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arXiv:1503.05731 · Physical review. B./Physical review. B

Nonlinear optical conductivity of U(1) spin liquids with large spinon Fermi surfaces

Yuan-Fei Ma, Tai Kai Ng

Published Jun 6, 2016• 2 citations
arXivHTMLPDF

Abstract

In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law $(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})$ response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\ensuremath{\omega}$ inside the spin liquids.

DOI
10.1103/physrevb.93.245109

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In this paper we study the nonlinear current response of U(1)U(1)U(1) spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field E(t)\mathbf{E}(t)E(t) within the framework of an effective U(1)U(1)U(1) gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law (\ensuremath∼\ensuremathω\ensuremathη)(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})(\ensuremath∼\ensuremathω\ensuremathη) response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency 3\ensuremathω3\ensuremath{\omega}3\ensuremathω inside the spin liquids.
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In this paper we study the optical properties of U(1)U(1)U(1) spin liquids with large spinon Fermi surfaces based on an expression for the bulk optical conductivity obtained through the Ioffe-Larkin composition rule. We show that the optical conductivity of U(1)U(1)U(1) spin liquids at energies above the charge gap has a unique feature that distinguishes them from ordinary insulators. In particular we propose the existence of a long-life surface plasmon mode propagating along the interface between a linear medium and the spin liquid at frequencies above the charge gap, which can be detected by the widely used Kretschmann-Raether three-layer configuration. The experiment provides a test that distinguishes between ordinary insulators and spin liquid states with large spinon Fermi surfaces.
We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as B2/3{B}^{2/3}B2/3 with magnetic field BBB at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.
This work studies the Zeeman magnetic field effect on a quantum spin liquid with a spinon Fermi surface. In the absence of gauge binding, the quantum spin liquid electronic density of states exhibits no Zeeman shift in the threshold energy. As the gauge binding increases, the band edge resonance peaks exhibit a reduced Zeeman shift and eventually have the Zeeman shift direction reversed for a sufficiently large gauge binding. The authors further suggest to use such anomalous Zeeman response to identify the gapless quantum spin liquid phase.
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Abstract Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in centrosymmetric systems starting from basic time dependent perturbation theory. We express the nonlinear current kernel as a sum of several causal response functions. These causal functions cannot be evaluated using perturbative field theory methods, since they are not contour ordered. Consequently, we associate each response function with a corresponding imaginary time ordered current correlation function, since the latter can be factorized using Wick’s theorem. The mapping between the response functions and the correlation functions, suitably analytically continued to real frequencies, is proven exactly. We derive constraints satisfied by the nonlinear current kernel and we prove a generalized f-sum rule for the nonlinear conductivity, all of which are consequences of particle number conservation. The constraints guarantee that the nonlinear static responses are free from spurious divergences. We apply the theory to compute the gauge invariant nonlinear conductivity of a system of noninteracting electrons in the presence of weak disorder. As special cases of this generalized nonlinear response, we discuss its third harmonic and its instantaneous terahertz Kerr signals. The formalism can be used to compute the nonlinear conductivity in symmetry broken phases of electronic systems such as superconductors, density waves and nematic states.