We investigate sum-rules applying to the Raman intensity in a strongly correlated system close to the Mott transition. Quite generally, it can be shown that, provided the frequency integration is performed up to a cutoff smaller than the upper Hubbard band, a sum-rule applies to the non-resonant Raman signal of a doped Mott insulator, resulting in an integrated intensity which is proportional to the doping level. We provide a detailed derivation of this sum-rule for the t-J model, for which the frequency cutoff can be taken to infinity and an unrestricted sum-rule applies. A quantitative analysis of the sum-rule is also presented for the d-wave superconducting phase of the t-J model, using slave boson methods. The case of the Hubbard model is studied in the framework of dynamical mean-field theory, with special attention to the cutoff dependence of the restricted sum-rule, and also to the intermediate coupling regime. The sum-rule investigated here is shown to be consistent with recent experimental data on cuprate superconductors, reporting measurements of Raman scattering intensities on an absolute scale.
We present theoretical results for the optical conductivity and the non-resonant Raman susceptibilities for three principal polarization geometries relevant to the square lattice. The susceptibilities are obtained using the recently developed extremely correlated Fermi liquid theory for the two-dimensional t-t'-J model, where t and t' are the nearest and second neighbor hopping. Our results are sensitively depending on t, t'. By studying this quartet of related dynamical susceptibilities, and their dependence on t, t', doping and temperature, we provide a useful framework for interpreting and …
Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-pro…
Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering both in the visible (Raman effect) and the X-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectrosco…
The exact solution for nonresonant A1g and B1g Raman scattering is presented for the simplest model that has a correlated metal-insulator transition--the Falicov-Kimball model, by employing dynamical mean field theory. In the general case, the A1g response includes nonresonant, resonant, and mixed contributions, the B1g response includes nonresonant and resonant contributions (we prove the Shastry-Shraiman relation for the nonresonant B1g response) while the B2g response is purely resonant. Three main features are seen in the nonresonant B1g channel: (i) the rapid appearance of low-energy spec…
Two magnon excitations and the nodal spin density wave (SDW) gap were observed in BaFe2As2 by Raman scattering. Below the SDW transition temperature (TSDW) nodal SDW gap opens together with new excitations in reconstructed electronic states. The two-magnon peak remains above TSDW and moreover the energy increases a little. The change from the long-range ordered state to the short-range correlated state is compared to the cuprate superconductors.
The Raman selection rules arise from the crystal symmetry and then determine the Raman activity and polarization of scattered phonon modes. However, these selection rules can be broken in resonant process due to the strong electron-phonon coupling effect. Here we reported the observation of breakdown of Raman selection rules in few-layer WS$_2$ by using resonant Raman scattering with dark A exciton. In this case, not only the infrared active modes and backscattering forbidden modes are observed, but the intensities of all observed phonon modes become strongest under paralleled-polarization and…
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 mod…
The two-magnon (2M) excitation at 3000 cm-1 in Sr_14Cu_24O_41 two-leg ladder is studied by Raman scattering. A slight anisotropy of the superexchange coupling J_{\perp}/J_{||} \approx 0.8 with J_{||} = 110 \pm 20 meV is proposed from the analysis of the magnetic scattering. The resonant coupling across the charge transfer gap increases the 2M intensity by orders of magnitude. The anisotropy of Raman scattering is dependent upon the excitation energy. The 2M relaxation is found to be correlated with the temperature dependent electronic Raman continuum at low frequencies.
