Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of ironbased and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a non-equilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merges into a single in-gap mode, with the mixing vanishing only close to the phase boundaries. For the d-wave ground state, we find that nematic interaction suppresses the damping of the collective oscillations in the short-time dynamics. Additionally, we find that even inside the nematic s+d-wave superconducting state, a Bardasis-Schrieffer-like mode leads to order parameter oscillations that strongly depend on the competition between the two pairing symmetries. We discuss the connection of our results to the recent pump-probe experiments on high-Tc superconductors.
Bardasis-Schrieffer modes in superconductors are fluctuations in subdominant pairing channels, e.g., d-wave fluctuations in an s-wave superconductor. This Rapid Communication shows that these modes also generically occur in excitonic insulators. In s-wave excitonic insulators, a p-wave Bardasis-Schrieffer mode exists below the gap energy, is optically active and hybridizes strongly with photons to form Bardasis-Schrieffer polaritons, which are observable in both far-field and near-field optical experiments.
We theoretically analyze the collective modes in unconventional superconductors focusing on Bardasis-Schrieffer (BS) mode and its contribution to the third harmonic generation currents. Starting from a model with competing superconducting pairing instabilities we add fluctuations of the fields beyond saddle point approximation and calculate their response to an applied pulsed electric field. To model phase fluctuations appropriately we take into account the effect of the long-range Coulomb interaction. While the phase mode is pushed into a plasmon frequency, as known from the literature, we sh…
In unconventional superconductors, understanding the form of the pairing interaction is the primary goal. In this regard, Raman spectroscopy is a very useful tool, as it identifies the ground state and also the subleading pairing channels by probing collective modes. Here we propose a general theory for multiband Raman response and identify new features in the spectrum that can provide a robust test for a pairing theory. We identify multiple Bardasis-Schrieffer type collective modes and connect the weights of these modes to the sub-leading gap structures within a microscopic pairing theory. Th…
We calculate the collective mode spectrum in models of superconductors with attractive interactions in s-and d channels as a function of their relative strength, across a phase diagram that includes transition between s, s+id, and d-wave ground states. For one-band systems, we recover the largely known results for the phase, amplitude, and Bardasis-Schrieffer modes of pure s or d-states, and show how the well-defined Bardasis-Schrieffer mode softens near the s + id phase boundary and evolves in a characteristic manner through the s + id phase as a mixed symmetry mode. For two-band systems, we …
Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band square lattice model with spin-spin interaction as an example, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse ca…
We theoretically study the low energy electromagnetic response of BCS type superconductors focusing on propagating collective modes that are observable with THz near field optics. The interesting frequency and momentum range is $ω< 2Δ$ and $q < 1/ξ$ where $Δ$ is the gap and $ξ$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and Carlson-Goldman modes using THz near field technique, although none of these modes couple linearly to far field radiation. Coupling of THz near field radiation to the amplitude …
Following the recent success of realizing exciton-polariton condensates in cavities, we examine the hybridization of cavity photons with the closest analog of excitons within a superconductor, states called Bardasis-Schrieffer (BS) modes. Though BS modes do not typically couple directly to light, one can engineer a coupling with an externally imposed supercurrent, leading to the formation of hybridized Bardasis-Schrieffer-polariton states, which we obtain both via direct solution and through the derivation of an effective Hamiltonian picture for the model. These new excitations have nontrivial…
We show that electronic Raman scattering affords a window into the essential properties of the pairing potential $V_{\mathbf{k},\mathbf{k^{\prime}}}$ of iron-based superconductors. In Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ we observe band dependent energy gaps along with excitonic Bardasis-Schrieffer modes characterizing, respectively, the dominant and subdominant pairing channel. The $d_{x^2-y^2}$ symmetry of all excitons allows us to identify the subdominant channel to originate from the interaction between the electron bands. Consequently, the dominant channel driving superconductivity results fro…
We explore ways in which the close proximity between graphene sheets and monolayers of 2D superconductors can lead to hybridization between their collective excitations. We consider heterostructures formed by combinations of graphene sheets and 2D superconductor monolayers. The broad range of energies in which the graphene plasmon can exist, together with its tunability, makes such heterostrucutres promising platforms for probing the many-body physics of superconductors. We show that the hybridization between the graphene plasmon and the Bardasis-Schrieffer mode of a 2D superconductor results …
We study Raman scattering in the superconducting state of alkali-intercalated iron selenide materials AxFe2-ySe2 (A=K,Rb,Cs) in which Fermi surface has only electron pockets. Theory predicts that both s-wave and d-wave pairing channels are attractive in this material, and the gap can have either s-wave or d-wave symmetry, depending on the system parameters. ARPES data favor $s-$wave superconductivity. We present the theory of Raman scattering in AxFe2-ySe2 assuming that the ground state has s-wave symmetry but $d-$ wave is a close second. We argue that Raman profile in d-wave B2g channel displ…
Superconductivity is a remarkably widespread phenomenon observed in most metals cooled down to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the celebrated Bardeen-Cooper-Schrieffer (BCS) theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in new and unexpected ways. In the case of the iron-based superconductors, this includes a new appreciation of the ways in which the presence of m…
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 superconductivi…
