Low-frequency Optical Conductivity Research Articles

Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7

The discovery of superconductivity with a critical temperature of about 80 K in La3Ni2O7 single crystals under pressure has received enormous attention. La3Ni2O7 is not superconducting under ambient pressure but exhibits a transition at T ∗ ≃ 115 K. Understanding the electronic correlations and charge dynamics is an important step towards the origin of superconductivity and other instabilities. Here, our optical study shows that La3Ni2O7 features strong electronic correlations which significantly reduce the electron’s kinetic energy and place this system in the proximity of the Mott phase. The low-frequency optical conductivity reveals two Drude components arising from multiple bands at the Fermi level. The transition at T ∗ removes the Drude component exhibiting non-Fermi liquid behavior, whereas the one with Fermi-liquid behavior is barely affected. These observations in combination with theoretical results suggest that the Fermi surface dominated by the Ni-d3z2−r2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{3{z}^{2}-{r}^{2}}$$\\end{document} orbital is removed due to the transition at T ∗. Our experimental results provide pivotal information for understanding the transition at T ∗ and superconductivity in La3Ni2O7.

Optical study of magnetic topological insulator MnBi4Te7

We present an infrared spectroscopy study of the magnetic topological insulator MnBi4Te7 with antiferromagnetic (AFM) order below the Néel temperature T N = 13 K. Our investigation reveals that the low-frequency optical conductivity consists of two Drude peaks, indicating a response of free carriers involving multiple bands. Interestingly, the narrow Drude peak grows strongly as the temperature decreases, while the broad Drude peak remains relatively unchanged. The onset of interband transitions starts around 2000 cm−1, followed by two prominent absorption peaks around 10000 cm−1 and 20000 cm−1. Upon cooling, there is a notable transfer of spectral weight from the interband transitions to the Drude response. Below T N, the AFM transition gives rise to small anomalies of the charge response due to a band reconstruction. These findings provide valuable insights into the interplay between magnetism and the electronic properties in MnBi4Te7.

Origin of charge density wave in the kagome metal CsV3Sb5 as revealed by optical spectroscopy

We report on a detailed study of the optical properties of CsV$_{3}$Sb$_{5}$ at a large number of temperatures above and below the charge-density-wave (CDW) transition. Above the CDW transition, the low-frequency optical conductivity reveals two Drude components with distinct widths. An examination of the band structure allows us to ascribe the narrow Drude to multiple light and Dirac bands, and the broad Drude to the heavy bands near the $M$ points which form saddle points near the Fermi level. Upon entering the CDW state, the opening of the CDW gap is clearly observed. A large portion of the broad Drude is removed by the gap, whereas the narrow Drude is not affected. Meanwhile, an absorption peak associated with interband transitions near the saddle points shifts to higher energy and grows in weight. These observations are consistent with the scenario that the CDW in CsV$_{3}$Sb$_{5}$ is driven by nesting of Fermi surfaces near the saddle points at $M$.

Optical and photoemission investigation of structural and magnetic transitions in the iron-based superconductor Sr0.67Na0.33Fe2As2

We report the temperature-dependent optical conductivity and ARPES studies of the iron-based superconductor (SC) Sr$_{0.67}$Na$_{0.33}$Fe$_2$As$_2$ in the high-temperature tetragonal paramagnetic phase; below the structural and magnetic transitions at $T_{\rm N}\simeq$125 K in the orthorhombic spin-density-wave (SDW)-like phase, and $T_r\simeq$42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDW order exist; and below the SC transition at $T_c\simeq$10 K. The free-carrier component in the optical conductivity is described by two Drude contributions; one strong and broad, the other weak and narrow. The broad Drude component decreases dramatically below $T_{\rm N}$ and $T_r$, with much of its strength being transferred to a bound excitation in the mid-infrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone-folding below $T_r$. Below $T_c$ the dramatic decrease in the low-frequency optical conductivity signals the formation of a SC energy gap. ARPES reveals hole-like bands at the center of the Brillouin zone (BZ), with both electron- and hole-like bands at the corners. Below $T_{\rm N}$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; while below $T_r$ the electron-like bands shift and split, giving rise to a low-energy excitation in the optical conductivity at ~20 meV. The magnetic states, with resulting SDW and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets, but appears to have relatively little impact on the SC in this material.

