Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density wave

We analyze the Hall conductivity $\sigma_{xy}(\omega)$ of a charge ordered state with momentum $\mathbf{Q}=(0,2Q)$ and calculate the intrinsic contribution to the Kerr angle $\Theta_K$ using the fully reconstructed tight-binding band structure for layered cuprates beyond the low energy hot spots model and particle hole symmetry. We show that such a unidirectional charge density wave (CDW), which breaks time reversal symmetry as recently put forward by Wang and Chubukov [Phys. Rev. B {\bf 90}, 035149 (2014)], leads to a nonzero polar Kerr effect as observed experimentally. In addition, we model a fluctuating CDW via a large quasiparticle damping of the order of the CDW gap and discuss possible implications for the pseudogap phase. We can qualitatively reproduce previous measurements of underdoped cuprates but making quantitative connections to experiments is hampered by the sensitivity of the polar Kerr effect with respect to the complex refractive index $n(\omega)$.Comment: 6 pages, 4 figure

On the Theory of Difference Frequency Quantum Oscillations

Quantum oscillations (QO) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface pockets, and the theory of magnetic breakdown explains the observation of sums of QO frequencies at high magnetic fields. Here we develop a quantitative theory of {\it difference frequency} QOs in two- and three-dimensional metals with multiple Fermi pockets with parabolic or linearly dispersing excitations. We show that a non-linear interband coupling, e.g. in the form of interband impurity scattering, can give rise to otherwise forbidden QO frequencies which can persist to much higher temperatures compared to the basis frequencies. We discuss the experimental implications of our findings for various material candidates, for example multi-fold fermion systems, and the relation to magneto intersubband oscillations known for coupled two-dimensional electron gases

Interband scattering- and nematicity-induced quantum oscillation frequency in FeSe

Understanding the nematic phase observed in the iron-chalcogenide materials is crucial for describing their superconducting pairing. Experiments on FeSe$_{1-x}$S$_x$ showed that one of the slow Shubnikov--de Haas quantum oscillation frequencies disappears when tuning the material out of the nematic phase via chemical substitution or pressure, which has been interpreted as a Lifshitz transition [Coldea et al., npj Quant Mater 4, 2 (2019), Reiss et al., Nat. Phys. 16, 89-94 (2020)]. Here, we present a generic, alternative scenario for a nematicity-induced sharp quantum oscillation frequency which disappears in the tetragonal phase and is not connected to an underlying Fermi surface pocket. We show that different microscopic interband scattering mechanisms - for example, orbital-selective scattering - in conjunction with nematic order can give rise to this quantum oscillation frequency beyond the standard Onsager relation. We discuss implications for iron-chalcogenides and the interpretation of quantum oscillations in other correlated materials

Quantum oscillations in a doped Mott insulator beyond Onsager's relation

The kinetic energy of electrons in a magnetic field is quenched resulting in a discrete set of highly degenerate Landau levels (LL) which gives rise to fascinating phenomena like the de Haas-van Alphen effect (dHvAe) or the integer and fractional quantum Hall effects. The latter is a result of interactions partially lifting the degeneracy within a given LL while inter-LL interactions are usually assumed to be unimportant. Here, we study the LL spectrum of the Hatsugai-Kohmoto model, a Hubbard-like model which is exactly soluble on account of infinite range interactions. For the doped Mott insulator phase in a magnetic field we find that the degeneracy of LLs is preserved but inter-LL interactions are important leading to a non-monotonous reconstruction of the spectrum. As a result, strong LL repulsion leads to aperiodic quantum oscillations of the dHvAe in contrast to Onsager's famous relation connecting oscillation frequencies with the Fermi surface areas at zero field. In addition, we find unconventional temperature dependencies of quantum oscillations and interaction-induced effective mass renormalizations. We discuss the general importance of inter-LL interactions for understanding doped Mott insulators in magnetic fields

Raman scattering in correlated thin films as a probe of chargeless surface states

Several powerful techniques exist to detect topologically protected surface states of weakly-interacting electronic systems. In contrast, surface modes of strongly interacting systems which do not carry electric charge are much harder to detect. We propose resonant light scattering as a means of probing the chargeless surface modes of interacting quantum spin systems, and illustrate its efficacy by a concrete calculation for the 3D hyperhoneycomb Kitaev quantum spin liquid phase. We show that resonant scattering is required to efficiently couple to this model's sublattice polarized surface modes, comprised of emergent Majorana fermions that result from spin fractionalization. We demonstrate that the low-energy response is dominated by the surface contribution for thin films, allowing identification and characterization of emergent topological band structures.Comment: 7 pages, 4 figures; added supplemental materia

Observing spin fractionalization in the Kitaev spin liquid via temperature evolution of indirect resonant inelastic x-ray scattering

Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, $T_L$ and $T_H$, which correspond to the characteristic energies of the two kinds of fractionalized excitations, $\mathbb{Z}_2$ gauge fluxes and Majorana fermions, respectively. While thermally excited $\mathbb{Z}_2$ gauge fluxes at temperature $T_L$ lead to a general broadening and softening of the response, the thermal proliferation of Majorana fermions at temperature $T_H \sim 10 \, T_L$ results in a significant shift of the spectral weight, both in terms of energy and momentum. Due to its exclusively indirect nature, the RIXS process we consider gives rise to a universal magnetic response and, from an experimental perspective, it directly corresponds to the $K$-edge of Ru$^{3+}$ in the Kitaev candidate material $\alpha$-RuCl$_3$.Comment: 8 pages, 5 figures, published version with infinitesimal change

Theory of Raman response in three-dimensional Kitaev spin liquids: application to β−\beta- and γ−\gamma-Li2_2IrO3_3 compounds

We calculate the Raman response for the Kitaev spin model on the $\mathcal{H}$-$0$, $\mathcal{H}$-$1$, and $\mathcal{H}$-$\infty$ harmonic honeycomb lattices. We identify several quantitative features in the Raman spectrum that are characteristic of the spin liquid phase. Unlike the dynamical structure factor, which probes both the Majorana spinons and flux excitations that emerge from spin fractionalization, the Raman spectrum in the Kitaev models directly probes a density of states of pairs of fractional, dispersing Majorana spinons. As a consequence, the Raman spectrum in all these models is gapless for sufficiently isotropic couplings, with a low-energy power law that results from the Fermi lines (or points) of the dispersing Majorana spinons. We show that the polarization dependence of the Raman spectrum contains crucial information about the symmetry of the ground state. We also discuss to what extent the features of the Raman response that we find reflect generic properties of the spin liquid phase, and comment on their possible relevance to $\alpha-$, $\beta-$ and $\gamma-$Li$_2$IrO$_3$ compounds.Comment: 19 pages, 10 figures. VERSION 2: Corrected Figure 5 and fixed inconsistencies between A and B chain-labelings. Also- a few typos and two new ref