Electronic Raman Scattering Research Articles

(n,m) Assignments of Metallic Single-Walled Carbon Nanotubes by Raman Spectroscopy: The Importance of Electronic Raman Scattering.

In this work, we report an accurate and convenient method that can be used to assign the chirality of all metallic single-walled carbon nanotubes (M-SWNTs). This method is designed based on the electronic Raman scattering (ERS) features, which are resonantly enhanced at the corresponding excitonic transition energies (Mii+ and Mii-). Using this method, we are able to accurately determine the electronic property Mii with the resolution of a vibrational Raman spectroscopy (∼0.3 meV), which is significantly higher than that of the electronic spectroscopies (∼3 meV). We use the Mii splitting value, which is found insensitive to environmental changes, as a universal criteria for (n,m) assignments in various environments. As an illustrative example, simply using a commercialized Raman spectrometer with two laser lines (1.959 and 2.330 eV), we are able to unambiguously assign 18 metallic chiralities with M11 in the 1.6-2.3 eV range in our samples. This method provides an accurate database of Mii's in a similar way as photoluminescence excitation spectroscopy does for Sii's. It can facilitate further systematic studies on the properties of M-SWNTs with defined chirality.

Gate-Dependent Electronic Raman Scattering in Graphene.

We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for nonresonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly observe Dirac fermion excitations in graphene opens the way to promising Raman investigations of electronic properties of graphene and other 2D crystals.

Effects of electron-electron interactions on the electronic Raman scattering of graphite in high magnetic fields

We report the observation of strongly temperature ($T$)-dependent spectral lines in electronic Raman-scattering spectra of graphite in a high magnetic field up to 45 T applied along the $c$ axis. The magnetic field quantizes the in-plane motion, while the out-of-plane motion remains free, effectively reducing the system dimension from 3 to 1. Optically created electron-hole pairs interact with, or shake up, the one-dimensional Fermi sea in the lowest Landau subbands. Based on the Tomonaga-Luttinger liquid theory, we show that interaction effects modify the spectral line shape from ${(\ensuremath{\omega}\ensuremath{-}\ensuremath{\Delta})}^{\ensuremath{-}1/2}$ to ${(\ensuremath{\omega}\ensuremath{-}\ensuremath{\Delta})}^{2\ensuremath{\alpha}\ensuremath{-}1/2}$ at $T$ = 0. At finite $T$, we predict a thermal broadening factor that increases linearly with $T$. Our model reproduces the observed $T$-dependent line shape, determining the electron-electron interaction parameter $\ensuremath{\alpha}$ to be $\ensuremath{\sim}$0.05 at 40 T.

Stimulated Electronic X-Ray Raman Scattering

We demonstrate strong stimulated inelastic x-ray scattering by resonantly exciting a dense gas target of neon with femtosecond, high-intensity x-ray pulses from an x-ray free-electron laser (XFEL). A small number of lower energy XFEL seed photons drive an avalanche of stimulated resonant inelastic x-ray scattering processes that amplify the Raman scattering signal by several orders of magnitude until it reaches saturation. Despite the large overall spectral width, the internal spiky structure of the XFEL spectrum determines the energy resolution of the scattering process in a statistical sense. This is demonstrated by observing a stochastic line shift of the inelastically scattered x-ray radiation. In conjunction with statistical methods, XFELs can be used for stimulated resonant inelastic x-ray scattering, with spectral resolution smaller than the natural width of the core-excited, intermediate state.

