Static Charge Susceptibility Research Articles

Modified GW method in electronic systems

A modified $GW$ approximation to many-body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects the high-order connected correlation functions. A covariant (preserving the Ward identities due to the charge conservation) scheme for the two-body correlators is employed, which holds the relation between the charge correlator and the charge susceptibility. The method is tested on the two-dimensional one-band Hubbard model. The results are compared with exact diagonalization, the $GW$ approximation, the fluctuation-exchange (FLEX) theory, and determinantal Monte Carlo approach. The comparison for the (one-body) Green's function demonstrates that it is more precise in the strong-coupling regime (especially away from half filling) than the $GW$ and FLEX approximations, which have a similar complexity. More importantly, this method indicates a Mott-Hubbard gap as the Hubbard $U$ increases, whereas the $GW$ and FLEX methods fail. In addition, the charge correlator obtained from the covariant scheme not only holds the consistency of the static charge susceptibility, but also makes a significant improvement over the random phase approximation calculations.

Collective plasmonic oscillations of zigzag boron-nitride nanotubes in the presence of Holstein phonons

In this paper, we study theoretically both dynamical and static charge susceptibilities of zigzag boron-nitride nanotube due to the effects of electron-phonon interaction. One can find the plasmonic oscillation modes of the system using the imaginary part of the dynamical charge susceptibility function. For this purpose, we implement Green's function approach in the context of the Holstein model Hamiltonian. According to the linear response theory, the charge response function will be obtained by calculating the correlation function of charge density-density operators. We also exploit the random phase approximation in order to correct the charge susceptibility due to the electron-phonon interaction. In addition, we present the static charge structure factor which can be a criterion for charge ordering of the system. Especially the effect of electron-phonon coupling, gap parameter, chemical potential, next-to-nearest-neighbor hopping amplitude, and tube diameter on the plasmonic modes of the system. The results indicate a change in the intensity, frequency position of sharp peaks, and the number of those in the imaginary part of the dynamical charge susceptibility function of zigzag boron-nitride nanotube system. Finally, the temperature behavior of the static charge structure factor of zigzag boron-nitride nanotube is studied and the effect of the mentioned parameters on this function has been investigated.

Spin correlations and spin-density wave phase in a finite-temperature quasi-one-dimensional electron gas

In this paper, we theoretically investigate the effect of temperature on spin correlations in an unpolarized quasi-one-dimensional electron gas (Q1DEG). The correlations are treated dynamically within quantum version of the self-consistent mean-field approach of Singwi et al Numerical results for the ↑↑ and ↑↓ components of static structure factor and pair-correlation function, and the wave vector dependent static spin and charge susceptibilities are presented over a wide range of temperature T and electron coupling r s . We find that the recently reported (2020 J. Phys.: Condens. Matter. 32 335403) non-monotonic T-dependence of the contact pair-correlation function g(r = 0; T) is driven primarily by an interplay between ↑↓ correlations and thermal effects. At a given temperature, the dynamics of both ↑↑ and ↑↓ correlations is found to become significant with increasing coupling r s , manifesting unambiguously as pronounced peak at 3.5k F (periodic oscillations) in the corresponding components of the structure factor (pair-correlation function). Analysis of static spin and charge susceptibilities reveals that an imbalance between ↑↑ and ↑↓ correlations may induce a transition to a spin-density wave (SDW) phase of wave vector ∼3.5k F above a critical coupling for a sufficiently high T, while to a long-wavelength SDW phase at a low T. Higher the temperature, higher is the predicted critical coupling for the SDW phase. Interestingly, transition to the SDW phase is found to precede the recently predicted Wigner crystal instability in the finite-T Q1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higher τ and r s . In addition, we have presented results for the free exchange-correlation energy, free correlation energy, and excess kinetic energy for the unpolarized and fully spin-polarized phases of the finite-T Q1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.