Optical conductivity of black phosphorus with a tunable electronic structure

Black phosphorus (BP) is a two-dimensional layered material composed of phosphorus atoms. Recently, it was demonstrated that external perturbations such as an electric field close the band gap in few-layer BP, and can even induce a band inversion, resulting in an insulator phase with a finite energy gap or a Dirac semimetal phase characterized by two separate Dirac nodes. At the transition between the two phases, a semi-Dirac state appears in which energy disperses linearly along one direction and quadratically along the other. In this work, we study the optical conductivity of few-layer BP using a lattice model and the corresponding continuum model, incorporating the effects of an external electric field and finite temperature. We find that the low-frequency optical conductivity scales a power law that differs depending on the phase, which can be utilized as an experimental signature of few-layer BP in different phases. We also systematically analyze the evolution of the material parameters as the electric field increases, and the consequence on the power-law behavior of the optical conductivity.

Infrared spectroscopic studies of the topological properties in CaMnSb2

We present temperature-dependent infrared spectroscopic studies of CaMnSb2, a proposed threedimensional topological material. The low plasma edge in the reflectivity spectrum and small Drude component in the optical conductivity indicate a very low carrier density. The low-frequency optical conductivity is well described by the superposition of a narrow and a broad Drude terms. Several linear components have been observed in the low-temperature optical conductivity, but none of them extrapolates to the origin, at odds with the optical response expected for three-dimensional Dirac fermions. A series of absorption peaks have been resolved in the high-frequency optical conductivity. The energy of these peaks agrees well with the interband transitions expected for the band structures from first-principles calculations. Intriguingly, the lowest band gap increases with decreasing temperature, mimic the temperature evolution of inverted bands. Furthermore, our theoretical calculations demonstrate the existence of weak coupling between two Sb-chains layers results in the topological trivial surface states in CaMnSb2.

Unusual electronic and vibrational properties in the colossal thermopower material FeSb2

The iron antimonide FeSb2 possesses an extraordinarily high thermoelectric power factor at low temperature, making it a leading candidate for cryogenic thermoelectric cooling devices. However, the origin of this unusual behavior is controversial, having been variously attributed to electronic correlations as well as the phonon-drag effect. The optical properties of a material provide information on both the electronic and vibrational properties. The optical conductivity reveals an anisotropic response at room temperature; the low-frequency optical conductivity decreases rapidly with temperature, signalling a metal-insulator transition. One-dimensional semiconducting behavior is observed along the b axis at low temperature, in agreement with first-principle calculations. The infrared-active lattice vibrations are also symmetric and extremely narrow, indicating long phonon relaxation times and a lack of electron-phonon coupling. Surprisingly, there are more lattice modes along the a axis than are predicted from group theory; several of these modes undergo significant changes below about 100 K, hinting at a weak structural distortion or phase transition. While the extremely narrow phonon line shapes favor the phonon-drag effect, the one-dimensional behavior of this system at low temperature may also contribute to the extraordinarily high thermopower observed in this material.

Infrared spectroscopy study of ironbased superconductor Li0.8Fe0.2 ODFeSe

We perform an in-plane optical spectroscopy measurement on iron-based superconductor Li0.8Fe0.2ODFeSe single crystal. At room temperature, the low frequency optical conductivity shows an incoherent characteristic; the Drude component is absent. With temperature decreasing, the Drude component develops and narrows rapidly. A well-defined plasma edge is observed in reflectance spectrum at temperature below 100 K, indicating a dramatically reduced scattering rate. The spectral weight contributed from free carriers is even smaller than that of FeSe single crystal. A number of phonon modes are visible in the measured spectra. We also observe clear spectral change below 160 cm-1 at 10 K, associated with the formation of superconducting energy gap in the superconducting state. The energy scale of the superconducting gap is comparable to the value measured by angle-resolved photoemission spectroscopy technique. Like FeSe and other iron pnictides, a clear temperature-induced spectral weight transfer at high energy is observed for Li0.8Fe0.2ODFeSe, indicating the presence of strong correlation effect.

Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite

We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to expose the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field. We consider an experimental manifestation (optical conductivity) of a new state of matter (so-called fermion condensate) realized in quantum spin liquids, for, in many ways, they exhibit typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite produce important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to reveal the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field.

Infrared probe of the gap evolution across the phase diagram of Ba1−xKxFe2As2

We measured the optical conductivity of superconducting single crystals of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with $x$ ranging from 0.40 (optimal doping, $T_c = 39$ K) down to 0.20 (underdoped, $T_c = 16$ K), where a magnetic order coexists with superconductivity. In the normal state, the low-frequency optical conductivity can be described by an incoherent broad Drude component and a coherent narrow Drude component: the broad one is doping-independent, while the narrow one shows strong scattering in the heavily underdoped compound. In the superconducting state, the formation of the condensate leads to a low-frequency suppression of the optical conductivity spectral weight. In the heavily underdoped region, the superfluid density is significantly suppressed, and the weight of unpaired carriers rapidly increases. We attribute these results to changes in the superconducting gap across the phase diagram, which could show a nodal-to-nodeless transition due to the strong interplay between magnetism and superconductivity in underdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$.

Self-dual quasiperiodic systems with power-law hopping

We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar Aubry-Andre model. For large enough $p$, their static properties are similar to those of the Aubry-Andre model, although the low-frequency conductivity in the localized phase is sensitive to $p$. For $p \leq 2.1$ the Aubry-Andre localization transition splits into three transitions; two distinct intermediate regimes with both localized and delocalized states appear near the self-dual point of the Aubry-Andre model. In the intermediate regimes, the density of states is singular continuous in much of the spectrum, and is approximately self-similar: states form narrow energy bands, which are divided into yet narrower sub-bands; we find no clear sign of a mobility edge. When $p < 1$, localized states are not stable in random potentials; in the present model, however, tightly localized states are present for relatively large systems. We discuss the frequency-dependence and strong sample-to-sample fluctuations of the low-frequency optical conductivity, although a suitably generalized version of Mott's law is recovered when the power-law is slowly decaying. We present evidence that many of these features persist in models that are away from self-duality.

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point.

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

Infrared spectroscopic study on lattice dynamics in CaFeO3

The change of the lattice dynamics upon the charge disproportionation (CD) transition has been investigated for the ${\mathrm{CaFeO}}_{3}$ crystal by measuring its infrared optical spectra. Across the CD transition, ${\mathrm{CaFeO}}_{3}$ undergoes a metal-insulator transition, and it is found that below ${T}_{CD}\ensuremath{\approx}290$ K the low-frequency optical conductivity gradually decreases to a rather low value and is dominated by a series of infrared-active phonons. Intriguingly, accompanied by the CD transition, two prominent phonon modes at $\ensuremath{\sim}243$ and $\ensuremath{\sim}559$ ${\mathrm{cm}}^{\ensuremath{-}1}\text{associated}$ with the vibrations of Fe-O bonds show obvious redshift and asymmetric line shapes characterized by a Fano profile, suggesting a strong electron-phonon coupling. This coupling behavior reveals an intimate relationship between charge and lattice in the CD transition of ${\mathrm{CaFeO}}_{3}$.