Pseusogap in Cuprates by Electronic Raman Scattering

We present Raman experiments on underdoped and overdoped Bi2Sr2CaCu2O8+δ (Bi-2212) single crystals. We reveal the pseudogap in the electronic Raman spectra in the B1g and B2g geometries. In these geometries we probe respectively, the antinodal (AN) and nodal (N) regions corresponding to the principal axes and the diagonal of the Brillouin zone. The pseudogap appears in underdoped regime and manifests itself in the B1g spectra by a strong depletion of the low energy electronic continuum as the temperature decreases. We define a temperature T* below which the depletion appears and the pseudogap energy, ωPG the energy at which the depeletion closes.The pseudogap is also present in the B2g spectra but the depletion opens at higher energy than in the B1g spectra. We observe the creation of new electronic states inside the depletion as we enter the superconducting phase. This leads us to conclude (as proposed by S. Sakai et al. [1]) that the pseudogap has a different structure than the superconducting gap and competes with it. We show that the nodal quasiparticle dynamic is very robust and almost insensitive to the pseudogap phase contrary to the antinodal quasiparticle dynamic. We finally reveal, in contrast to what it is usually admitted, an increase of the nodal quasiparticle spectral weight with underdoping. We interpret this result as the consequence of a possible Fermi surface disturbances in the doping range p = 0.1 − 0.2.

Quantitative Comparison between Electronic Raman Spectra and Angle-resolved Photoemission Spectra in Superconducting State of Bi2212

Abstract In this paper we present the calculations of electronic Raman scattering (ERS) spectra for B1 g and B2 g geometries using angle- resolved photoemission spectroscopy (ARPES) spectra of nearly optimally doped cuprate superconductor Bi2Sr2CaCu2O8 (Bi2212), Tc=92K. Calculations were taken on the Fermi surface (FS) in the superconducting state at temperature well below Tc and the results were quantitatively compared to the experimental data. It shows that there is a good agreement in B1 g while the peak position in B2 g is about 100 cm-1 lower than the experimental one. This result indicates that the scattering rate is not large enough to explain Raman spectra and additional contribution should be taken into account to reproduce ERS spectra.

Electronic Transport and Raman Scattering in Size-Controlled Nanoperforated Graphene

We demonstrate the fabrication and study of the structure-property relationships of large-area (>1 cm(2)) semiconducting nanoperforated (NP) graphene with tunable constriction width (w = 7.5-14 nm), derived from CVD graphene using block copolymer lithography. Size-tunable constrictions were created while minimizing unintentional doping by using a dual buffer layer pattern-transfer method. An easily removable polymeric layer was sandwiched between an overlying silicon oxide layer and the underlying graphene. Perforation-size was controlled by overetching holes in the oxide prior to pattern transfer into graphene while the polymer protected the graphene from harsh conditions during oxide etching and lift off. The processing materials were removed using relatively mild solvents yielding the clean isolation of NP graphene and thereby facilitating Raman and electrical characterization. We correlate the D to G ratio as a function of w and show three regimes depending on w relative to the characteristic Raman relaxation length. Edge phonon peaks were also observed at 1450 and 1530 cm(-1) in the spectra, without the use of enhancement methods, due to high density of nanoconstricted graphene in the probe area. The resulting NP graphene exhibited semiconducting behavior with increasing ON/OFF conductance modulation with decreasing w at room temperature. The charge transport mobility decreases with increasing top-down reactive ion etching. From these comprehensive studies, we show that both electronic transport and Raman characteristics change in a concerted manner as w shrinks.

Electronic Raman Scattering in Quantum Wells

Abstract Using a generalized self-consistent field theory we have investigated the electronic resonant Raman scattering process in modulation-doped GaAs-AlGaAs single quantum wells. Charge- and spin-density excitations spectra were calculated varying the width of the well as well as the density of the electron gas. In the low density regime, we observed the collapse of Hartree term of charge-density excitations as found experimentally by Ernst et al. [1] . Concerning the resonance with the incomming laser light, we predict the existence of high energy excitations which are connected with excited states of the quantum wells.

Observation of Electronic Raman Scattering in Metallic Carbon Nanotubes

We present experimental measurements of the electronic contribution to the Raman spectra of individual metallic single-walled carbon nanotubes (MSWNTs). Photoexcited carriers are inelastically scattered by a continuum of low-energy electron-hole pairs created across the graphenelike linear electronic subbands of the MSWNTs. The optical resonances in MSWNTs give rise to well-defined electronic Raman peaks. This resonant electronic Raman scattering is a unique feature of the electronic structure of these one-dimensional quasimetals.

