Effects Of Vertex Corrections Research Articles

Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas

We theoretically consider the effect of vertex correction on spin pumping from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG) in which the Rashba and Dresselhaus spin-orbit interactions coexist. The Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon absorption. We show that the Gilbert damping due to elastic spin-flipping is strongly enhanced by the vertex correction when the ratio of the two spin-orbit interactions is near a special value at which the spin relaxation time diverges while that due to magnon absorption shows only small modification. We also show that the shift in the resonant frequency due to elastic spin-flipping is strongly enhanced in a similar way as the Gilbert damping.

Phenomenological studies on neutral B-meson decays into J/psi f_1 and eta _c f_1

The axial-vector mesons f_1(1285) and f_1(1420) are particularly viewed as the mixtures of flavor states f_n and f_s with mixing angle varphi . In order to determine this angle, we study the B_{d,s}^0rightarrow J/psi f_1(1285,1420) and B_{d,s}^0rightarrow eta _c f_1(1285,1420) decays in perturbative QCD (PQCD) approach, including the effects of vertex corrections, nonfactorizable diagrams and penguin operators. Not only the branching fractions, but also the direct CP asymmetries and the polarization fractions are calculated. It is found that the branching fractions of these decays are large enough to be measured in the running LHCb and Belle-II experiments. Moreover, in comparison with the observed {mathcal {B}}(B_{d,s}^0 rightarrow J/psi f_1(1285)), B_s^0 rightarrow (J/psi , eta _c) f_1(1420) decays have large branching fractions, which could be measured promisingly through f_1(1420) rightarrow K_S^0 K^pm pi ^mp in experiments. We also propose several ratios that could be used to further constrain the absolute value of the mixing angle varphi , but its sign cannot be determined yet in these decays. The direct CP asymmetries of these decays indicate the penguin pollution in the B_d^0 rightarrow (J/psi , eta _c) f_1 decays cannot be neglected. We acknowledge that there are large theoretical uncertainties arising from the distribution amplitudes of axial-vector mesons and charmonium states, and more precise nonperturbative parameters are called. The comparisons between our results and future experimental data would help us to understand the nature of f_1 states and to test the PQCD approach.

Enhanced and stable spin Hall conductivity in a disordered time-reversal and inversion symmetry broken topological insulator thin film

We consider a disordered topological insulator thin film placed on the top of a ferromagnetic insulator with a perpendicular exchange field M and subjected to a perpendicular electric field. The presence of ferromagnetic insulator causes that bottom surface states of the topological insulator thin film become spin polarized and the electric field provides a potential difference V between the two surface states, resulting in breaking of time-reversal and inversion symmetry in the system. Using Kubo formalism and employing the first Born approximation as well as the self-consistent Born approximation, we calculate the spin Hall conductivity. We find that for small values of V, a large spin conductivity can be generated through large values of M away from the charge neutrality point. But for large values of V, the spin conductivity can be promoted even with small values of M around the charge neutrality point. The effect of vertex corrections and the stability of the obtained large spin conductivity against disorders are also examined.

Full versus quasiparticle self-consistency in vertex-corrected GW approaches

Using seven semiconductors and insulators with band gaps covering the range from 1 to 10 eV we systematically explore the performance of two different variants of self-consistency associated with the famous Hedin system of equations: the full self-consistency and the so-called quasiparticle approximation to it. The pros and cons of these two variants of self-consistency are sufficiently well documented in the literature for the simplest GW approximation to the Hedin equations. Our study, therefore, aims primarily at the level of theory beyond GW approximation, i.e., at the level of theory which includes vertex corrections. Whereas quasiparticle self-consistency has certain advantages at the GW level (a well-known fact), the situation becomes quite different when vertex corrections are included. In the variant with full self-consistency, vertex corrections (both for polarizability and for self-energy) systematically reduce the calculated band gaps making them closer to the experimental values. In the variant with quasiparticle self-consistency, however, an inclusion of the same diagrams has a considerably larger effect and calculated band gaps become severely underestimated. Different effects of vertex corrections in two variants of self-consistency can be related to the $Z$-factor cancellation which plays a positive role in quasiparticle self-consistency at the GW level of theory but appears to be destructive for the quasiparticle approximation when higher-order diagrams are included. The second result of our study is that we were able to reproduce the results obtained with the questaal code using our flapwmbpt code when the same variant of self-consistency (quasiparticle) and the same level of vertex corrections (for polarizability only, static approximation for screened interaction, and Tamm-Dancoff approximation for the Bethe-Salpeter equation) are used.

Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation

We solve the anisotropic, full-bandwidth and non-adiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The non-adiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface restricted Eliashberg-theory calculations. We find that non-adiabatic contributions to the superconducting gap can be positive, negative or negligible, depending on the dimensionality of the considered system, the degree of non-adiabaticity, and the coupling strength. We further examine non-adiabatic effects on the transition temperature and the electron-phonon coupling constant. Our treatment emphasizes the importance of overcoming previously employed approximations in estimating the impact of vertex corrections on superconductivity and opens a pathway to systematically study vertex correction effects in systems such as high-$T_c$, flat band and low-carrier density superconductors.

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a charge-ordered state emerges before the superconducting state upon doping the parent compound. We study this phenomenon by computing the charge response function of the Hubbard model including frequency-dependent local vertex corrections that satisfy the compressibility sum-rule. We find that upon approaching the Mott phase from the overdoped side, the charge fluctuations at wave vectors connecting hot spots are suppressed much faster than at the other wave-vectors. It leads to a momentum dependence of the dressed charge susceptibility that is very different from either the bare susceptibility or from the susceptibility obtained from the random phase approximation. We also find that the paramagnetic lightly hole-doped Mott phase at finite-temperature is unstable to charge ordering only at zero wave-vector, confirming the results previously obtained from the compressibility. Charge order is driven by the frequency-dependent scattering processes that induce an attractive particle-hole interaction at large interaction strength and small doping.

Conservation laws, vertex corrections, and screening in Raman spectroscopy

We present a microscopic theory for the Raman response of a clean multiband superconductor accounting for the effects of vertex corrections and long-range Coulomb interaction. The measured Raman intensity, $R(\Omega)$, is proportional to the imaginary part of the fully renormalized particle-hole correlator with Raman form-factors $\gamma(\vec k)$. In a BCS superconductor, a bare Raman bubble is non-zero for any $\gamma(\vec k)$ and diverges at $\Omega = 2\Delta +0$, where $\Delta$ is the largest gap along the Fermi surface. However, for $\gamma(\vec k) =$ const, the full $R(\Omega)$ is expected to vanish due to particle number conservation. It was long thought that this vanishing is due to the singular screening by long-range Coulomb interaction. We argue that this vanishing actually holds due to vertex corrections from the same short-range interaction that gives rise to superconductivity. We further argue that long-range Coulomb interaction does not affect the Raman signal for $any$ $\gamma(\vec k)$. We argue that vertex corrections eliminate the divergence at $2\Delta$ and replace it with a maximum at a somewhat larger frequency. We also argue that vertex corrections give rise to sharp peaks in $R(\Omega)$ at $\Omega < 2\Delta$, when $\Omega$ coincides with the frequency of one of collective modes in a superconductor, e.g, Leggett mode, Bardasis-Schrieffer mode, or an excitonic mode.

Non-perturbative Production Rate of Photons with a Lattice Quark Propagator: Effect of Vertex Correction

We analyze the production rate of photons from the thermal medium above the deconfinement temperature with a quark propagator obtained from a lattice QCD numerical simulation. The photon-quark vertex is determined gauge-invariantly, so as to satisfy the Ward-Takahashi identity. The obtained photon production rate shows a suppression compared to perturbative results.

Effect of vertex corrections on the possibility of chiral symmetry breaking induced by long-range Coulomb repulsion in graphene

In this paper, we consider the possibility of chiral (charge or spin density wave) symmetry breaking in graphene due to long-range Coulomb interaction by comparing the results of the Bethe-Salpeter and functional renormalization-group approaches. The former approach performs a summation of ladder diagrams in the particle-hole channel and reproduces the results of the Schwinger-Dyson approach for the critical interaction strength of the quantum phase transition. The renormalization-group approach combines the effect of different channels and allows to study the role of vertex corrections. The critical interaction strength, which is necessary to induce the symmetry breaking in the latter approach, is found in the static approximation to be ${\ensuremath{\alpha}}_{c}={e}^{2}/(\ensuremath{\epsilon}{v}_{F})\ensuremath{\approx}1.05$ without considering the Fermi velocity renormalization, and ${\ensuremath{\alpha}}_{c}=3.7$ with accounting the renormailzation of the Fermi velocity. The latter value is expected to be, however, reduced, when the dynamic screening effects are taken into account, yielding the critical interaction, which may be comparable to the one in freely suspended graphene. We show that the vertex corrections are crucially important to obtain the mentioned values of critical interactions.

