Nonlinear optical effects in inversion-symmetry-breaking superconductors

Abstract

We study nonlinear optical responses in superconducting systems with inversion (I) symmetrybreaking order parameters. We first show that any superconducting system with I and time-reversal (T ) symmetries requires an I-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a 1D toy model of an I-breaking superconductor to numerically calculate linear and nonlinear conductivities, including shift current and second harmonic generations (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG response compare to the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in cuprates [1]. Finally, we confirm the generality of our observations regarding nonlinear responses of I-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model.

Enhanced Shift Currents in Monolayer 2D GeS and SnS by Strain-Induced Band Gap Engineering

“…The electrons are excited to coherent superpositions, which allows for the net current flow ascribed to the asymmetry of the potential, in a process where it has firmly been verified that only symmetry inversion must be broken but there is no requirement for polarization. 15 , 16 …”

Theory of optical responses in clean multi-band superconductors

“…Matrix elements of this operator are important in our analysis because they describe the transition amplitudes. In the clean limit, the real part of the optical conductivity tensor is given by where ω is the frequency of light, f n m = f n − f m is the difference between the Fermi distribution of the n th band f n , , and ω m n = ω m − ω n , where 9 , 30 . The delta function is replaced by the Lorentzian distribution when the mean free path is finite.…”

“…Equation ( 3 ) is positive-semidefinite when c = a . Therefore, interband transitions are completely forbidden only when symmetries impose at every k 30 . The relevant symmetry operators should be k -local ( k → k ).…”

“…The first condition (i) just means breaking inversion symmetry when other unitary symmetries do not exist, which was demonstrated in ref. 30 . The second (ii) implies that the superconductor may host stable BFSs 27 , 32 .…”

“…Our theory establishes the existence of the true clean-limit optical responses beyond the Mattis–Bardeen theory in multiband superconductors. While we focus on linear responses in the current work, our classification of optical transitions applies to nonlinear optical responses also 30 . Since nonlinear optical conductivity tensors have more components than the linear counterpart, they give richer information on the symmetry of the system.…”