We show that ultra-cold atoms with synthetic spin-orbit coupling in Raman lattices can be used as versatile quantum simulators to explore the connections between correlated Chern insulators and strongly-coupled four-Fermi field theories related to the Gross-Neveu model in (2+1) dimensions. Exploiting this multidisciplinary perspective, we identify a large-$N$ quantum anomalous Hall (QAH) effect in absence of any external magnetic field, and use it to delimit regions in parameter space where these correlated topological phases appear, the boundaries of which are controlled by strongly-coupled f…
The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher order spin density excitations. This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for …
Iron-based superconducting layered compounds have the second highest transition temperature after cuprate superconductors. Their discovery is a milestone in the history of high-temperature superconductivity and will have profound implications for high-temperature superconducting mechanism as well as industrial applications. Raman scattering has been extensively applied to correlated electron systems including the new superconductors due to its unique ability to probe multiple primary excitations and their coupling. In this review, we will give a brief summary of the existing Raman experiments …
We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. W…
Raman selection rules for electronic and magnetic excitations in BaFe2As2 were theoretically investigated and applied them to the separate detection of the nodal and anti-nodal gap excitations at the spin density wave (SDW) transition and the separate detection of the nearest and the next nearest neighbor exchange interaction energies. The SDW gap has Dirac nodes, because many orbitals participate in the electronic states near the Fermi energy. Using a two-orbital band model the electronic excitations near the Dirac node and the anti-node are found to have different symmetries. Applying the sy…
We report a polarization-resolved Raman spectroscopy study of the orbital dependence of the quasiparticles properties in the prototypical multi-band Fermi liquid Sr\textsubscript{2}RuO\textsubscript{4}. We show that the quasiparticle scattering rate displays $ω^{2}$ dependence as expected for a Fermi liquid. Besides, we observe a clear polarization-dependence in the energy and temperature dependence of the quasiparticle scattering rate and mass, with the $d_{xz/yz}$ orbital derived quasiparticles showing significantly more robust Fermi liquid properties than the $d_{xy}$ orbital derived ones. …
Based on a two-band model, we study the electronic Raman scattering intensity in both normal and superconducting states of iron-pnictide superconductors. For the normal state, due to the match or mismatch of the symmetries between band hybridization and Raman vertex, it is predicted that overall $B_{1g}$ Raman intensity should be much weaker than that of the $B_{2g}$ channel. Moreover, in the non-resonant regime, there should exhibit a interband excitation peak at frequency $ω\simeq 7.3 t_1 (6.8t_1)$ in the $B_{1g}$ ($B_{2g}$) channel. For the superconducting state, it is shown that $β$-band c…
Low energy excitations in the multiferroic material TbMnO3 have been investigated by Raman spectroscopy. Our observations reveal the existence of two peaks at 30 cm-1 and 60 cm-1. They are observed in the cycloidal phase below the Curie temperature but not in the sinusoidal phase, suggesting their magnetoelectric origin. While the peak energies coincide with the frequencies of electromagnons measured previously by transmission spectroscopy, they show surprisingly different selection rules, with the 30 cm-1 excitation enhanced by the electric field of light along the spontaneous polarization. T…
Magnetic circular dichroism of THz modes and selection rules of Raman-active optical phonons in the polar altermagnet candidate \ce{Mn2Mo3O8}
University of Augsburg（奥格斯堡大学）；Kazan (Volga region) Federal University（喀山（伏尔加沿岸）联邦大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）
We present an exact solution for electronic Raman scattering in a single-band, strongly correlated material, including nonresonant, resonant and mixed contributions. Results are derived for the spinless Falicov-Kimball model, employing dynamical mean field theory; this system can be tuned through a Mott metal-insulator transition.
We report the observation of the $A_{\rm g}$-symmetric one-magnon Raman peak in the magnon Bose-Einstein condensation phase of TlCuCl$_{3}$. Its Raman shift traces the one-magnon energy at the magnetic $Γ$ point, and its intensity is proportional to the squared transverse magnetization. The appearance of the one-magnon Raman scattering originates from the exchange magnon Raman process and reflects the change of the magnetic-state symmetry. Using the bond-operator representation, we theoretically clarify the Raman selection rules, being consistent with the experimental results.
We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.
The Raman-active phonons in perovskite-like LaMn1-xCoxO3 (x = 0, 0.2, 0.3, 0.4, and 1.0) were studied by measuring Raman spectra at temperatures of 295 and 5 K. The changes in the spectra with Co doping are correlated with the decrease of orthorhombic distortions. Surprisingly more phonon lines than allowed for the rhombohedral LaCoO3 structure were observed in the spectra.
We have studied polarized Raman spectra of (TMTSF)2PF6 single crystals in the wide spectral and temperature range using different laser energies. We observed and assigned 23 Raman active modes. The carbon C=C in-phase and out-of-phase stretching modes at 1464 cm-1 and 1602 cm-1 show strong electron-molecular-vibration coupling. The mode at about 1565 cm-1 is temperature independent below 50 K due to the methyl group motion freezing. For (TMTSF)2PF6 in the spin density wave phase for a temperature induced dimensionality 1D (quarter filled dimerized linear chain with correlated electrons) the sp…
A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provide information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB_6.
It is proven that the sum rules for X-ray magnetic dichroism (XMCD) spectra that are used to separate spin and orbital contributions to the magnetic moment are formally correct for an arbitrary strength of electron-electron interactions. However, their practical application for strongly correlated systems can become complicated due to the spectral density weight spreading over a broad energy interval. Relevance of incoherent spectral density for the XMCD sum rules is illustrated by a simple model of a ferromagnet with orbital degrees of freedom.
Nonlinear processes involving frequency-mixing of light fields set the basis for ultrafast coherent spectroscopy of collective modes in solids. In certain semimetals and semiconductors, generation of coherent phonon modes can occur by a displacive force on the lattice at the difference-frequency mixing of a laser pulse excitation on the electronic system. Here, as a low-frequency counterpart of this process, we demonstrate that coherent phonon excitations can be induced by the sum-frequency components of an intense terahertz light field, coupled to intraband electronic transitions. This nonlin…
The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green's function. It is shown that the sum rule in the paramagnetic state is evidently violated within the planar t-J model at low doping while for the related Hubbard model, even in the presence of next-nearest-neighbor hopping, no clearcut exception is found.
We discuss the problem of a possible "violation" of the optical sum rule in the normal (non superconducting) state of strongly correlated electronic systems, using our recently proposed DMFT+Sigma approach, applied to two typical models: the "hot - spot" model of the pseudogap state and disordered Anderson - Hubbard model. We explicitly demonstrate that the general Kubo single band sum rule is satisfied for both models. However, the optical integral itself is in general dependent on temperature and characteristic parameters, such as pseudogap width, correlation strength and disorder scattering…
We propose a scheme to dynamically generate optical flux lattices with nontrivial band topology using amplitude-modulated Raman lasers and radio-frequency (rf) magnetic fields. By tuning the strength of Raman and rf fields, three distinct phases are realized at unit filling for a unit cell. Respectively, these three phases correspond to normal insulator, topological Chern insulator, and semimetal. Nearly nondispersive bands are found to appear in the topological phase, which promises opportunities for investigating strongly correlated quantum states within a simple cold-atom setup. The validit…
Polarized Raman scattering and infrared reflection spectra of hexagonal HoMnO$_3$ single crystals in the temperature range 10-300 K are reported. Group-theoretical analysis is performed and scattering selection rules for the second order scattering processes are presented. Based on the results of lattice dynamics calculations, performed within the shell model, the observed lines in the spectra are assigned to definite lattice vibrations. The magnetic ordering of Mn ions, which occurs below T$_N$=76 K, is shown to effect both Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and,…
In spin-1/2 Mott insulators, non-magnetic quantum liquid phases are often argued to arise when the system shows no magnetic ordering, but identifying positive signatures of these phases or related spinon quasiparticles can be elusive. Here we use Raman scattering to provide three signatures for spinons in a possible spin-orbit quantum liquid material Ba${}_4$Ir${}_3$O${}_{10}$: (1) A broad hump, which we show can arise from Luttinger Liquid spinons in Raman with parallel photon polarizations normal to 1D chains; (2) Strong phonon damping from phonon-spin coupling via the spin-orbit interaction…
We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation also extends the known nonequilibrium moment sum rules for the Green's functions to the third moment). These sum rules are used to further test the accuracy of nonequilibrium solutions to the many-body problem; for example, we illustrate how well the self-energy sum rules are satisfied for the Falicov-Kimball model in infinite dimensions and placed in a unifor…
