Self-energy Effects Research Articles

Orbital-dependent self-energy effects and consequences for the superconducting gap structure in multiorbital correlated electron systems

We perform a theoretical study of the effects of electronic correlations on the superconducting gap structure of multi-band superconductors. In particular, by comparing standard RPA-based spin-fluctuation mediated gap structures to those obtained within the FLEX formalism for an iron-based superconductor, we obtain directly the feedback effects from electron-electron interactions on the momentum-space gap structure. We show how self-energy effects can lead to an orbital inversion of the orbital-resolved spin susceptibility, and thereby invert the hierarchy of the most important orbitals channels for superconducting pairing. This effect has important consequences for the detailed gap variations on the Fermi surface. We expect such self-energy feedback on the pairing gap to be generally relevant for superconductivity in strongly correlated multi-orbital systems.

Self-energy screening effects in the g factor of Li-like ions

We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order $\alpha^5\ln\alpha$ and obtaining approximate results for the $\alpha^5$ and $\alpha^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects.

Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides

This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the valley extrema in TMDs, energy bands split into Landau levels with a Zeeman shift in the presence of a uniform out-of-plane external magnetic field. The Landau level indices are symmetric in the $K$ and $K'$ valleys. We develop a numerical approach to compute the single band g-factors from first principles without the need for a sum over unoccupied bands. Many-body effects are included perturbatively within the GW approximation. Non-local exchange and correlation self-energy effects in the GW calculations increase the magnitude of single band g-factors compared to those obtained from density functional theory. Our first principles results give spin- and valley-split Landau levels, in agreement with recent optical experiments. The exciton g-factors deduced in this work are also in good agreement with experiment for the bright and dark excitons in monolayer WSe$_2$, as well as the lowest-energy bright excitons in MoSe$_2$-WSe$_2$ heterobilayers with different twist angles.

Temperature and magnetic field dependent Raman study of electron-phonon interactions in thin films of Bi2Se3 and Bi2Te3 nanoflakes

We have investigated two-dimensional nanostructures of the topological insulators ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ by means of temperature and magnetic field dependent Raman spectroscopy. The surface contribution of our samples was increased by using thin films of dropcasted nanoflakes with the aim of enhancing their topological properties. Raman spectroscopy provides a contact-free method to investigate the behavior of topological properties with temperature and magnetic fields at lower dimensions. The temperature dependent Raman study reveals anharmonic phonon behavior for ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ indicative of a two-phonon relaxation mechanism in this material. Contrary to this, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ shows clear deviations from a two-phonon anharmonic decay model at temperatures below 120 K exhibiting a hardening and broadening, especially of the ${A}_{1\text{g}}^{2}$ mode. Similarly, the magnetic field dependent self-energy effects are only observed for the ${A}_{1\text{g}}^{2}$ mode of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, showing a broadening and hardening with increasing field. We interpret our results in terms of corrections to the phonon self-energy for ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ at temperatures below 120 K and magnetic fields above 4 T due to electron-hole pair excitations associated with the conducting surface states. The phonon renormalization with increasing magnetic field is explained by a gap opening in the Dirac cone that enables phonon coupling to the changing electric susceptibility.

QED corrections to the g factor of Li- and B-like ions

QED corrections to the $g$ factor of Li-like and B-like ions in a wide range of nuclear charges are presented. Many-electron contributions as well as radiative effects on the one-loop level are calculated. Contributions resulting from the interelectronic interaction, the self-energy effect, and most of the terms of the vacuum-polarization effect are evaluated to all orders in the nuclear coupling strength $Z\alpha$. Uncertainties resulting from nuclear size effects, numerical computations, and uncalculated effects are discussed.

Effects of momentum-dependent quasiparticle renormalization on the gap structure of iron-based superconductors

We discuss the influence of momentum-dependent correlations on the superconducting gap structure in iron-based superconductors. Within the weak coupling approach including self-energy effects at the one-loop spin-fluctuation level, we construct a dimensionless pairing strength functional which includes the effects of quasiparticle renormalization. The stationary solution of this equation determines the gap function at $T_c$. The resulting equations represent the simplest generalization of spin fluctuation pairing theory to include the effects of an anisotropic quasiparticle weight. We obtain good agreement with experimentally observed anisotropic gap structures in LiFeAs, indicating that the inclusion of quasiparticle renormalization effects in the existing weak-coupling theories can account for the observed anomalies in the gap structure of Fe-based superconductors.