Effects of Vertex Corrections on the Chirality-Driven Anomalous Hall Effect

The anomalous Hall effect due to spin chirality, a non-coplanar spin configuration, studied previously for the case of weak exchange coupling [G. Tatara and H. Kawamura, J. Phys. Soc. Jpn. 71, 2613 (2002)] is reexamined here by taking account of vertex corrections due to normal impurities. This amounts to considering the diffusive nature of electron motion, as well as spin conservation at the scattering from normal impurities, and introduces the spin diffusion length. The preexisting circular persistent current, responsible for the anomalous Hall response, is identified by calculating the “typical” magnitude of the equilibrium current.

Spin torques and charge transport on the surface of topological insulator

We study various aspects of interplay between two-dimensional helical electrons, realized on the surface of a three-dimensional topological insulator, and the magnetization of a ferromagnet coupled to them. The magnetization is assumed to be perpendicular to the surface, with small transverse fluctuations $\mathbit{u}$. In the first part of this paper, we calculate spin torques that the helical electrons exert on the magnetization. Up to first orders with respect to $\mathbit{u}$, space/time derivative and electric current, we have determined all torques, which include Gilbert damping, spin renormalization, current-induced spin-orbit torques, and gradient corrections to them. Thanks to the identity between the velocity and spin in this model, these torques have exact interpretation in terms of transport phenomena, namely, diagonal conductivity, (anomalous) Hall conductivity, and corrections to them due to ordinary Hall effect on top of the anomalous one. These torque (and transport) coefficients are studied in detail with particular attention to the effects of vertex corrections and type of impurities (normal and magnetic). It is shown rigorously that the conventional current-induced torques, namely, spin-transfer torque and the so-called $\ensuremath{\beta}$ term, are absent. An electromotive force generated by spin dynamics, which is the inverse to the current-induced spin-orbit torque, is also studied. In the second part, we study the feedback effects arising as combinations of current-induced spin-orbit torques and spin-dynamics-induced electromotive force. It is demonstrated that the Gilbert damping process in this system is completely understood as a feedback effect. Another feedback effect, which may be called ``magnon-drag electrical conductivity,'' is shown to violate the exact correspondence between spin-torque and transport phenomena demonstrated in the first part.

Effects of the electron-electron interaction on the surface of three-dimensional topological insulators

In the GW approximation, it has been shown that, owing to the electron-electron interaction, plasma satellites appear in the spectral function of a two-dimensional electron system on the surface of a topological insulator. They are due to the resonance plasmon-hole scattering. The contribution of satellites to the single-electron density of states is responsible for the downward energy shift of the minimum of the density, which is compared to the Dirac point in the experiment. To analyze the effect of vertex corrections on the resulting spectrum, a method has been proposed that goes beyond the GW approximation by summing ladder diagrams in the expansion of both the polarization function and self-energy. It has been shown with this method that the multiple electron-hole scattering hardly changes the resulting spectrum.

Pseudo-gap and Vertex Correction of Electron–Phonon Interaction in High Transition-Temperature Superconductors

The strong-coupling Eliashberg theory plus vertex correction is used to calculate the maps of transition temperature (Tc) in parameter-space characterizing superconductivity. Based on these Tc maps, complex crossover behaviors are found when electron–phonon interaction increases from weak-coupling region to strong-coupling region. The doping-dependent Tc of cuprate superconductors and most importantly the emergence of pseudo-gap region can be explained as the effects of vertex correction.

Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections

The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. We use the Two-Particle Self-Consistent approach that satisfies crucial constraints such as the Mermin-Wagner theorem, the Pauli principle and sum rules in order to reach non-perturbative regimes. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The two types of vertex corrections that we find are the antiferromagnetic analogs of the Maki-Thompson and Aslamasov-Larkin contributions of superconducting fluctuations to the conductivity but, contrary to the latter, they include non-perturbative effects. The resulting analytical expressions must be evaluated numerically. The calculations are impossible unless a number of advanced numerical algorithms are used. A maximum entropy approach is specially developed for analytical continuation of our results. The numerical results are for nearest neighbor hoppings. In the pseudogap regime induced by two-dimensional antiferromagnetic fluctuations, the effect of vertex corrections is dramatic. Without vertex corrections the resistivity increases as we enter the pseudogap regime. Adding vertex corrections leads to a drop in resistivity, as observed in some high temperature superconductors. At high temperature, the resistivity saturates at the Ioffe-Regel limit. At the quantum critical point and beyond, the resistivity displays both linear and quadratic temperature dependence and there is a correlation between the linear term and the superconducting transition temperature. A hump is observed in the mid-infrared range of the optical conductivity in the presence of antiferromagnetic fluctuations.