Plasmonic excitations and charge structure factor in armchair boron nitride nanotubes

In this paper we investigated theoretically both dynamical and static charge susceptibilities of armchair Boron-Nitride nanotube(BNNT). Using the imaginary part of the dynamical charge susceptibility function, one can find the plasmonic modes of the system. For this purpose we implement Green's function approach in the context of the tight-binding model hamiltonian. According to linear response theory the charge response function will be obtained via calculating the correlation function of charge density-density operators. Also we present the static charge structure factor which can be a criterion for charge ordering of the system. Especially the effect of gap parameter and chemical potential on the plasmon modes and static charge structure factor of armchair BNNT are investigated. Our results show that the chemical potential changes the number of plasmon modes and their positions. Furthermore chemical potential and gap parameter affect on the static charge susceptibility and consequently charge ordering of the BNNT is changed. • The investigation of charge structure factors of armchair nanotubes. • The study of chemical potential and gap parameter on dynamical susceptibility of nanotube. • The investigation of static structure factor behavior as a function of temperature.

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.

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.

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.

Magnetic field effects on charge structure factors of gapped graphene structure

We present the behaviors of dynamical and static charge susceptibilities of undoped gapped graphene using the Green's function approach in the context of tight binding model Hamiltonian. Specially, the effects of magnetic field on the plasmon modes of gapped graphene structure are investigated via calculating correlation function of charge density operators. Our results show the increase of magnetic field leads to disappear high frequency plasmon mode for gapped case. We also show that low frequency plasmon mode has not affected by increase of magnetic field and chemical potential. Finally the temperature dependence of static charge structure factor of gapp graphene structure is studied. The effects of both magnetic field and gap parameter on the static structure factor are discusses in details.

Static Charge Susceptibility in the t-J-V Model

We describe the static charge susceptibility and correlation function of the charge density in the twodimensional t-J-V model based on the method of equations of motion for the relaxation functions of the Hubbard operators. We obtain the dependence of the susceptibility and correlation function on the hole concentration and temperature. Charge density waves can develop if the intersite Coulomb interaction is sufficiently strong.

Invalidity of the Fermi liquid theory and magnetic phase transition in quasi-1D dopant-induced armchair-edged graphene nanoribbons

Based on theoretically tight-binding calculations considering nearest neighbors and Green’s function technique, we show that the magnetic phase transition in both semiconducting and metallic armchair graphene nanoribbons with width ranging from 9.83 Å to 69.3 Å would be observed in the presence of injecting electrons by doping. This transition is explained by the temperature-dependent static charge susceptibility through calculation of the correlation function of charge density operators. This work showed that charge concentration of dopants in such system plays a crucial role in determining the magnetic phase. A variety of multicritical points such as transition temperatures and maximum susceptibility are compared in undoped and doped cases. Our findings show that there exist two different transition temperatures and maximum susceptibility depending on the ribbon width in doped structures. Another remarkable point refers to the invalidity (validity) of the Fermi liquid theory in nanoribbons-based systems at weak (strong) concentration of dopants. The obtained interesting results of magnetic phase transition in such system create a new potential for magnetic graphene nanoribbon-based devices.

Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach

We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consist of the particle content, the dispersion relations, and a universal dressing transformation which accounts for interparticle interactions. We consider quantum integrable models and we focus on the one-dimensional fermionic Hubbard model. By linearizing hydrodynamic equations, we provide exact closed-form expressions for Drude weights, generalized static charge susceptibilities, and charge-current correlators valid on the hydrodynamic scale, represented as integral kernels operating diagonally in the space of mode numbers of thermodynamic excitations. We find that, on hydrodynamic scales, Drude weights manifestly display Onsager reciprocal relations even for generic (i.e., noncanonical) equilibrium states, and establish a generalized detailed balance condition for a general quantum integrable model. We present exact analytic expressions for the general Drude weights in the Hubbard model, and explain how to reconcile different approaches for computing Drude weights from the previous literature.

\u201c1kF \u201d singularities and finite density ABJM theory at strong coupling

We study non-analytic behavior in the static charge susceptibility in finite density states of the ABJM theory using its holographic dual. Emphasis is placed on a particular state characterized by vanishing entropy density at zero temperature, and Fermi surface-like singularities in various fermionic correlation functions. The susceptibility exhibits branch points in the complex momentum plane, with a real part quantitatively very similar to the location of the Fermi surface singularities.