Photoelectric process in GaAs quantum dot

We study the photoelectric process in single electron charged spherical GaAs/Ga1-yAlyAs quantum dot. The effective mass approximation is used with the finite potential at the dot matrix interface including the effect of self-energy. The total cross section of photoelectric process is investigated with the variation of incident photon energy and the molar concentration y of Al in Ga1-yAlyAs matrix material.

Mobility of spin polarons with vertex corrections

The mobility of holes in the spin polaron theory is discussed in this paper using a representation where holes are described as spinless fermions and spins as normal bosons. The hard-core bosonic operator is introduced through the Holstein–Primakoff transformation. Mathematically, the theory is implemented in the finite temperature (Matsubara) Green’s function method. The expressions for the zeroth-order term of the hole mobility is determined explicitly for hole occupation factor taking the form of Fermi–Dirac distribution and the classical Maxwell–Boltzmann distribution function. These are proportional to the relaxation time and the square of the renormalization factor. In the Ising limit, we showed that the mobility is zero and the holes are localized. The calculation of the hole mobility is generalized by considering the vertex corrections, which included the ladder diagrams. One of the vertex functions in the hole mobility can be evaluated using the Ward identity for hole-spin wave weak interaction. We also derived an expression for the hole mobility with vertex corrections in the low-temperature limit and vanishing self-energy effects. Our calculation is made up to second-order correction in the case where the hole occupation factor follows the Fermi–Dirac distribution.

Magnetic force theory combined with quasi-particle self-consistent GW method

We report a successful combination of magnetic force linear response theory with quasiparticle self-consistent GW method. The self-consistently determined wavefunctions and eigenvalues can just be used for the conventional magnetic force calculations. While its formulation is straightforward, this combination provides a way to investigate the effect of GW self-energy on the magnetic interactions which can hardly be quantified due to the limitation of current GW methodology in calculating the total energy difference in between different magnetic phases. In ferromagnetic 3d elements, GW self-energy slightly reduces the d bandwidth and enhances the interactions while the same long-range feature is maintained. In antiferromagnetic transition-metal monoxides, QSGW significantly reduces the interaction strengths by enlarging the gap. Orbital-dependent magnetic force calculations show that the coupling between eg and the nominally-empty 4s orbital is noticeably large in MnO which is reminiscent of the discussion for cuprates regarding the role of Cu-4s state. This combination of magnetic force theory with quasiparticle self-consistent GW can be a useful tool to study various magnetic materials.

Neutron-proton pairing in nuclear matter

The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the \emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is established with the parameters calibrated to the microscopically calculated energy gap.

Plasmonic performance of AuxAgyCu1−x−y alloys from many-body perturbation theory

We present a detailed appraisal of the optical and plasmonic properties of ordered alloys of the form AuxAgyCu1-x-y, as predicted by means of first-principles many-body perturbation theory augmented by a semi-empirical Drude–Lorentz model. In benchmark simulations on elemental Au, Ag, and Cu, we find that the random-phase approximation (RPA) fails to accurately describe inter-band transitions when it is built upon semi-local approximate Kohn–Sham density-functional theory band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow d-bands which contribute strongly throughout the low-energy spectral range (0–6 eV), may be modeled very expediently using band-stretching operators that imitate the effect of a perturbative self-energy correction incorporating quasiparticle (QP) mass renormalization. We thereby establish a convenient work-flow for carrying out approximated spectroscopic calculations on alloys and, in particular here, we have considered alloy concentrations down to 12.5% in , including all possible crystallographic orderings of face-centred cubic type. We develop a pragmatic procedure for calculating the Drude plasmon frequency from first principles, including self-energy effects, as well as a semi-empirical scheme for interpolating the plasmon inverse lifetimes between stoichiometries. A distinctive M-shaped profile is observed in both quantities for binary alloys, in qualitative agreement with previous experimental findings. A range of optical and plasmonic figures of merit are discussed, and plotted for ordered at three representative solid-state laser wavelengths. On this basis, we predict that certain compositions may offer improved performance over elemental Au for particular application types. We predict that while the loss functions for both bulk and surface plasmons are typically diminished in strength through binary alloying, certain stoichiometric ratios may exhibit higher-quality (longer-lived) localized surface-plasmons and surface-plasmon polaritons, at technologically-relevant wavelengths, than those in elemental Au.