Unconventional peak structure in the Raman spectra due to magnon excitation at low temperature is observed in spinel magnet ${\rm MnV_2O_4}$, where a noncollinear spin state is realized by geometrical frustration. We propose a new mechanism to induce such a Raman scattering process due to a one-magnon excitation of the noncollinear spin state. Novel features of the scattering such as selection rules and peak position observed experimentally in ${\rm MnV_2O_4}$ can be explained quite naturally by considering the present one-magnon process. We also discuss that such one-magnon process may exist …
We perform Raman spectroscopy studies on $α$-RuCl$_3$ at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about $p_1=1.1$~GPa and $p_2=1.7$~GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of $α$-RuCl$_3$ layers develops at $p_1=1.1$~GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the…
We study the optical, Raman, and ac Hall response of the doped Mott insulator within the dynamical mean-field theory ($d=\infty$) for strongly correlated electron systems. The occurence of the {\it isosbectic} point in the optical conductivity is shown to be associated with the frequency dependence of the generalized charge susceptibility. We compute the Raman response, which probes the fluctuations of the "stress tensor", and show that the scattering is characterized by appreciable incoherent contributions. The calculated ac Hall constant and Hall angle also exhibit the isosbectic points. The…
We show that in multi-band metals the correlations are strongly affected by the Hund's rule coupling, which depending on the filling promotes metallic, insulating or bad-metallic behavior. The quasiparticle coherence and the proximity to a Mott insulator are influenced distinctly and, away from single- and half-filling, in opposite ways. A strongly correlated bad-metal far from a Mott phase is found there. We propose a concise classification of 3d and 4d transition-metal oxides within which the ubiquitous occurrence of strong correlations in Ru- and Cr-based oxides, as well as the recently mea…
Nonresonant inelastic light and X-ray scattering is investigated for the spinless Falicov-Kimball model on an infinite-dimensional hypercubic lattice with a charge-density-wave phase at half filling. The many-body density of states (DOS) is found for different values of the Coulomb repulsion $U$, ranging from a dirty metal to a Mott insulator. At zero temperature, the charge gap is exactly equal to $U$; increasing the temperature rapidly fills the gap with subgap states. The nonresonant response function for Raman and inelastic X-ray scattering shows peaks connected with transitions over the g…
We present inelastic light scattering measurements of EuO and Eu$_{1-x}$La$_{x}$B$_6$ ($x$=0, 0.005, 0.01, 0.03, and 0.05) as functions of doping, B isotope, magnetic field, and temperature. Our results reveal a variety of distinct regimes as a function of decreasing T: (a) a paramagnetic semimetal regime, which is characterized by a collision-dominated electronic scattering response whose scattering rate $Γ$ decreases with decreasing temperature; (b) a spin-disorder scattering regime, which is characterized by a collision-dominated electronic scattering response whose scattering rate $Γ$ scal…
We use dynamical mean field theory to find an exact solution for inelastic light scattering in strongly correlated materials such as those near a quantum-critical metal-insulator transition. We evaluate the results for $\textbf{q}=0$ (Raman) scattering and find that resonant effects can be quite large, and yield a triple resonance, a significant enhancement of nonresonant scattering peaks, a joint resonance of both peaks when the incident photon frequency is on the order of $U$, and the appearance of an isosbestic point in all symmetry channels for an intermediate range of incident photon freq…
We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of th…
Spectral moment sum rules are presented for the inhomogeneous many-body problem described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous many-body problem like strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering like a charge density wave or a spin density wave. We also show …
Strongly Enhanced Charge-Density Waves and Correlated Insulating State in Atomically Thin 1$T$-TaS$_2$
Nanjing University（南京大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Spallation Neutron Source Science Center（散裂中子源科学中心）；National Institute for Materials Science（国立材料研究所）；Center for Shared Scientific Research Facilities, Nanjing University（南京大学共享科研设施中心）
