Charge Collective Modes Research Articles

Spin-orbit interaction enabled electronic Raman scattering from charge collective modes

Spin-orbit interaction enabled electronic Raman scattering from charge collective modes

Superconductivity in the regime of attractive interactions in the Tomonaga-Luttinger liquid

While the vast majority of known physical realizations of the Tomonaga-Luttinger liquid (TLL) have repulsive interactions defined with the dimensionless interaction parameter $K_{\rm c}<1$, we here report that Rb$_2$Mo$_3$As$_3$ is in the opposite TLL regime of attractive interactions. This is concluded from a TLL-characteristic power-law temperature dependence of the $^{87}$Rb spin-lattice relaxation rates over broad temperature range yielding the TLL interaction parameter for charge collective modes $K_{\rm c}=1.4$. The TLL of the one-dimensional band can be traced almost down to $T_{\rm c} = 10.4 $~K, where the bulk superconducting state is stabilized by the presence of a three-dimensional band and characterized by the $^{87}$Rb temperature independent Knight shift and the absence of Hebel-Slichter coherence peak in the relaxation rates. The small superconducting gap measured in high magnetic fields reflects either the importance of the vortex core relaxation or the uniqueness of the superconducting state stemming from the attractive interactions defining the precursor TLL.

Charge structure factors of doped armchair nanotubes in the presence of electron–phonon interaction

We present the behaviors of both dynamical and static charge susceptibilities of doped armchair nanotubes using the Green function approach in the context of Holstein-model Hamiltonian. Specially, the effects of magnetization and gap parameter on the the plasmon modes of armchair nanotube are investigated via calculating correlation function of charge density operators. Random phase approximation has been implemented to find the interacting dynamical charge susceptibility. The electrons in this systems interacts with each other by mediation of dispersionless Holstein phonons. Our results show that the increase of gap parameter leads to decreasing intensity of charge collective mode. Also the frequency position of the collective mode tends to higher frequencies due to the gap parameter. Furthermore the number of collective excitation mode decreases with chemical potential in the presence of electron–phonon interaction. Finally the temperature dependence of static charge structure factor of armchair nanotubes is studied. The effects of the gap parameter, magnetization and electron–phonon interaction on the static structure factor are addressed in details.

Anisotropic Collective Charge Excitations in Quasimetallic 2D Transition-Metal Dichalcogenides.

The quasimetallic 1T′ phase 2D transition‐metal dichalcogenides (TMDs) consist of 1D zigzag metal chains stacked periodically along a single axis. This gives rise to its prominent physical properties which promises the onset of novel physical phenomena and applications. Here, the in‐plane electronic correlations are explored, and new mid‐infrared plasmon excitations in 1T′ phase monolayer WSe2 and MoS2 are observed using optical spectroscopies. Based on an extensive first‐principles study which analyzes the charge dynamics across multiple axes of the atomic‐layered systems, the collective charge excitations are found to disperse only along the direction perpendicular to the chains. Further analysis reveals that the interchain long‐range coupling is responsible for the coherent 1D charge dynamics and the spin–orbit coupling affects the plasmon frequency. Detailed investigation of these charge collective modes in 2D‐chained systems offers opportunities for novel device applications and has implications for the underlying mechanism that governs superconductivity in 2D TMD systems.

Dynamical and Static Charge Structure Factors of Doped Zigzag Nanotubes

We present the behaviors of both dynamical and static charge susceptibilities of doped zigzag graphene like nanotube using the Green’s function approach in the context of tight binding model Hamiltonian. Specially, the effects of tube diameter, gap parameter and electron doping on the the plasmon modes of zigzag nanotube are investigated via calculating correlation function of charge density operators. Our results show the increase of gap parameter leads to decrease intensity of charge collective mode. Also the frequency position of the collective mode tends to higher frequencies with increase of gap parameter. We also study the effects of chemical potential on frequency positions of plasmon mode of zigzag nanotube. Finally the temperature dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of tube diameter and gap parameter on the temperature dependence of static structure factor are addressed in details.

