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arXiv:1410.6330 · Physical Review B

Surface plasmons and reflectance of U(1) spin liquid states with large spinon Fermi surfaces

Yuan-Fei Ma, Tai Kai Ng

Published Feb 9, 2015• 4 citations
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Abstract

In this paper we study the optical properties of $U(1)$ 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 $U(1)$ 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.

DOI
10.1103/physrevb.91.075106

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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 develop a mean-field theory of the 1D spin-1 antiferromagnetic Heisenberg model, using a two-orbital fermionic representation for the spin-1 operators. Two ansatz with different orbital pairing symmetries are discussed and the projected mean-field ground states with their corresponding parent Hamiltonians have also been obtained. Then we study the U(1) spin liquid state with large spinon Fermi surfaces. The physical conductivity obtained through Ioffe-Larkin composition rule can support surface plasmon modes propagating along the interface between the spin liquid and a linear medium, which can be excited using a Kretschmann-Raether configuration. Next we generalize the linear current response to including nonlinear effects under the perturbation of a time dependent but spatially uniform electric field in the framework of an effective U(1) gauge theory derived through a Fermi-liquid-like approach. The nonlinear susceptibility can support waves with triple frequency inside the spin liquids through the process of third harmonic generation. As a byproduct during the Fermi-liquid approach, we generalize the standard Landau Fermi liquid theory to describe the intrinsic anomalous Hall conductivity, based on some general symmetric considerations. Fitting result of the anomalous Hall conductivity is well consistent with the experimental data, and behaves better in lower frequency range than the simple two-band model.
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 $(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})$ 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.
Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, we carry out a systematic projective symmetry group analysis and mean-field study of candidate U(1)U(1)U(1) spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight U(1)U(1)U(1) spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​. Further connection of this spinon Fermi surface U(1)U(1)U(1) spin liquid with YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.
The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.
Motivated by the recent proposal that several candidate materials such as YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ could be spinon Fermi surface spin liquids, we explore the experimental consequences of the external magnetic fields on this exotic state. Specifically, we focus on the weak field regime where the spin-liquid state is well preserved and the spinon remains to be a good description of the magnetic excitations. From the spin-1/2 nature of the spinon excitation, we predict the unique features of the spinon continuum when the weak magnetic field is applied to the system. Due to the small energy scale of the exchange interactions between the local moments in the spin-liquid candidate like YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, our proposal for the spectral weight shifts and spectral crossing in the magnetic fields can be immediately tested by inelastic neutron scattering experiments. Several other experimental aspects about the spinon Fermi surface and the spinon excitations are discussed and proposed. Our work provides an experimental scheme to examine the fractionalized spinon excitation and the candidate spin-liquid states in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, the 6H-B phase of Ba3NiSb2O9{\mathrm{Ba}}_{3}{\mathrm{NiSb}}_{2}{\mathrm{O}}_{9}Ba3​NiSb2​O9​, and other relevant materials.
A recent experiment has reported oscillations of the thermal conductivity of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ driven by an in-plane magnetic field that are reminiscent of the quantum oscillations in metals. At first glance, these observations are consistent with the presence of the long-sought-after spinon Fermi surface state. Strikingly, however, the experiment also reported vanishing thermal Hall conductivity coexisting with the oscillations of the longitudinal one. Such absence of the thermal Hall effect must originate from crystalline symmetries of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. But if the system was a traditional spinon Fermi surface state, these symmetries would also necessarily prohibit the emergence of a magnetic field acting on the spinons, in stark contradiction with the presence of quantum oscillations in experiments. To reconcile these observations, we introduce a new class of symmetry enriched ``pseudoscalar'' U(1) spin liquids in which certain crystalline symmetries act as a particle-hole conjugation on the spinons. The associated pseudoscalar spinon Fermi surface states allow for the coexistence of an emergent Landau quantizing magnetic field while having an exactly zero thermal Hall conductivity. We develop a general theory of these states by constructing Gutzwiller-projected wave functions and describing how they naturally appear as U(1) spin liquids with a distinctive projective symmetry group implementation of crystalline symmetries in the fermionic parton representation of spins. We propose that the field induced quantum disordered state in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ descends from a pseudoscalar spinon Fermi surface state that features compensated spinon-particle and spinon-hole pockets possibly located around the MMM points of its honeycomb Brillouin zone. These points are connected via a wave vector associated with the emergence of the competing zig-zag antiferromagnetic state.