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In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-called Luttinger-Abrikosov-Benelavskii phase of isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity., (© 2024 IOP Publishing Ltd.)

We study the Landau levels and magneto-optical properties of bulk black phosphorus (BP) subjected to an in-plane magnetic field along the armchair direction based on an effectivek⋅pHamiltonian. We analytically obtain the Landau levels by the perturbation method, which agrees well with the results of numerical diagonalization. By using the Kubo formula, we find the magneto-optical transition selection rules and conductance spectra for inter-band transitions are highly anisotropic. In particular, for linearly polarized light along the armchair direction, the magneto-optical transition selection rule isΔn= 0, where n is the Landau level index. However, for linearly polarized light along the zigzag and stacking direction, the magneto-optical transition selection rules becomeΔn= ±1. The magneto-optical conductance excited by linearly polarized light along the armchair direction is two order of magnitude larger than those excited by linearly polarized light along the zigzag and stacking direction because the inter-band coupling only exists in the armchair direction. Our results are useful to detect the band parameters of BP and design magnetically controlled optical devices based on it., (© 2022 IOP Publishing Ltd.)

We investigate the dynamic optical transition of monolayer silicene in the presence of external electric and exchange fields within the low-energy tight-binding model. Applying external electric and exchange fields breaks the silicene band structure spin and valley degeneracies. Three phases of silicene corresponding to different strengths of perpendicular electric field with respect to the spin-orbit coupling (Δ z < Δ so , Δ z = Δ so and Δ z > Δ so ) are considered. We obtain the spin-valley-dependent optical responses to the incoming circularly polarized light using the Kubo formula. We show and discuss how the magnitude and direction of the transverse and longitudinal optical responses of such a system change with the electric and exchange fields. Our calculations suggest that the intraband part of the longitudinal optical response as well as the initial point of the interband part have strong dependencies on the exchange field. Furthermore, we show that one of the spin subbands plays a dominant role in the response to polarized light. Depending on the type of incident light polarization, the dominant subband may change. Our results shed light on the relation between silicene dynamic optical responses and externally applied fields., (© 2022 IOP Publishing Ltd.)

We investigate the linear optical conductivities of the newly-discovered triple-component semimetals. Due to the exactly flat band, the optical conductivity relates to the transition between the zero band and the conduction band directly reflecting the band structure of the conduction electrons in contrast to the other materials. For the low-energy models with various monopole charges, the diagonal conductivities show strong anisotropy. The ω -dependence of interband conductivities for a general low-energy model is deduced. The real part of the interband σ xx always linearly depends on the optical frequency, while the one of σ zz is proportional to ω 2/ n -1 . This can be a unique fingerprint of the monopole charge. For the lattice models, there also exists the optical anomalous Hall conductivity, where a sign change may appear. The characteristic frequencies of the kink structures are calculated, strictly. Our work will help us to establish the basic picture of linear optical response in topological triple-component semimetals and identify them from other materials., (© 2021 IOP Publishing Ltd.)

In this work, we study the band structures and intrinsic anomalous Hall conductivity (AHC) of the ferromagnetic multiorbital tight-binding (TB) model derived from the transition metal compound Sr 2 RuO 4 under periodic driving of monochromatic polarized light. Within the framework of the Floquet theory, we adopt the continued fraction technique to attain the effective Hamiltonian valid in the weak-driving and low-frequency regimes, and the related Green's functions which are further employed for the transport calculations based on the Kubo formalism. The high-frequency circularly and linearly polarized light has limited impacts on the band structures, while the low-frequency light with the photon energy smaller than the bandwidth of the system opens up bandgaps at the edges of the Floquet-Brillouin zone since the transitions between Floquet sidebands become significant. For intrinsic AHC, the left-handed circularly polarized (LCP) light plays a distinct role on AHC compared to the right-handed circularly polarized (RCP) light. Furthermore, it reveals that the roles of LCP and RCP light can be interchanged by altering the incident plane of light. Finally, the intrinsic AHC with the interplay between the short-range disorder and circularly polarized light is also investigated., (© 2021 IOP Publishing Ltd.)

We systematically investigate the anisotropic magneto-conductivity and planar Hall effect in tilted magnetic topological semimetals in the frame of Kubo formula by considering the vertex correction of velocity. The nonzero anisotropic magneto-conductivity is due to the intrinsic magnetization by magnetic doping rather than the external magnetic field previously studied in literatures. In the scenario, tilt, which is common in band structure, plays a key role in this anisotropic magneto-conductivity. This anisotropic magneto-conductivity completely originates from the band anisotropy. The vertex correction only amends the magnitude, but does not change the qualitative behavior of the longitudinal conductivity. However, the planar Hall conductivity is always zero for tilt along both x and y directions in vivid contrast to the case arising from an external magnetic field. Our work offers a route to understand the anisotropic magneto-conductivity effect in tilted Weyl semimetals with Zeeman field. It will be helpful to get a deeper understanding of the transport characteristic in tilted topological semimetals., (© 2021 IOP Publishing Ltd.)