Phase of Cuprates
(2017)
We present a general scenario for high-temperature superconducting cuprates, based on the presence of dynamical charge density waves (CDWs) and to the occurrence of a CDW quantum critical point, which occurs, e.g., at doping p ≈ 0.16 in YBa2Cu3O6 + δ (YBCO). In this framework, the pseudogap temperature T∗ is interpreted in terms of a reduction of the density of states due to incipient CDW and, at lower temperature to the possible formation of incoherent superconducting pairs. The dynamically fluctuating character of CDW accounts for the different temperatures at which the CDW onset revealed by X-ray scattering (Tons(p)), and the static three-dimensional CDW ordering appear. We also investigate the anisotropic character of the CDW-mediated scattering. We find that this is strongly anisotropic only close to the CDW quantum critical point (QCP) at low temperature and very low energy. It rapidly becomes nearly isotropic and marginal-Fermi-liquid-like away from the CDW QCP and at finite (even rather small) energies. This may reconcile the interpretation of Hall measurements in terms of anisotropic CDW scattering with recent photoemission experiments Bok, J.M., et al. Sci. Adv. 2, e1501329 (2016).
Phase separation and proximity effects in itinerant ferromagnet/superconductor heterostructures
(2018)
Heterostructures made of itinerant ferromagnets and superconductors are studied. In contrast to most previous models, ferromagnetism is not enforced by an effective Zeeman field but induced in a correlated single-band model (CSBM) that displays itinerant ferromagnetism as a mean-field ground state. In this model superconductivity and magnetism are both calculated self-consistently. We calculate the magnitude of the magnetization, the superconducting correlations, and variations of the charge density self-consistently for a superconducting-magnetic bilayer by solving the Bogoliubov–de Gennes equations on a two-dimensional lattice. We determine all three quantities as a function of the Coulomb repulsion U and the ferromagnetic exchange interaction J. The CSBM displays a variety of features not present in the Zeeman exchange model—for example, the occurrence of electronic phase separation and the competition of magnetic and superconducting orders far away from the interface.
Nanoscale 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. These inhomogeneities have profound consequences for the electron–phonon coupling since they allow for long-range pairing interactions due to the reduced screening supplemented by the enhancement of the electron–phonon vertex due to strong correlations. In this chapter we review the particular contribution of the Stuttgart-Tartu-Cottbus group to this field and discuss how the current status of experimental results provides affirmation to their ideas.
Besides significant electronic correlations, high-temperature superconductors also show a strong coupling of electrons to a number of lattice modes. Combined with the experimental detection of electronic inhomogeneities and ordering phenomena in many high-Tc compounds, these features raise the question as to what extent phonons are involved in the associated instabilities. Here we address this problem based on the Hubbard model including a coupling to phonons in order to capture several salient features of the phase diagram of hole-doped cuprates. Charge degrees of freedom, which are suppressed by the large Hubbard U near half-filling, are found to become active at a fairly low doping level. We find that possible charge order is mainly driven by Fermi surface nesting, with competition between a near-$(\pi ,\pi )$ order at low doping and antinodal nesting at higher doping, very similar to the momentum structure of magnetic fluctuations. The resulting nesting vectors are generally consistent with photoemission and tunneling observations, evidence for charge density wave order in YBa2Cu3O$_{7-\delta }$ including Kohn anomalies, and suggestions of competition between one- and two-q-vector nesting.
We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov–de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.
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Stability of ferromagnetism within the time-dependent Gutzwiller approximation for the Hubbard model
(2011)
High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin–charge locking
(2017)
Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La1.875Ba0.125CuO4 across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.
Localized Gap States in LiCoO2 and their Influence on the Transport Properties in Li-Ion Batteries
(2010)
Restored strange metal phase through suppression of charge density waves in underdoped YBa2Cu3O7–δ
(2021)
The normal state of optimally doped cuprates is dominated by the “strange metal” phase that shows a linear temperature (T) dependence of the resistivity persisting down to the lowest T. For underdoped cuprates, this behavior is lost below the pseudogap temperature T*, where charge density waves (CDWs), together with other intertwined local orders, characterize the ground state. We found that the T-linear resistivity of highly strained, ultrathin, underdoped YBa2Cu3O7–δ films is restored when the CDW amplitude, detected by resonant inelastic x-ray scattering, is suppressed. This observation suggests an intimate connection between the onset of CDWs and the departure from T-linear resistivity in underdoped cuprates. Our results illustrate the potential of using strain control to manipulate the ground state of quantum materials.
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.
The spin-Hall effect is the generation of a transverse spin-current induced by a longitudinal electric field. Among the various scattering mechanisms which can induce a finite spin-Hall effect we focus on the intrinsic contribution arising from a Rashba-type spin–orbit (RSO) coupling which for couplings linear in momentum usually vanishes. Here we show that non-homogeneity in the spin–orbit coupling arising from structure inversion asymmetry gives rise to a finite spin-Hall effect which we exemplify for a system with striped Rashba spin–orbit coupling.
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.
It is shown that non-homogeneity in the spin-orbit coupling (SOC) arising from structure inversion asymmetry gives rise to a finite intrinsic spin Hall conductivity in contrast with the corresponding case of a homogeneous SOC in the disordered two-dimensional electron gas. In particular, we examine the inhomogeneity arising from a striped modulation of the Rashba type spin-orbit coupling. A corresponding structure could be realized at oxide interfaces with periodic top gating or in semiconductor heterostructures.