The effect of intense laser field on the Electronic Raman Scattering of shallow donor impurities in quantum dots

The laser-field dependence of energy levels and donor-related Electronic Raman Scattering is investigated by a quasi-analytical approach. The differential cross section involved in this process is calculated as a function of secondary radiation photon energy. We find that the laser field amplitude and confinement strength have an important influence on the Raman scattering. And the transitions between lower electronic energy states are more sensitive to the laser field.

Impact of the spin-density-wave order on the superconducting gap ofBa(Fe1−xCox)2As2

We report a doping-dependent electronic Raman-scattering measurements on iron-pnictide superconductor $\text{Ba}{({\text{Fe}}_{1\ensuremath{-}x}{\text{Co}}_{x})}_{2}{\text{As}}_{2}$ single crystals. The ${\text{B}}_{2g}$ Raman spectrum at optimal doping is consistent with a strongly anisotropic gap on the electron pocket. Upon entering the coexistence region between superconducting (SC) and spin-density-wave (SDW) orders, the effective pairing energy scale is strongly reduced. Our results are interpreted in terms of a competition between SC and SDW orders for electronic states at the Fermi level. Our findings advocate for a strong connection between the SC and SDW gaps anisotropies which are both linked to interband interactions.

Impurity Effects on Energy Gap in Bi2Sr2CaCu2O8+y Investigated by Electronic Raman Scattering

The Raman scattering experiments were carried out in Zn-doped and Zn-free Bi 2 Sr 2 CaCu 2 O 8+y with optimal hole concentration below and above T c . The energy of pair-breaking peak in the B 1g Raman spectrum, corresponding to the magnitude of superconducting gap 2Δ 0 , is suppressed by 1% Zn-doping. In the normal state, the B 1g Raman spectrum for Zn-doped sample shows no pseudogap behaviour, suggesting that the pseudogap is strongly smeared by Zn-doping.

Mechanism of Pseudogap Detected by Electronic Raman Scattering: Phase Fluctuation or Hidden Order?

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudo-gap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they are smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave (DDW) order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the B1g channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW+SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.

Electronic Raman Scattering in Graphene

Linear dispersion near the Dirac points in the band structure of graphenes can give rise to novel physical properties. We calculate the electronic contribution to the Raman spectra in graphenes, which also shows novel features. In the clean limit, the Raman spectrum in the undoped graphene is linear (with a universal slope against impurity scattering) at low energy due to the linear dispersion near the Dirac points, and it peaks at a position corresponding to the van Hove singularity in the band structure. In a doped graphene, the electronic Raman absorption is forbidden up to a vertical inter-band particle-hole gap. Beyond the gap the spectrum follows the undoped case. In the presence of impurities, absorption within the gap (in the otherwise clean case) is induced, which is identified as the intra-band contribution. The Drude-like intra-band contribution is seen to be comparable to the higher energy inter-band Raman peak. The results are discussed in connection to experiments.

Studies of Electronic Raman scattering in CdS/HgS cylindrical quantum dot quantum well structures

Electronic Raman scattering (ERS) is investigated in CdS/HgS cylindrical quantum dot quantum well. The ERS cross-section is calculated as a function of the frequency shift. The process involves an interband electronic transition and an intraband transition between quantized subbands. Different scattering configurations are discussed and the selection rules for the processes are also studied. Rich spectra are found and interpreted. The ERS studied here can be used to provide direct information about the electron band structure of these systems.

Dichotomy in quasiparticles dynamics of underdoped cuprates in the superconducting state

We report electronic Raman scattering (ERS) measurements for a set of underdoped (p=0.09–0.16) mercury-based HgBa2CuO4+δ (Hg-1201, Tcmax=95K) cuprates. Inelastic light scattering (Raman effect) is a powerful experimental method for studying quasiparticles (QP) dynamics. Changing the polarization of incident and scattered light allows us to probe the QP dynamics in selected areas of the Fermi surface. By exploring the superconducting dome from the optimal doping to the underdoped one, we show unambiguously the existence of two distinct dynamics, respectively for the nodal (B2g symmetry) and the anti-nodal (B1g symmetry) QPs. As cuprates are underdoped, both an increasing of the amplitude and a loss of the intensity for the superconducting gap are observed, coherently with other charge spectroscopies such as ARPES or STM. On the contrary, the behavior of nodal QPs is totally different since the peak associated with the superconductivity in this symmetry follows Tc, and thus, shifts to the lower energies as we underdope the system. We finally show that these two features are only seen in the superconducting state.

