Electron-phonon renormalization in cuprate superconductors

Electron-phonon (e-ph) renormalization effects in a model cuprate system CaCuO2 are studied by employing density functional theory based methods. Whereas calculations based on the local spin-density approximation (LSDA) predicts negligible e-ph coupling effects of the half-breathing Cu-O bond stretching mode, the inclusion of a screened on-site Coulomb interaction (U) in the LSDA+U calculations greatly enhances the e-ph coupling strength of this mode. The full-breathing mode, on the other hand, shows a much weaker e-ph renormalization effect.     

Weak localization and coulomb interaction in disordered systems

Interacting electrons, diffusing in a two-dimensional (2d) disordered system, are studied. The renormalization group equations, including both localization effects and Coulomb correlations, are derived. We encounter a qualitatively new situation: the constants describing electron interaction diverge as a result of the renormalization when a certain scale is achieved, whereas the resistence proves to be finite. Calculation of the spin density correlation function reveals that the system exhibits a tendency for spin density rearrangement.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

Full current statistics in the regime of weak coulomb interaction

We evaluate the full statistics of the current via a Coulomb island that is strongly coupled to the leads. This strong coupling weakens Coulomb interaction. We show that in this case the effects of the interaction can be incorporated into the renormalization of transmission eigenvalues of the scatterers that connect the island and the leads. We evaluate the Coulomb blockade gap in the current-voltage characteristics, the value of the gap being exponentially suppressed as compared to the classical charging energy of the island.     

The Friction and Diffusion Coefficients with Maxwellian Scatters

The Fokker-Planck coefficients for Coulomb interaction, or the friction coefficient (Δυ_α) (the average change in velocity) and the diffusion coefficient (Δυ_αΔυ_α), are evaluated by an appropriate variable change technique. This approach reduces the five-fold integral expressions of the Fokker-Planck coefficients to one-fold integral without meeting the divergence difficulties. A new Debye cutoff parameter Δυ_αmin, instead of the customary θ_min cutoff avoids the error incurred through the customary neglecting of velocity dependence of the Coulomb logarithm. The dominant terms of the new results are similar to Chandrasekhar's results. A non-dominant term, which can exceed the dominant one in the case of υ_α² > υ_βt²lnA is added for (Δυ_α||²).     

The Two-Dimensional Hubbard Model on the Honeycomb Lattice

We consider the two-dimensional (2D) Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analyticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the thermal ground state.     

Electrostatic model of band-gap renormalization and the photoluminescence line shape in a GaAs/AlGaAs two-dimensional layer at a high excitation level

An electrostatic model for calculating the band-gap renormalization in a two-dimensional (2D) semiconductor layer (quantum well) due to the Coulomb interaction between nonequilibrium charge carriers has been proposed. Consideration is given only to the first quantum-well energy levels for electrons and heavy holes. The exchange and correlation energies are calculated for the first time taking into account the charge-carrier potential energyfluctuations created by electrons and holes along the 2D layer. A relationship for the screened Coulomb potential along the 2D layer is derived, which, within the extremely narrow quantum-well approximation, transforms into the known expression. The band-gap renormalization and the photoluminescence line shape for the GaAs 2D layer in an Al_xGa_1?x As matrix are computed depending on the concentration of nonequilibrium electrons and holes. The calculated band-gap renormalization is in agreement with the available experimental data at a high photoexcitation of the quantum well when the electrons and holes form the 2D plasma.     

Charge Gap in One-Dimensional Extended Hubbard Model

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.     

Magnetic field studies of the frictional drag between coupled two-dimensional electronic systems – Coulomb versus phonon coupling

The coupling between systems of two spatially separated two-dimensional (2D) electron gases and between systems of a separated 2D electron gas and a 2D hole gas is studied as a function of magnetic field . The small barrier (30 nm) separated coupled electron gases showed a transition from a phonon dominated interaction at to a Coulomb dominated one at quantising fields. For large barriers (190 nm) phonons have been found to be the dominant coupling mechanism both at zero and finite fields. However, for all barriers investigated we could observe novel screening effects manifested in a suppression of the coupling at half-filled Landau levels. For the coupled electron–hole gases we have investigated samples with large barriers ( ) so that the coupling is both in zero and finite fields dominated by phonon mediated processes. The enhanced screening effects could not be observed in those samples possibly due to the less pronounced quantisation of the hole gas.     

