We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two
examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is observable through the Purcell effect. When combining the superconductor, graphene, and the quantum emitters, a number of experimental knobs become available for unveiling and studying the electrodynamics of superconductors.
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 $omega < 2Delta$ and $
q < 1/xi$ where $Delta$ is the gap and $xi$ 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 mode requires particle-hole symmetry breaking while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-THz frequency range. In a system of two superconducting layers with nanometer scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well defined resonance peaks in the near-field THz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two dimensional superconductors, realized for example in samples of high T$_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the THz near field radiation.
We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical pote
ntial, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor $sigma^{(3)}$ whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for $sigma^{(3)}$ for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.
On the basis of negative transport coefficients, it has been argued that the quantum oscillations observed in underdoped YBa(2)Cu(3)O(6+x) in high magnetic fields must be due to antinodal electron pockets. We point out a counter example in which elec
tron-like transport in a hole-doped cuprate is associated with Fermi-arc states. We also present evidence that the antinodal gap in YBa(2)Cu(3)O(6+x) is robust to modest applied magnetic fields. We suggest that these observations should be taken into account when interpreting the results of the quantum oscillation experiments.