Charge susceptibilities of armchair graphene nanoribbon in the presence of magnetic field

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 tight binding model Hamiltonian. Specifically, the effects of magnetic field on the the plasmon modes of armchair graphene nanoribbon are investigated via calculating the correlation function of charge density operators. Our results show that the increase of magnetic field makes the high-frequency plasmon mode for both metallic and insulating cases disappear. We also show that low-frequency plasmon mode for metallic nanoribbon appears due to increase of magnetic field. Furthermore, the number of collective excitation modes increases with ribbon width at zero magnetic field. Finally, the temperature dependence of the static charge structure factor of armchair graphene nanoribbon is studied. The effects of both magnetic field and ribbon width on the static charge structure factor are discussed in detail.

Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s0 are presented, whereby the positivity of F s0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t'-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U, at densities far from half filling.

Fluctuating charge order in the cuprates: Spatial anisotropy and feedback from superconductivity

We analyze the form of static charge susceptibility $\chi(q)$ in underdoped cuprates near axial momenta $(Q,0)$ and $(0,Q)$ at which short-range static charge order has been observed. We show that the momentum dependence of $\chi (q)$ is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. Comin et al., Science 347, 1335 (2015)]. We also argue that density and current components of the charge order parameter are affected differently by superconductivity --- the charge-density component is reduced less than the current component and hence extends deeper into the superconducting state. This gives rise to two distinct charge order transitions at zero temperature.

Spin polarized electrons in a metallic quantum wire

We obtain explicit expressions for the spin-resolved density response functions of a spin polarized metallic quantum wire by including the first-order exchange and self-energy contributions to the random-phase approximation. These are used to calculate the spin-resolved static structure factors, pair-correlation functions, and correlation energy of the system for various values of the spin-polarization parameter ζ. The inclusion of first-order correction is found to bring the present approximate theory in overall very good agreement with the recent quantum Monte Carlo simulations by Shulenburger et al. [L. Shulenburger, M. Casula, G. Senatore, R.M. Martin, J. Phys. A 42, 214021 (2009)]. Particularly, we find excellently close results for the fully spin-polarized (i.e., ζ = 1) electrons for even larger coupling (r s ~ 4), implying a fairly good description of exchange correlations. Interestingly, there is no crossover found from para- to ferro-magnetic ground state. The static charge and spin susceptibilities, and spin sound are obtained analytically and found to be in good agreement with the available quantum Monte Carlo simulations. Furthermore, we present results for the wavevector dependent static charge density, spin density, and charge-spin density susceptibilities for some wire parameters. The dispersion of spin sound has also been obtained and found to be strongly dependent on wire width and density parameter.

Fermi liquid approach to the quantumRCcircuit: Renormalization group analysis of the Anderson and Coulomb blockade models

We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum RC geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.

Slave-boson field fluctuation approach to the extended Falicov-Kimball model: Charge, orbital, and excitonic susceptibilities

Based on the $\mathrm{SO}(2)$-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov--Kimball model are calculated. Analyzing the phase without long-range order, we find instabilities toward charge order, orbital order, and the excitonic insulator (EI) phase. The instability toward the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the semiconductor-EI transition supporting a crossover scenario between a BCS-type electron-hole condensation and a Bose--Einstein condensation of preformed bound electron-hole pairs.

Screening of4fmoments and delocalization in the compressed light rare earths

Spin and charge susceptibilities and the 4f^n, 4f^{n-1}, and 4f^{n+1} configuration weights are calculated for compressed Ce (n=1), Pr (n=2), and Nd (n=3) metals using dynamical mean field theory combined with the local-density approximation. At ambient and larger volumes these trivalent rare earths are pinned at sharp 4f^n configurations, their 4f moments assume atomic-limiting values, are unscreened, and the 4f charge fluctuations are small indicating little f state density near the Fermi level. Under compresssion there is dramatic screening of the moments and an associated increase in both the 4f charge fluctuations and static charge susceptibility. These changes are coincident with growing weights of the 4f^{n-1} configurations, which it is argued are better measures of delocalization than the 4f^{n+1} weights which are compromised by an increase in the number of 4f electrons caused by rising 6s, 6p bands. This process is continuous and prolonged as a function of volume, with strikingly similarity among the three rare earths, aside from the effects moderating and shifting to smaller volumes for the heavier members. The observed alpha-gamma collapse in Ce occurs over the large-volume half of this evolution, the Pr analog at smaller volumes, and Nd has no collapse.