Electron-Phonon Coupling from AbInitio Linear-Response Theory within the GW Method: Correlation-Enhanced Interactions and Superconductivity in Ba_{1-x}K_{x}BiO_{3}.

We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the GW method. This approach, named GW perturbation theory (GWPT), is applied to calculate the electron-phonon (e-ph) interactions with the full inclusion of the GW nonlocal, energy-dependent self-energy effects, going beyond density-functional perturbation theory. Avoiding limitations of the frozen-phonon technique, GWPT gives access to e-ph matrix elements at the GW level for all phonons and scattering processes, and the computational cost scales linearly with the number of phonon modes (wave vectors and branches) investigated. We demonstrate the capabilities of GWPT by studying the e-ph coupling and superconductivity in Ba_{0.6}K_{0.4}BiO_{3}. We show that many-electron correlations significantly enhance the e-ph interactions for states near the Fermi surface, and explain the observed high superconductivity transition temperature of Ba_{0.6}K_{0.4}BiO_{3} as well as its doping dependence.

Modeling Electron Injection at Semiconductor–Molecule Interfaces using First-Principles Dynamics Simulation: Effects of Nonadiabatic Coupling, Self-energy, and Surface Models

Excited electron transfer across semiconductor–molecule heterogeneous interfaces is central to various future electronic and optoelectronic devices. At the same time, first-principles modeling of s...

Derivation of the zeroth retardation order Boltzmann equation from nonstandard space–time Wigner quantum kinetics

A derivation of the equation of motion satisfied by a prototype of the forward space–time Wigner distribution, that incorporates a Fourier transformation of truncated time shifts as compared with the standard Wigner distribution, is carried out in the case of a many-body system within the formalism of nonequilibrium Green’s functions of quantum field theory. In particular, the single-particle equation found in López and Soler (2016) is recovered when the self-energy interaction effects are neglected. Then, a sinc-corrected quantum kinetic Boltzmann equation is derived that rules the evolution of the standard Wigner transform, which is shown to be reduced to the usual Boltzmann equation when only binary elastic collisions are considered.

Orbital selectivity versus Pomeranchuk instability in the iron–chalcogenide superconductors: A two-loop renormalization group study

We perform a two-loop renormalization group (RG) analysis of a 2D effective multiband model, which is relevant for describing the low-energy properties of some iron–chalcogenide superconducting materials. Crucial ingredients in this analysis are the calculation of higher-order contributions in the RG scheme that go beyond the widely-used parquet approximation and the consequent inclusion of nontrivial self-energy effects of the model that yield an anisotropic renormalization of the quasiparticle weight in the system. The motivation of our work is the experimental discovery by Sprau et al. (2017) that orbitally-selective renormalization of the quasiparticle weight in the Hund’s metal phase at moderate temperatures underpins the highly unusual gap in the superconducting phase of the FeSe compound at lower temperatures. One prediction we arrive here is that the underlying origin of nematicity in these systems may indeed come from orbital-selectivity, instead of a Pomeranchuk instability in the d± channel. This orbital selectivity is driven by the presence of stripe-type antiferromagnetic fluctuations in the model. Therefore, we argue that the present RG results may provide a scenario from a weak-to-moderate coupling perspective, in which the role of orbital selectivity to describe the physical properties of some iron–chalcogenide superconductors is emphasized.

Proton-proton [formula omitted] pairing in neutron stars

The onset of S01 proton spin-singlet pairing in neutron-star matter is studied in the framework of the BCS theory including medium polarization effects. The strong three-body coupling of the diproton pairs with the dense neutron environment and the BCS self-energy effects severely reduce the gap magnitude, so to reshape the scenario of the proton superfluid phase inside the star. At low density the vertex corrections due to the medium polarization are attractive in most isospin-asymmetry range and tend to favor that pairing. However quantitative estimates of their effect on the energy gap do not give significant changes. Implications of the new scenario on the role of the S01 proton pairing in neutron-star cooling are briefly discussed.