Electronic Raman Scattering from Superconductors in the Vortex State: Experimental Features and Theoretical Issues

In a superconductor, single-particle excitations created by adding or removing an electron require a minimum energy given by the absolute value | | of the superconducting energy gap . An applied magnetic field enters a type II superconductor in the form of Abrikosov vortices. Around the core of each vortex the super current flows with a circulation equal to h. For conventional superconductors the cores are believed to contain only “normal” metallic electrons. These potentially offer sources of damping for various excitations. The gap may depend on the wavevector k of the added or removed particle, and in the vortex state, on its position. Indeed, according to Ginzburg–Landau theory, is proportional to the superconducting order parameter, which acquires a position-dependent phase, the “winding phase,” that changes by 2π around any closed path that winds once around a vortex. In 1961, Abrikosov and Falkovskii [1] predicted that electronic Raman scattering at small momentum transfer from a clean BCS superconductor should reveal the gap as a discontinuous sharp rise to a peak at an energy transfer equal to twice the gap, i.e. at 2 . Sometimes referred to as a “pair-breaking peak,” the 2 feature results from the creation during the lightscattering process of an electron–hole pair, each part of which requires a minimum energy of [2]. Subsequent theoretical work was based on Greens function approaches. See [3–5] for examples. This paper presents a brief survey of the few experiments that probed the effect of a magnetic field

Interplay between the pseudogap and superconductivity in underdopedHgBa2CuO4+δsingle crystals

We report a doping-dependent electronic Raman scattering (ERS) study of $\mathrm{Hg}{\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{4+\ensuremath{\delta}}$ (Hg-1201) single crystals. We investigate the dynamics of the antinodal and nodal quasiparticles. We show that the dynamical response of the antinodal quasiparticles is strongly reduced towards the underdoped regime in both the normal and superconducting states. When probing the nodal quasiparticles, we are able to distinguish between the energy scale of the pseudogap and that of the superconducting gap. A simple model relating the suppression of the dynamical response of the antinodal quasiparticles to fluctuations related to a competing phase is proposed.

Donor and Donor Bound Exciton Spectroscopy in Wurtzite GaN Heterostructures

Neutral donor bound excitons (I 2 ) and donor related electronic Raman scattering (ERS) in wurtzite GaN epilayers deposited onto Si, 6H-SiC, Al 2 O 3 and GaN substrates are studied at low temperature by high-resolution selective photoluminescence spectroscopy (SPL). Due to the presence of a large strain distribution in the heterostructures, the observation of the I 2 excited states under selective laser excitation is possible from tensile to compressive strain along the [0001] direction. It is shown that the I 2 spectra strongly depend on which valence band (A or B) the bound exciton hole belongs to. Resonant ERS and resonantly excited two-electron spectra reveal that two main different residual donor species are present both in MBE and MOCVD epitaxial samples. The donor binding energies are shown to vary noticeably with the biaxial strain field.

Donor and Donor Bound Exciton Spectroscopy in Wurtzite GaN Heterostructures

Neutral donor bound excitons (I2) and donor related electronic Raman scattering (ERS) in wurtzite GaN epilayers deposited onto Si, 6H-SiC, Al2O3 and GaN substrates are studied at low temperature by high-resolution selective photoluminescence spectroscopy (SPL). Due to the presence of a large strain distribution in the heterostructures, the observation of the I2 excited states under selective laser excitation is possible from tensile to compressive strain along the [0001] direction. It is shown that the I2 spectra strongly depend on which valence band (A or B) the bound exciton hole belongs to. Resonant ERS and resonantly excited two-electron spectra reveal that two main different residual donor species are present both in MBE and MOCVD epitaxial samples. The donor binding energies are shown to vary noticeably with the biaxial strain field.