Local field corrections in two-dimensional coupled electron–LO phonon systems

We theoretically investigate the effects of vertex corrections on the many-body properties of a two-dimensional electron gas system in which the electrons are coupled to the LO phonons under adiabatic conditions. We calculate the vertex-corrected electron self-energy, spectral function, damping rate, lifetime and inelastic mean free path in a coupled electron–LO phonon system at zero temperature. Because of the adiabatic situation, we neglect the phonon vertex correction in our calculations. We go beyond the random phase approximation (RPA) and consider the short-range exchange and correlation interactions by using the Hubbard and Singwi–Tosi–Land–Sjölander (STLS) approximations. In general, our results show that by decreasing the electron density, the vertex effects become more significant and the STLS approximation has a stronger effect than does the Hubbard approximation. We find that including the vertex corrections yields sharper quasiparticle peaks compared with the RPA approach. In addition, longer quasiparticle lifetimes and mean free paths are obtained when the vertex corrections are taken into account.

Effects of vertex corrections on diagrammatic approximations applied to the study of transport through a quantum dot

In the present work, we calculate the conductance through a single quantum dot weakly coupled to metallic contacts. We use the spin-1/2 Anderson model to describe the quantum dot, while considering a finite Coulomb repulsion. We solve the interacting system using the noncrossing approximation (NCA) and the one-crossing approximation (OCA). We obtain the linear response conductance as a function of temperature and energy position of the localized level. From the comparison of both approximations we extract the role of the vertex corrections, which are introduced in the OCA calculations and neglected in the NCA scheme. As a function of the energy position, we observe that the diagrams omitted within the NCA are really important for appropriately describing transport phenomena in Kondo systems as well as in the mixed valence regime. On the other hand, as a function of temperature, the corrections introduced by the OCA partly recover the universal scaling properties known from numerical approaches such as the numerical renormalization group.

Effect of vertex corrections on longitudinal transport through multilayered nanostructures: Dynamical mean-field theory approach applied to the inhomogeneous Falicov-Kimball model

Inhomogeneous dynamical mean-field theory is employed to calculate the vertex-corrected electronic charge transport for multilayered devices composed of semi-infinite metallic lead layers coupled through a strongly correlated material barrier region. The barrier region can be tuned from a metal to a Mott insulator through adjusting the interaction strength and the particle filling. We use the Falicov-Kimball model to describe the barrier region because an exact expression for the vertex corrections is known, allowing us to determine their effect on transport. The dc conductivity is calculated and we find the effects of the vertex corrections are relatively small, manifesting themselves in a small reduction in the resistance-area product. This reduction saturates in absolute magnitude as the barrier layer becomes thick, as expected due to the vanishing nature of the vertex corrections in bulk. The vertex corrections have a larger relative effect on the resistance-area product for more metallic and thinner devices.

Enhanced Spin Susceptibility toward the Charge-Ordering Transition in a Two-Dimensional Extended Hubbard Model

We investigate the charge and spin susceptibilities in the vicinity of a charge-ordering transition point on the basis of a two-dimensional extended Hubbard model with nearest-neighbor Coulomb interaction on a square lattice. In order to evaluate the leading contribution of vertex corrections, we construct a new iterative method generating a series of non-skeleton diagrammatic conserving approximations, and utilize the first approximation for the calculation of response functions. This approximation can determine a charge-ordering transition point and static susceptibilities on an equal footing in a sense that the compressibility and spin-susceptibility sum rules are satisfied. As a prominent effect of vertex corrections, we find that the uniform spin susceptibility is enhanced owing to charge fluctuations that develop toward the charge-ordering transition. We also discuss the experimental relevance of our theory for organic conductors, together with its connection to Landau's Fermi-liquid theory.

Covariant and self-consistent vertex corrections for pions and isobars in nuclear matter

We evaluate the pion and isobar propagators in cold nuclear matter self-consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the {pi}N{delta} vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the {delta} resonance at nuclear saturation density. The pionic soft modes are much less pronounced than in previous studies.

Photoabsorption off nuclei with self-consistent vertex corrections

We study photoproduction off nuclei based on a self-consistent and covariant many-body approach for the pion and isobar propagation in infinite nuclear matter. For the first time the t-channel exchange of an in-medium pion is evaluated in the presence of vertex correction effects consistently. In particular the interference pattern with the s-channel in-medium nucleon and isobar exchange contribution is considered. Electromagnetic gauge invariance is kept as a consequence of various Ward identities obeyed by the computation. Adjusting the set of Migdal parameters to the data set we predict an attractive mass shift for the isobar of about 50 MeV at nuclear saturation density.