Effective numbers of charge carriers in doped graphene: The generalized Fermi liquid approach

The single-band current-dipole Kubo formula for the dynamical conductivity of heavily doped graphene from Kup\v{c}i\'{c} [Phys. Rev. B 91, 205428 (2015)] is extended to a two-band model for conduction $\pi$ electrons in lightly doped graphene. Using a posteriori relaxation-time approximation in the two-band quantum transport equations, with two different relaxation rates and one quasi-particle lifetime, we explain a seemingly inconsistent dependence of the dc conductivity $\sigma^{\rm dc}_{\alpha \alpha}$ of ultraclean and dirty lightly doped graphene samples on electron doping, in a way consistent with the charge continuity equation. It is also shown that the intraband contribution to the effective number of conduction electrons in $\sigma^{\rm dc}_{\alpha \alpha}$ vanishes at $T=0$ K in the ultraclean regime, but it remains finite in the dirty regime. The present model is shown to be consistent with a picture in which the intraband and interband contributions to $\sigma^{\rm dc}_{\alpha \alpha}$ are characterized by two different mobilities of conduction electrons, the values of which are well below the widely accepted value of mobility in ultraclean graphene. The dispersions of Dirac and $\pi$ plasmon resonances are reexamined to show that the present, relatively simple expression for the dynamical conductivity tensor can be used to study simultaneously single-particle excitations in the dc and optical conductivity and collective excitations in energy loss spectroscopy experiments.Comment: 13 pages, 11 figure

Two-dimensional conical dispersion in ZrTe5 evidenced by optical spectroscopy

Zirconium pentatelluride was recently reported to be a 3D Dirac semimetal, with a single conical band, located at the center of the Brillouin zone. The cone's lack of protection by the lattice symmetry immediately sparked vast discussions about the size and topological/trivial nature of a possible gap opening. Here we report on a combined optical and transport study of ZrTe5, which reveals an alternative view of electronic bands in this material. We conclude that the dispersion is approximately linear only in the a-c plane, while remaining relatively flat and parabolic in the third direction (along the b axis). Therefore, the electronic states in ZrTe5 cannot be described using the model of 3D Dirac massless electrons, even when staying at energies well above the band gap 6 meV found in our experiments at low temperatures.Comment: Physical Review Letters 122, 217402 (2019). Corrected acknowledgment

Distinguishing the gapped and Weyl semimetal scenario in ZrTe5\mathrm{Zr}{\mathrm{Te}}_{5}: Insights from an effective two-band model

Here we study the static and dynamic transport properties of a low-energy two-band model proposed previously in Martino et al. [PRL 122, 217402 (2019)], with an anisotropic in-plane linear momentum dependence and a parabolic out-of-plane dispersion. The model is extended to include a negative band gap, which leads to the emergence of a Weyl semimetal (WSM) state, as opposed to the gapped semimetal (GSM) state when the band gap is positive. We calculate and compare the zero- and finite-frequency transport properties of the GSM and WSM cases. The DC properties that are calculated for the GSM and WSM cases are Drude spectral weight, mobility, and resistivity. We determine their dependence on the Fermi energy and crystal direction. The in- and out-of-plane optical conductivities are calculated in the limit of the vanishing interband relaxation rate for both semimetals. The main common features are an ω1/2 in-plane and ω3/2 out-of-plane frequency dependence of the optical conductivity. We seek particular features related to the charge transport that could unambiguously point to one ground state over the other, based on the comparison with the experiment. Differences between the WSM and GSM are in principle possible only at extremely low carrier concentrations and at low temperatures

Neutron Capture on the s-Process Branching Point 171Tm via Time-of-Flight and Activation

Here we study the static and dynamic transport properties of a low-energy two-band model proposed previously in Martino et al. [PRL 122, 217402 (2019)], with an anisotropic in-plane linear momentum dependence and a parabolic out-of-plane dispersion. The model is extended to include a negative band gap, which leads to the emergence of a Weyl semimetal (WSM) state, as opposed to the gapped semimetal (GSM) state when the band gap is positive. We calculate and compare the zero- and finite-frequency transport properties of the GSM and WSM cases. The DC properties that are calculated for the GSM and WSM cases are Drude spectral weight, mobility, and resistivity. We determine their dependence on the Fermi energy and crystal direction. The in- and out-of-plane optical conductivities are calculated in the limit of the vanishing interband relaxation rate for both semimetals. The main common features are an ω^1/2 in-plane and ω^3/2 out-of-plane frequency dependence of the optical conductivity. We seek particular features related to the charge transport that could unambiguously point to one ground state over the other, based on the comparison with the experiment. Differences between the WSM and GSM are in principle possible only at extremely low carrier concentrations and at low temperatures