The effects of electron-phonon coupling and magnetic field on charge structure factors of armchair graphene nanoribbons

We present the behaviors of both dynamical and static charge susceptibilities of undoped armchair graphene nanoribbon using the Green’s function approach in the context of Holstein model Hamiltonian. Specially, the effects of magnetic field and electron-phonon coupling strength on the plasmon modes of armchair graphene nanoribbon are investigated via calculating correlation function of charge density operators. Random phase approximation has been implemented to find the interacting dynamical charge susceptibility. The electrons in this systems interacts with each other by mediation of dispersionless Holstein phonons. Our results show the increase of electron phonon coupling strength leads to decrease intensity of charge collective mode. Also the frequency position of the collective mode tends to higher frequencies with electron phonon coupling. We also show that the frequency positions of plasmon mode of armchair nanoribbon are not affected by the increase of magnetic field. Furthermore the number of collective excitation mode increases with ribbon width in the presence of electron-phonon interaction. Finally the temperature dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of magnetic field, ribbon width and electron-phonon interaction on the static structure factor are addressed in details.

Photoelectron Collection Efficiency Measurement of Vp81 Photocathode

We present experimental measurement of photoelectron collection efficiency of a new organic semiconductor photocathode Vp81in pure methane and argon methane mixtures in different ratios as a function of applied reduced electric field at a gas pressure of 200 torr. It is confirmed that collection efficiency increases in charge collection mode and reaches near the vacuum value at high gas gain. The general universal behavior was also confirmed as predicted by some authors.

Transverse spin susceptibilities of doped armchair graphene nanoribbon due to electron-phonon interaction

We present the behaviors of both dynamical and static charge susceptibilities of undoped armchair graphene nanoribbon using the Green's function approach in the context of Holstein model Hamiltonian. Specially, the effects of magnetic field and electron-phonon coupling strength on the plasmon modes of armchair graphene nanoribbon are investigated via calculating correlation function of charge density operators. Random phase approximation has been implemented to find the interacting dynamical charge susceptibility. The electrons in this systems interacts with each other by mediation of dispersionless Holstein phonons. Our results show the increase of electron phonon coupling strength leads to decrease intensity of charge collective mode Also the frequency position of the collective mode tends to higher frequencies with electron phonon coupling. We also show that the frequency positions of plasmon mode of armchair nanoribbon are not affected by increase of magnetic field. Furthermore the number of collective excitation mode increases with ribbon width in the presence of electron-phonon interaction. Finally the temperature dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of both magnetic field, ribbon width and electron-phonon interaction on the static structure factor are addressed in details.

Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, \chi({\bf q},\omega). The imaginary part, \chi''({\bf q},\omega), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. \chiχ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure \chi({\bf q},\omega) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure \chiχ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as “M-EELS”, allows direct measurement of \chi''({\bf q},\omega) with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi_22Sr_22CaCu_22O_{8+x}8+x (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.

Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

The charge dynamical response function of the Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slightly affects the renormalization of the quasiparticle mass. In contrast a negative notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density we find that it enhances (reduces) the damping of the zero-sound mode. Furthermore it softens (hardens) the upper-Hubbard-band collective mode at positive (negative) doping. It is also shown that our results differ markedly from the random-phase approximation in the strong-coupling limit, even at high doping, while they compare favorably with existing quantum Monte Carlo numerical simulations.

Nonlinear Conductivity and Collective Charge Excitations in the Lowest Landau Level

For weakly disordered fractional quantum Hall phases, the nonlinear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wave vectors by electrical transport. Incompressible phases, irradiated at slightly above the magnetoroton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Nonlinear conductivity can probe composite fermions' charge excitations in compressible filling factors.

Triplet superconductivity in a model ofLi0.9Mo6O17

Superconductivity in the quasi-one-dimensional material Li$_{0.9}$Mo$_6$O$_{17}$ is analyzed based on a multiorbital extended Hubbard model. We found strong charge fluctuations at two different momenta ${\bf Q_1}$ and ${\bf Q_2}$ giving rise to two different charge ordered phases. Evaluating the superconducting vertex, we found superconductivity near strong charge fluctuations at ${\bf Q_1}$. The order parameter has the p-wave symmetry with nodes on the Fermi surface. The metallic state displays a characteristic charge collective mode ${\bf Q_1}$ due to nesting and for on-site Hubbard repulsion sufficiently large, a charge critical mode ${\bf Q_2}$ driven by Coulomb repulsion, which softens at the proximity to the transition. The results are quite robust for different coupling parametrizations. A phase diagram discussing the relevance of the model to the physics of the material is proposed.