Detailed optical spectroscopy of hybridization gap and hidden-order transition in high-qualityURu2Si2single crystals

We present a detailed temperature and frequency dependence of the optical conductivity measured on clean high quality single crystals of URu$_{2}$Si$_{2}$ of $ac$- and $ab$-plane surfaces. Our data demonstrate the itinerant character of the narrow 5f bands, becoming progressively coherent as temperature is lowered below a cross-over temperature $T^*{\sim}75~K$. $T^*$ is higher than in previous reports as a result of a different sample preparation, which minimizes residual strain. We furthermore present the density-response (energy-loss) function of this compound, and determine the energies of the heavy fermion plasmons with $a$-and $c$-axis polarization. Our observation of a suppression of optical conductivity below 50~meV both along $a$ and $c$-axis, along with a heavy fermion plasmon at 18~meV, points toward the emergence of a band of coherent charge carriers crossing the Fermi energy and the emergence of a hybridization gap on part of the Fermi surface. The evolution towards coherent itinerant states is accelerated below the hidden order temperature $T_{HO}=17.5$~K. In the hidden order phase the low frequency optical conductivity shows a single gap at $\sim 6.5$meV, which closes at $T_{HO}$.

Optical observation of spin-density-wave fluctuations in Ba122 iron-based superconductors

In iron-based superconductors, a spin-density-wave (SDW) magnetic order is suppressed with doping and unconventional superconductivity appears in close proximity to the SDW instability. The optical response of the SDW order shows clear gap features: substantial suppression in the low-frequency optical conductivity, alongside a spectral weight transfer from low to high frequencies. Here, we study the detailed temperature dependence of the optical response in three different series of the Ba122 system [Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$, Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ and BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$]. Intriguingly, we found that the suppression of the low-frequency optical conductivity and spectral weight transfer appear at a temperature $T^{\ast}$ much higher than the SDW transition temperature $T_{SDW}$. Since this behavior has the same optical feature and energy scale as the SDW order, we attribute it to SDW fluctuations. Furthermore, $T^{\ast}$ is suppressed with doping, closely following the doping dependence of the nematic fluctuations detected by other techniques. These results suggest that the magnetic and nematic orders have an intimate relationship, in favor of the magnetic-fluctuation-driven nematicity scenario in iron-based superconductors.

Pressure-dependent optical investigations ofα−(BEDT-TTF)2I3: Tuning charge order and narrow gap towards a Dirac semimetal

Infrared optical investigations of $\alpha$-(BEDT-TTF)$_2$I$_3$ have been performed in the spectral range from 80 to 8000~cm$^{-1}$ down to temperatures as low as 10~K by applying hydrostatic pressure. In the metallic state, $T > 135$~K, we observe a 50\% increase in the Drude contribution as well as the mid-infrared band due to the growing intermolecular orbital overlap with pressure up to 11~kbar. In the ordered state, $T<T_{\rm CO}$, we extract how the electronic charge per molecule varies with temperature and pressure: Transport and optical studies demonstrate that charge order and metal-insulator transition coincide and consistently yield a linear decrease of the transition temperature $T_{\rm CO}$ by $8-9$~K/kbar. The charge disproportionation $\Delta\rho$ diminishes by $0.017~e$/kbar and the optical gap $\Delta$ between the bands decreases with pressure by -47~cm$^{-1}$/kbar. In our high-pressure and low-temperature experiments, we do observe contributions from the massive charge carriers as well as from massless Dirac electrons to the low-frequency optical conductivity, however, without being able to disentangle them unambiguously.

Quantum diffusion of electrons in quasiperiodic and periodic approximant lattices in the rare earth-cadmium system

Icosahedral quasicrystals are characterised by the absence of a distinct Drude peak in their low-frequency optical conductivity and the same is true of their crystalline approximants. We have measured the optical conductivity of i-GdCd, an icosahedral quasicrystal, and two approximants, GdCd and YCd. We find that there is a significant difference in the optical properties of these compounds. The approximants have a zero frequency peak, characteristic of a metal, whereas the quasicrystal has a striking minimum. This is the first example where the transport properties of a quasicrystal and its approximant differ in such a fundamental way. Using a generalised Drude model introduced by Mayou, we find that our data are well described by this model. It implies that the quantum diffusion of electron wave packets through the periodic and quasiperiodic lattices is responsible for these dramatic differences: in the approximants, the transport is superdiffusive, whereas the quasicrystals show subdiffusive motion of the electrons.

Electrodynamic response in the electronic nematic phase ofBaFe2As2

We perform, as a function of uniaxial stress, a temperature-dependent optical-reflectivity investigation of the parent Fe-arsenide compound ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ over a broad spectral range, from the far infrared up to the ultraviolet, across the coincident structural tetragonal-to-orthorhombic and spin-density-wave (SDW) phase transitions at ${T}_{s,N}=135$ K. Our results provide knowledge to the complete electrodynamic response of the title compound over a wide energy range as a function of both tunable variables. For temperatures below ${T}_{s,N}$, varying the uniaxial stress in situ affects the twin domain population and yields hysteretic behavior of the optical properties as the stress is first increased and then decreased, whereas for temperatures above ${T}_{s,N}$ the stress-induced optical anisotropy is reversible, as anticipated. In particular, by analyzing the low-frequency infrared response, we obtain detailed insight to the effects determining the intrinsic anisotropy of the (metallic) charge dynamics in the orthorhombic state, and similarly the induced one due to applied uniaxial stress at higher temperatures in the tetragonal phase. The low-frequency optical conductivity thus allows establishing a link to the $dc$ transport properties and reveals that they are determined almost exclusively by changes in the Drude weight, therefore by the anisotropy in the Fermi surface parameters. Finally, we show that the spectral weight distribution in the SDW state occurs for energies below approximately 1 eV, and therefore points towards a correlation mechanism due to Hund's coupling rather than on-site Coulomb interactions.

Novel aspects of charge and lattice dynamics in the hole-doped manganite La0.67Sr0.33MnO3

Previous infrared studies on the hole-doped manganite La0.67Sr0.33MnO3 (LSMO) have analysed its charge dynamics in terms of one type of charge carrier despite evidence of both electron and hole Fermi surfaces. Here, we investigate the charge dynamics of an LSMO film with infrared and optical spectroscopy in order to provide a complete picture of metallic conduction. In the ferromagnetic metallic phase, the low-frequency optical conductivity is best explained by a two-carrier model comprising electrons and holes. The number densities, effective masses and relaxation response of the delocalized electrons and holes are quantified. We discover that only one-third of the doped charges are coherent and contribute to the dc transport. Metallic LSMO cannot be classified as a bad metal at low temperatures because the mean free path of the coherent, mobile charge carriers exceeds the Ioffe–Regel–Mott limit. The incoherent spectral response of the doped charges manifests itself as a broad mid-infrared feature. We also report the first observation of splitting of an infrared-active phonon due to local Jahn–Teller distortion in the vicinity of the thermally driven transition to the nonmetallic, paramagnetic phase in LSMO. This demonstrates that infrared spectroscopy is capable of detecting the presence of local lattice distortions in correlated electron systems.

Novel P-T Phase Diagram of the Multiorbital Mott Insulator Sr2VO4.

The electrical and optical properties of the Mott insulator Sr2VO4 are investigated under high pressure on a phase pure polycrystalline sample. The system undergoes a pressure-driven insulator to metal transition (IMT) with a crossover between 20 and 24 GPa. The effect of pressure on the thermally driven electronic changes resulting from spin-orbital ordering transitions is studied. A multiorbital analysis of the low frequency optical conductivity spectra suggests a bandwidth-controlled and orbital selective nature of the Mott IMT transition. Dramatic enhancement of the low energy spectral weight in the high pressure correlated metallic phase is explained in terms of the formation of a quasiparticle peak in the spectral function of the narrow and degenerate d(yz,zx) orbitals. Our results overall establish a novel electronic phase diagram of tetragonal Sr2VO4.