Manifestations of the electron-phonon interaction range in angle-resolved photoemission spectra

Numerous angle-resolved photoemission spectroscopy (ARPES) studies of a wide class of low-density metallic systems, ranging from doped transition metal oxides to quasi-two-dimensional interfaces between insulators, exhibit phonon sidebands below the quasiparticle peak as a unique hallmark of polaronic correlations. Here, we single out properties of ARPES spectra that can provide a robust estimate of the effective range (screening length) of the electron-phonon interaction, regardless of the limited experimental resolution, dimensionality, and particular features of the electronic structure, facilitating a general methodology for an analysis of a whole class of materials

Low-energy excitations in type-II Weyl semimetal Td -MoTe2 evidenced through optical conductivity

Molybdenum ditelluride, MoTe2, is a versatile material where the topological phase can be readily tuned by manipulating the associated structural phase transition. The fine details of the band structure of MoTe2, key to understanding its topological properties, have proven difficult to disentangle experientially due to the multiband character of the material. Through experimental optical conductivity spectra, we detect two strong low-energy interband transitions. Both are linked to excitations between spin-orbit split bands. The lowest interband transition shows a strong thermal shift, pointing to a chemical potential that dramatically decreases with temperature. With the help of ab initio calculations and a simple two-band model, we give qualitative and quantitative explanations of the main features in the temperature-dependent optical spectra up to 400 meV

Addressing shape and extent of Weyl cones in TaAs by Landau level spectroscopy

International audienceTaAs is a prime example of a topological semimetal with two types of Weyl nodes, W 1 and W 2 , whose bulk signatures have proven elusive. We apply Landau level spectroscopy to crystals with multiple facets and identify-among other low-energy excitations between parabolic bands-the response of a cone extending over a wide energy range. Comparison with density functional theory studies allows us to associate this conical band with nearly isotropic W 2 nodes. In contrast, W 1 cones, which are more anisotropic and less extended in energy, appear to be buried too deep beneath the Fermi level. They cannot be accessed directly. Instead, the excitations in their vicinity give rise to an optical response typical of a narrow-gap semiconductor rather than a Weyl semimetal

Optical conductivity of the type-II Weyl semimetal TaIrTe⁴

TaIrTe4 is an example of a candidate Weyl type-II semimetal with a minimal possible number of Weyl nodes. Four nodes are reported to exist in a single plane in k space. The existence of a conical dispersion linked toWeyl nodes has yet to be shown experimentally. Here, we use optical spectroscopy as a probe of the band structure on a low-energy scale. Studying optical conductivity allows us to probe intraband and interband transitions with zero momentum. In TaIrTe4, we observe a narrow Drude contribution and an interband conductivity that may be consistent with a tilted linear band dispersion up to 40 meV. The interband conductivity allows us to establish the effective parameters of the conical dispersion; effective velocity v = 1.1 × 104 m/s and tilt γ = 0.37. The transport data, Seebeck and Hall coefficients, are qualitatively consistent with conical features in the band structure. Quantitative disagreement may be linked to the multiband nature of TaIrTe4

A surrogate measure of stomatal aperture

It is proposed that a measurement of the peristomatal criterion for choosing a technique is scale of measurement: groove distance (PGD) of guard cells on surface depending on the purpose of the study, researchers may impressions of leaf epidermis can act as a surrogate wish to investigate the conductances of canopies, plants, measure of stomatal aperture. To test this idea, leaves, and sub-leaf areas, or the widths of individual investigations were carried out on two species, one in pores (van Gardingen et al., 1997). The characterization which it is possible to make direct measurements of of patches and trends in stomatal aperture over leaf pore width with relative ease (Commelina communis surfaces (Terashima et al., 1988; Downton et al., 1988; L.) and one whose stomata are so small that this is Smith et al., 1989) has renewed interest in methods difficult (Phaseolus vulgaris L.). Leaf water vapour appropriate for the whole leaf scale and below. Despite conductance measurements were first taken with a the fact that advances in IRGA-based porometry and porometer, then, without delay, a silicone rubber measurement of chlorophyll fluorescence allow direct and impression of the leaf was made of the area directly indirect measurement of stomatal activity in small areas under the porometer cup. From a positive replica of of leaves (Daley et al., 1989; Parkinson et al., 1990), this impression, stomatal aperture, PGD and pore there is still a need for accurate measurements of indi