Electronic structure, magnetoexcitons and valley polarized electron gas in 2D crystals

We describe here recent work on the electronic properties, magnetoexcitons and valley polarised electron gas in 2D crystals. Among 2D crystals, monolayer MoS2 has attracted significant attention as a direct-gap 2D semiconductor analogue of graphene. The crystal structure of monolayer MoS2 breaks inversion symmetry and results in K valley selection rules allowing to address individual valleys optically. Additionally, the band nesting near Q points is responsible for enhancing the optical response of MoS2.We show that at low energies the electronic structure of MoS2 is well approximated by the massive Dirac Fermion model. We focus on the effect of magnetic field on optical properties of MoS2. We discuss the Landau level structure of massive Dirac fermions in the two non-equivalent valleys and resulting valley Zeeman splitting. The effects of electron-electron interaction on the valley Zeeman splitting and on the magneto-exciton spectrum are described. We show the changes in the absorption spectrum as the self-energy, electron-hole exchange and correlation effects are included. Finally, we describe the valley-polarised electron gas in WS2 and its optical signature in finite magnetic fields.

Conductance smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire

In a recent high-quality experimental work on normal metal--superconducting nanowire junctions arXiv:1807.01940 (2018), strong anisotropic suppression of induced superconductivity has been observed in tunnel conductance measurements in the presence of applied magnetic field with variable orientation. Following this finding, we investigate theoretically the dependence of tunnel conductance on the direction of the Zeeman field in order to understand the operational mechanisms and to extract effective system parameters. Second, motivated by a generic discrepancy between experiment and theory, i.e., many in-gap and above-gap conductance features predicted by theory are barely observed in experiments, we study several mechanisms possibly responsible for the suppression of the theoretically predicted conductance features (e.g., length of the nanowire, self-energy effect due to the proximity effect, finite temperature, finite dissipation, and multiband effect). One essential finding in the current work is that only by a combined understanding of both suppression mechanisms can we extract effective system parameters from the experimental data (e.g., the effective nanowire-superconductor coupling, the effective Land\'e $g$ factor, and the chemical potential of the semiconducting nanowire). In addition, we consider topologically trivial Andreev bound states in hybrid nanowires in the presence of potential inhomogeneities, such as external quantum dots or potential inhomogeneities inside the nanowire. We compare the anisotropic, field-dependent features induced by these nontopological Andreev bound states with the corresponding features produced by topological Majorana zero modes in pristine nanostructures, so that we can provide guidance to differentiate between the topologically trivial and nontrivial cases.

Theoretical study of impurity-induced magnetism in FeSe

Experimental evidence suggests that FeSe is close to a magnetic instability, and recent scanning tunneling microscopy (STM) measurements on FeSe multilayer films have revealed stripe order locally pinned near defect sites. Motivated by these findings, we perform a theoretical study of locally induced magnetic order near nonmagnetic impurities in a model relevant for FeSe. We find that relatively weak repulsive impurities indeed are capable of generating short-range magnetism, and explain the driving mechanism for the local order by resonant eg-orbital states. In addition, we investigate the importance of orbital-selective self-energy effects relevant for Hund's metals, and show how the structure of the induced magnetization cloud gets modified by orbital selectivity. Finally, we make concrete connection to STM measurements of iron-based superconductors by symmetry arguments of the induced magnetic order, and the basic properties of the Fe Wannier functions relevant for tunneling spectroscopy.

Induced p-Wave Pairing in Bose-Fermi Mixtures.

Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of p-wave pairing between spin polarized fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency and momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical temperature. Focusing on experimentally relevant systems, we perform a systematic analysis varying the boson-boson and boson-fermion interaction strength as well as their masses, and identify the most suitable system for realizing a p-wave superfluid. Our results show that such a superfluid indeed is experimentally within reach using light bosons mixed with heavy fermions.