Coulomb quantum kinetics in pulse-excited semiconductors

The quantum kinetic equations of the electron and hole densities and the interband polarization are derived for a laser-pulse-excited semiconductor with Coulomb interaction including renormalization effects, excitonic effects and scattering with memory kernels. Numerical solutions of this set of non-Markovian, nonlinear integro-differential equations are obtained for a statically screened Coulomb potential.     

Quantum phase transitions to charge-ordered and Wigner-crystal states under the interplay of lattice commensurability and long-range Coulomb interactions

The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) approximately 2 for the filling n=1/2, showing a large reduction from r(s) approximately 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.     

Correlated electron tunneling through two separate quantum dot systems with strong capacitive interdot coupling

A system consisting of two independently contacted quantum dots with a strong electrostatic interaction shows an interdot Coulomb blockade when the dots are weakly tunnel coupled to their leads. How the blockade can be overcome by correlated tunneling when tunnel coupling to the leads increases is studied experimentally. The experimental results are compared with numerical renormalization group calculations using predefined (measured) parameters. Combining our experimental and theoretical results we identify transport through Kondo correlations due to the electrostatic interaction between the two dots.     

More comments on asymptotic freedom

The effective Coulomb interaction between sources with SU(2) color charge is reinvestigated at the one-loop order of perturbation theory. This quantity is shown to be formally identical with the effective Coulomb interaction between electric charges in the QED of massless, charged, vector fields with anomalous magnetic moments. This correspondence allows the one-loop Yang-Mills charge renormalization factor to be deduced from a knowledge of the size and origins of this quantity in massless scalar and spinor QED. Careful consideration of the analogy with QED suggests a mechanism for asymptotic freedom in the Feynman gauge.     

Chirality-induced dynamic kohn anomalies in graphene

We develop a theory for the renormalization of the phonon energy dispersion in graphene due to the combined effects of both Coulomb and electron-phonon (e-ph) interactions. We obtain the renormalized phonon energy spectrum by an exact analytic derivation of the phonon self-energy, finding three distinct Kohn anomalies (KAs) at the phonon wave vector q=omega/v, 2k_{F}+/-omega/v for LO phonons and one at q=omega/v for TO phonons. The presence of these new KAs in graphene, in contrast to the usual KA q=2k_{F} in ordinary metals, originates from the dynamical screening of e-ph interaction (with a concomitant breakdown of the Born-Oppenheimer approximation) and the peculiar chirality of the graphene e-ph coupling.     

Calculation of proton-deuteron breakup reactions including the Coulomb interaction between the two protons

The Coulomb interaction between the two protons is fully included in the calculation of proton-deuteron breakup with realistic interactions for the first time. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn +Delta to a coupled-channel two-baryon potential, allowing for single virtual Delta-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. The Coulomb effect on breakup observables is seen at all energies in particular kinematic regimes.     

Eliashberg theory with the external pair potential

Based on BCS model with the external pair potential formulated in a work Grigorishin (2017) [1], analogous model with electron-phonon coupling and Coulomb coupling is proposed. The generalized Eliashberg equations in the regime of renormalization of the order parameter are obtained. High temperature asymptotics and effect of Coulomb pseudopotential on them are investigated: as in the BCS model the order parameter asymptotically tends to zero as temperature rises, but the accounting of the Coulomb pseudopotential leads to existence of critical temperature. The effective Ginzburg-Landau theory is formulated for such model.     

Singularities of the S matrix in the complex plane of the Coulomb coupling constant

It is shown that bound states and resonances in systems arising during the interaction of a charged particle with isobaric nuclei can be described with the aid of the trajectory of the poles of the S matrix in the complex plane of the Coulomb coupling constanta. The behavior of the singularities of the S matrix in thea plane is examined in detail for the case of a Coulomb field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 21–24, April, 1982.     

Phonon-induced many-body renormalization of the electronic properties of graphene

We develop a theory for the electron-phonon interaction effects on the electronic properties of graphene. We analytically calculate the electron self-energy, spectral function, and the band velocity renormalization due to phonon-mediated electron-electron interaction, finding that phonon-mediated electron-electron coupling has a large effect on the graphene band structure renormalization. Our analytic theory successfully captures the essential features of the observed graphene electron spectra in the angle-resolved photoemission experiments, predicting a kink at approximately 200 meV below the Fermi level and a reduction of the band velocity by approximately 10-20% at the experimental doping level.     

Evidence for the importance of extended Coulomb interactions and forward scattering in cuprate superconductors

The prevalent view of the high-temperature superconducting cuprates is that their essential low-energy physics is captured by local Coulomb interactions. However, this view been challenged recently by studies indicating the importance of longer-range components. Motivated by this, we demonstrate the importance of these components by examining the electron-phonon (e-ph) interaction with acoustic phonons in connection with the recently discovered renormalization in the near-nodal low-energy (~8-15 meV) dispersion of Bi(2)Sr(2)CaCu(2)O(8+δ). By studying its nontrivial momentum and doping dependence we conclude a predominance of forward scattering arising from the direct interplay between the e-ph and extended Coulomb interactions. Our results thus demonstrate how the low-energy renormalization can provide a pathway to new insights into how these interactions interplay with one another and influence pairing and dynamics in the cuprates.     

不带奇异数的双重子态（英文）

在手征SU（3） 夸克模型下应用共振群方法讨论了三个非奇异的双重子态的性质。计算中的模型参数取自我们以前的工作,拟合核子-核子相互作用散射相移确定下来的。首先,研究了氘核的性质,这是非常重要的,因为氘核是多年来实验上唯一发现的双重子态。氘核属于核子-核子系统,它是自旋为S =1 和同位旋为T =0 的双重子态。我们计算了氘核的结合能、散射长度以及氘核的相对运动波函数,结果表明手征SU（3） 夸克模型可以合理描述氘核的性质并且发现张量力对形成松散束缚态的氘核是重要的。然后,给出了S = 3 和T =0 的ΔΔ双重子态的理论预言结果,这里考虑了分波耦合和隐色道耦合效应,计算了结合能和均方根半径。结果表明,隐色道耦合效应比分波耦合效应大,也就是说隐色道耦合效应在形成（ΔΔ）_ST=30 双重子态中是重要的。我们的理论预言结果在几十个MeV 左右,低于ΔΔ道的阈值但是高于NΔπ的阈值. 出乎意料地,我们的预言结果很接近最近2014 年WASA的实验结果。接着,给出了对S = 0 和T =3 的ΔΔ双重子态性质的最新研究结果,这里在以前的单道计算基础上考虑了隐色道耦合效应。结果表明,隐色道耦合对（ΔΔ）ST=03的结合能也有较大的影响。但是,和（ΔΔ）_ST=30 一样,它的质量低于ΔΔ道的阈值但是高于NΔπ的阈值。最后,对S = 3 以及S = 0 两个不同ΔΔ自旋态,详细比较了两者结构之间的差异。结果表明,σ'介子交换和OGE 交换对自旋S = 0 和S = 1 态提供的吸引作用分别是主要的,从而导致耦合道计算中系统的结合能变大。In the present work we discuss three dibaryons without strangeness in the chiral SU(3) quark model by solving the resonating group method (RGM) equation. In the calculation, the model parameters are taken from our previous work in which the nucleon-nucleon (NN) scattering phase shifts are fitted quite well. Firstly, the structure of deuteron is discussed, which is very important since it is the first dibaryon confirmed by experiment in the past many years. Deuteron belongs to NN system with spin S =1 and isospin T =0, the binding energy, scattering length and the relative wave functions of deuteron are discussed. The results show that the chiral SU(3) quark model describes the properties of deuteron quite well and tensor interaction is important in forming the deuteron loosely bound. Secondly, the predicted results of ΔΔ dibaryon with S =3 and T =0 are shown, the resultant binding energy and size of root-mean-square (RMS) of six quarks are calculated by including the L coupling and hidden color channel (CC) coupling. The results show that the CC coupling effect is much larger than the L mixing effect, which means that CC coupling plays an important role in forming the spin S =3 ΔΔ dibayon state. Our predicted binding energy is several tens MeV, it is lower than the threshold of the ΔΔ channel and higher than the mass of NΔπ. Unexpectedly, our predicted mass is quite close to the recent confirmation by WASA experiments in 2014. Thirdly, we present our new results of ΔΔ dibaryon with S = 0 and T =3, obtained recently by extending the single-channel calculation to including the CC coupling. It is seen that the CC coupling also has a relatively large effect on (ΔΔ)ST=03 state. However, its mass is still lower than the threshold of the ΔΔ channel and higher than the mass of NΔπ, similar as that of (ΔΔ)_ST=30 state. Finally, we further make some comparisons between S = 3 and S = 0 ΔΔ states to show the difference of the two dibaryons. The results show that the attractive interactions from σ' meson and OGE exchanges are dominantly important for S =0 and S =3 states, respectively, so their binding energies all become larger in coupled-channel calculation.