Intrinsic damping of collective spin modes in a two-dimensional fermi liquid with spin-orbit coupling.

A Fermi liquid with spin-orbit coupling (SOC) is expected to support a new set of collective modes: oscillations of magnetization in the absence of the magnetic field. We show that these modes are damped by the electron-electron interaction even in the limit of an infinitely long wavelength (q=0). The linewidth of the collective mode is on the order of Δ¯2/E(F), where Δ¯ is a characteristic spin-orbit energy splitting and E(F) is the Fermi energy. Such damping is in stark contrast to known damping mechanisms of both charge and spin collective modes in the absence of SOC, all of which disappear at q=0, and arises because none of the components of total spin is conserved in the presence of SOC.

Charge fluctuations in the unconventional metallic state ofLi0.9Mo6O17

Charge fluctuations in the quasi-one-dimensional material Li0.9Mo6O17 are analyzed based on a multi orbital extended Hubbard model. A charge ordering transition induced by Coulomb repulsion is found with a charge ordering pattern different from a conventional charge density wave driven by Fermi surface nesting. The metallic state displays a characteristic charge collective mode which softens signalling the proximity to the transition. We argue that the strong scattering between electrons generated by these charge order fluctuations can lead to the unconventional metallic state observed above the superconducting transition temperature in Li0.9Mo6O17.

Direct observation of bulk charge modulations in optimally dopedBi1.5Pb0.6Sr1.54CaCu2O8+δ

Bulk charge density modulations, recently observed in high critical-temperature ($T_\mathrm{c}$) cuprate superconductors, coexist with the so-called pseudogap and compete with superconductivity. However, its direct observation has been limited to a narrow doping region in the underdoped regime. Using energy-resolved resonant x-ray scattering we have found evidence for such bulk charge modulations, or soft collective charge modes (soft CCMs), in optimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+\delta}$ (Pb-Bi2212) around the summit of the superconducting dome with momentum transfer $q_{\parallel}\sim0.28$ reciprocal lattice units (r.l.u.) along the Cu-O bond direction. The signal is stronger at $T\simeq T_\mathrm{c}$ than at lower temperatures, thereby confirming a competition between soft CCMs and superconductivity. These results demonstrate that soft CCMs are not constrained to the underdoped regime, suggesting that soft CCMs appear across a large part of the phase diagram of cuprates and are intimately entangled with high-$T_\mathrm{c}$ superconductivity.

Evidence for phonon-like charge and spin fluctuations from an analysis of angle-resolved photoemission spectra of La2−xSrxCuO4superconductors

In high temperature superconductors we provide evidence of spin and mixed phonon-charge collective modes as mediators of the effective electron-electron interaction and suggestive of a charge and spin density wave instability competing with superconductivity. Indeed, we show that the so-called kinks and waterfalls observed in angle-resolved photoemission spectra of La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$, a prototypical high-${T}_{c}$ superconducting cuprate, are due to the coupling of quasiparticles with two distinct nearly critical collective modes with finite characteristic wave vectors, typical of charge and spin fluctuations. The simultaneous presence of these two modes reconciles the long standing dichotomy whether kinks are due to phonons or spin waves.

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly-critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.

On the contribution of nearly critical spin and charge collective modes to the Raman spectra of high- Tc cuprates

We discuss how Raman spectra are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high- T c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover, spin modes should be more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuate with high frequency.

Intermediate dimensional character of charge transfer excitation modes in a two-leg cuprate ladder

Collective charge modes in the cuprate ladder compound Sr 14 Cu 24 O 41 are studied over the one-dimensional Brillouin zone using resonant inelastic X-ray scattering. Low energy (2–4 eV) spectral weight across the Mott gap is dominated by a broad, dispersive feature containing two distinct peaks that may be interpreted as independent modes. Details of low energy dispersion, intensity distribution across the Brillouin zone and peak composition fall between the characteristic spectra of quasi-1D (e.g. SrCuO 2) and -2D cuprates (e.g. Nd 2CuO 4). We demonstrate that dispersion and splitting between the two observed modes can be understood in a variant of the strong coupling limit (Hubbard- U ⪢ t ) with a single band Hubbard model.

Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

Phonon anomalies observed in various high Tc cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary.