Particle-hole Channel Research Articles

Robust topological superconductivity in spin–orbit coupled systems at higher-order van Hove filling

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin–orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities (VHSs) and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle–particle and particle-hole channels associated with higher-order VHSs, we find that the chiral p±ip pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong spin–orbit coupling (SOC) and offers fresh insights into the exploration of topological superconductivity.

Improved effective vertices in the multiorbital two-particle self-consistent method from dynamical mean-field theory

In this paper, we present a multiorbital form of the two-particle self-consistent approach (TPSC) where the effective local and static irreducible interaction vertices are determined by means of the dynamical mean-field theory (DMFT). This approach replaces the approximate ansatz equations for the double-occupations $\ensuremath{\langle}{n}_{\ensuremath{\alpha},\ensuremath{\sigma}}^{}{n}_{\ensuremath{\beta},{\ensuremath{\sigma}}^{\ensuremath{'}}}^{}\ensuremath{\rangle}$ by sampling them directly for the same model using DMFT. Compared to the usual Hartree-Fock-like ansatz, this leads to more accurate local vertices in the weakly correlated regime and provides access to stronger correlated systems that were previously out of reach. This approach is extended by replacing the local component of the TPSC self-energy by the DMFT impurity self-energy, which results in an improved self-energy that incorporates strong local correlations but retains a nontrivial momentum dependence. We find that this combination of TPSC and DMFT provides a significant improvement over the multiorbital formulation of TPSC as it allows to determine the components of the spin vertex without artificial symmetry assumptions and opens the possibility to include the transversal particle-hole channel. The new approach is also able to remove unphysical divergences in the charge vertices in TPSC. We find a general trend that lower temperatures can be accessed in the calculation. Benchmarking single-particle quantities, such as the local spectral function with other many-body methods, we find significant improvement in the more strongly correlated regime.

Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework (II): The program DIRQFAM v2.0.0

We describe the new version 2.0.0 of the code DIRQFAM that calculates the multipole response of even-even axially symmetric deformed nuclei using the framework of relativistic self-consistent mean-field models. The response is calculated by implementing the finite amplitude method for relativistic quasiparticle random phase approximation. In the new version, we have implemented the following features: (i) meson-exchange interactions, (ii) low-rank method for calculating induced densities and currents, (iii) generalized minimal residual method (GMRES), (iv) evaluation of the nucleon localization function, (v) extraction of the QRPA transition matrix elements and eigenfrequencies, (vi) evaluation of the H11 part of the induced Hamiltonian, (vii) multipole excitation operators up to J≤5 are now included. Program summaryProgram title:DIRQFAM v2.0.0CPC Library link to program files:https://doi.org/10.17632/6gv8nxg4ns.2Licensing provisions: GPLv3Programming language: Fortran 90.External routines/libraries: BLAS/LAPACK, version 3.1. or higher.Journal reference of previous version: A. Bjelčić, T. Nikšić, Comp. Phys. Comm. 253, 107184 (2020).Does the new version supersede the previous version?: YesNature of problem: Multipole response of deformed even-even open-shell nuclei can be calculated using the quasiparticle finite amplitude method (QFAM), based on the relativistic self-consistent mean-field models. The particle-hole channel is described by a zero-range relativistic effective interaction or interaction based on meson exchange, while the particle-particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force. The method can be applied to perform systematic studies of collective modes even in heavy deformed nuclei.Solution method: The current implementation computes the multipole response by solving the QFAM equations in a self-consistent iteration scheme. At each iteration the QFAM solutions are updated using the GMRES method. The QFAM amplitudes are expanded in the simplex-y harmonic oscillator basis.Summary of revisions:1.meson-exchange interaction are included in the code;2.calculation of the nucleon localization function;3.extraction of the QRPA transition matrix elements and eigenfrequencies;4.evaluation of the H11 part of the induced Hamiltonian;5.multipoles excitation operators up to J≤5 are included;6.low-rank method for calculating induced densities and currents;7.generalized minimal residual method;8.dynamic memory allocation;9.reduced memory requirements;Additional comments including restrictions and unusual features: Open-shell even-even nuclei with parity conserved axially symmetric ground states are considered. An electric multipole operator with J≤5 is used to calculate the response function.

Odd frequency pairing in a quantum critical metal

We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(\Omega_n)\sim 1/|\Omega_n|^\gamma$ (the $\gamma$-model). This interaction gives rise to a non-Fermi liquid in the normal state and is attractive for pairing. The two trends compete with each other. We search for odd-frequency solutions for the pairing gap $\Delta (\omega_m)= -\Delta(\omega_m)$. We show that for $\gamma <1$, odd-frequency superconductivity looses the competition with a non-Fermi liquid and does not develop. We show that the pairing does develop in the extended model in which interaction in the pairing channel is larger than the one in the particle-hole channel. For $\gamma >1$, we argue that the original model is at the boundary towards odd-frequency pairing and analyze in detail how superconductivity is triggered by a small external perturbation. In addition, we show that for $\gamma >2$, the system gets frozen at the critical point towards pairing in a finite range in the parameter space. This give rise to highly unconventional phase diagrams with flat regions.

Influence of impurities on the electronic structure in cuprate superconductors

The impurity is inherently manifest in cuprate superconductors, as cation substitution or intercalation is necessary for the introduction of charge carriers, and its influence on the electronic state is at the heart of a great debate in physics. Here based on the microscopic octet scattering model, the influence of the impurity scattering on the electronic structure of cuprate superconductors is investigated in terms of the self-consistent $T$-matrix approach. The impurity scattering self-energy is evaluated firstly in the Fermi-arc-tip approximation of the quasiparticle excitations and scattering processes, and the obtained results show that the decisive role played by the impurity scattering self-energy in the particle-hole channel is the further renormalization of the quasiparticle band structure with a reduced quasiparticle lifetime, while the impurity scattering self-energy in the particle-particle channel induces a strong deviation from the $d$-wave behavior of the superconducting gap, leading to the existence of a finite gap over the entire electron Fermi surface. Moreover, these impurity scattering self-energies are employed to study the exotic features of the line shape in the quasiparticle excitation spectrum and the autocorrelation of the quasiparticle excitation spectra, and the obtained results are then compared with the corresponding experimental data. The theory therefore also indicates that the unconventional features of the electronic structure in cuprate superconductors is generated by both the strong electron correlation and impurity scattering.

Exciton and fermion-pair condensation at non-zero temperature

A thermodynamic study of a many-particle two-level system with the SU(2) ⊗ SU(2)-symmetry interaction in the particle–particle and particle–hole channels is carried out. Using the symmetry of the system, its free energy and phase diagram are calculated. It is demonstrated that the superconducting (particle–particle) and excitonic (particle–hole) condensates are both formed in the considered system which undergoes two phase transitions. The calculated phase diagram represents qualitatively the phase diagram typical for materials with the high-temperature superconducting properties, including the existence of two phase transitions, the first and second order phase transitions, triple and tricritical points.

Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes

We uncover a novel two-particle Berry phase mechanism to realize exotic corner modes in second-order topological insulators (TIs) and topological superconductors (TSCs) with time-reversal symmetry. We show that the nontrivial pseudospin textures of edge states in two different types of two-dimensional TIs give rise to the novel two-particle geometric phases in the particle-hole and particle-particle channels, respectively, for which the edge mass domain walls or intrinsic $\pi$-junctions emerge across corners when an external magnetic field or $s$-wave superconductivity is considered, hosting Dirac or Majorana corner modes. Remarkably, with this mechanism we predict the Majorana Kramers pair of corner modes by directly coupling the edge of a type-II time-reversal invariant TI to a uniform $s$-wave SC, in sharp contrast to the previous proposals which rely on unconventional SC pairing or complex setting for fine-tuned SC $\pi$-junction. We find Au/GaAs(111) to be a realistic material candidate for realizing such Majorana Kramers pair of corner modes.

BAZI TEK ÇEKİRDEKLİ GERMANYUM İZOTOBU İÇİN DEFORME VE KÜRESEL ÇEKİRDEKLERİN LOG(FT) DEĞERLERİ

The log(ft) values of the allowed 𝛽± decay between odd-A spherical and deformed nuclei are studied for germanium isotopes in this paper. The Pyatov Method (PM) and the Schematic Model (SM)) are used to the GT strength distributions, including the schematic residual spin-isospin interaction between nucleons in the particle-hole and particle-particle channels. Particle-hole and particle-particle interaction parameters are calculated respectively with X_ph^GT= 5.2 A^(0.7 ) MeV and X_pp^GT= 0.58 A^(0.7 ) MeV. Deformed Woods-Saxon potential is used in calculations of single-particle energies and wave functions. The results are also compared with previous experiment values wherever available.

Charge radii, moments, and masses of mercury isotopes across the N=126 shell closure

Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source (VADLIS) with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the N=126 shell closure, the electromagnetic moments of Hg207, and more precise mass values of Hg206–208. The odd-even staggering (OES) of the mean square charge radii and the kink at N=126 are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of the results on the underlying single-particle structure. The observed features are defined predominantly in the particle-hole channel in CDFT, since both are present in the calculations without pairing. However, the magnitude of the kink is still affected by the occupation of the ν1i11/2 and ν2g9/2 orbitals with a dependence on the relative energies as well as pairing.5 MoreReceived 4 August 2021Accepted 20 October 2021DOI:https://doi.org/10.1103/PhysRevC.104.054322Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesNuclear structure & decaysRare & new isotopesSpectroscopic factors & electromagnetic momentsProperties190 ≤ A ≤ 219Electric momentMagnetic momentNuclear bindingTechniquesMass spectrometryNuclear density functional theoryPhotoionizationRadioactive beamsAccelerators & BeamsAtomic, Molecular & OpticalNuclear Physics

Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations

Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional correlated electron systems. Here we study the arguably simplest version of these $\pi$-tons based on the semi-analytical random phase approximation (RPA) ladder in the transversal particle-hole channel. The vertex corrections to the optical conductivity are calculated directly for real frequencies. We validate that the RPA qualitatively reproduces the {\pi}-ton vertex corrections to the Drude peak in the Hubbard model. Depending on the temperature we find vertex corrections to broaden or sharpen the Drude peak.

Delineating chiral separation effect in two-color dense QCD

We study the chiral separation effect (CSE) in two-color and two-flavor QCD to delineate quasiparticle pictures in dense matter from low to high temperatures. Both massless and massive quarks are discussed. We particularly focus on the high density domain where diquarks form a color-singlet condensate with the electric charge $1/3$. The condensate breaks the baryon number and $U(1{)}_{A}$ axial symmetry, and induces the electromagnetic Meissner effects. Within a quark quasiparticle picture, we compute the chiral separation conductivity at one-loop. We have checked that Nambu-Goldstone modes, which should appear in the improved vertices as required by the Ward-Takahashi identities, do not contribute to the chiral-separation conductivity due to their longitudinal natures. In the static limit, the destructive interferences in the particle-hole channel, as in the usual Meissner effects, suppress the conductivity (in the chiral limit, to $1/3$ of that of the normal phase). This locally breaks the universality of the CSE coefficients, provided quasiparticle pictures are valid in the bulk matter.

Beta decay logft values for zinc isotopes by using pn-QRPA

Allowed Fermi (F), Gamow-Teller (GT), and first forbidden (FF) transitions were simulated using Pyatov Method (PM) and Schematic Model (SM) for even-even neutron rich isotopes of Zinc. The Fermi beta-decay calculations were obtained by the pure the Pyatov Method without introducing effective values of coupling constants using the proton-neutron quasi-particle random phase approximation (pn-QRPA). The pn-QRPA was utilized in the particle-hole (ph) and particle-particle (pp) channels in the PM and SM for the GT transitions. For FF transitions, only the corresponding ph channel in the SM was considered in the calculations. We solved the secular equations of Fermi, Gamow-Teller, and first forbidden transitions for eigenvalues and eigenfunctions of corresponding Hamiltonians. A spherical shape was assigned for each Zn nuclei throughout all simulations. Compared to the experimental studies, in general, the calculated logft values of the allowed F and GT transitions of PM and SM simulations were found to be closer to the experimental values. Alongside logft values, simulated half-lives obtained in this work are also in excellent agreement with experimental counterparts for the FF excitations.

β-decay of N = 126 isotones for the r-process nucleosynthesis

The β-decay properties of nuclei with neutron number N = 126 is investigated in this paper. Two different versions of the proton-neutron quasi particle random phase (pn-QRPA) model were employed to compute β-decay rates and half-lives for the N = 126 isotones. The first set of calculation solves the pn-QRPA equations using the schematic model (SM) approach. The Woods-Saxon potential was employed as a mean-field basis. A spherical shape assigned for each waiting point nuclei throughout all simulations. Both allowed Gamow-Teller (GT) and first-forbidden (FF) transitions were considered in the particle-hole (ph) channel. The second set uses the pn-QRPA model in deformed Nilsson basis to calculate β-decay rates for allowed GT and unique first-forbidden (U1F) transitions under terrestrial and stellar conditions. Our results are in agreement with shell model findings that first-forbidden transitions lead to a considerable decrement in the calculated half-lives of the isotones. Inclusion of the first-forbidden contribution led to a decent agreement of our computed terrestrial β-decay half-lives with measured ones, much better than the previous calculations. The possible implication of the waiting point nuclei on r-process nucleosynthesis is discussed briefly.

Frequency-dependent functional renormalization group for interacting fermionic systems

We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency domain and reformulates them as a series of linear integral equations in the particle-particle, particle-hole and particle-hole exchange channels. We show that the linearity of the equations offers numerous computational advantages and leads to converged, stable solutions for a variety of Hamiltonians. As the expansion is in the coupling between channels, the truncations that are necessary to making the scheme computationally viable still lead to equations that treat contributions from all channels equally. As a first benchmark we apply the two-loop fRG equations to the single impurity Anderson model. We consider the sources of error within the fRG, the computational cost associated with each, and how the choice of regulator affects the flow of the fRG. We then use the optimal truncation scheme to study the Extended Hubbard Hamiltonian in one and two dimensions. We find that in many cases of interest the fRG flow converges to a stable vertex and self-energy from which we can extract the various correlation functions and susceptibilities of interest.

Investigation of the effective interactions for the Emery model by the constrained random-phase approximation and constrained functional renormalization group

The effective interaction of downfolded low-energy models for electrons in solids can be obtained by integrating out the high energy bands away from the target band near the Fermi level. Here we apply the constrained random-phase approximation (cRPA) and constrained functional renormalization group (cfRG), which can go beyond cRPA by including all one-loop diagrams, to calculate and compare the effective interactions of the three-band Emery model, which is often used to investigate cuprate high-temperature superconductors. At half-filling we find that the effective interaction increases as the charge transfer energy (${\mathrm{\ensuremath{\Delta}}}_{dp}$) increases and similar behavior is obtained as a function of the interatomic $2p\text{\ensuremath{-}}3d$ interaction (${U}_{dp}$). However, the effective interaction is more sensitive to ${\mathrm{\ensuremath{\Delta}}}_{dp}$ than ${U}_{dp}$. For most of the parameter sets, the effective static interaction is overscreened in cRPA compared to cfRG. The low-energy models at half-filling are solved within dynamical mean-field theory (DMFT). The results show that despite the different static interactions, the systems with cRPA and cfRG interaction exhibit a Mott transition at similar values of ${\mathrm{\ensuremath{\Delta}}}_{dp}$. We also investigate the effective interaction as a function of doping. The cfRG effective interaction decreases as the electron number increases and displays a trend opposite to that of cRPA. Antiscreening is observed for the hole-doped case. For all the cases studied, the near cancellation of the direct particle-hole channel is observed. This indicates that at least for the downfolding of the on-site interaction terms, methods beyond cRPA may be required.

Bipolaron formed through electron-hole excitation

We investigate the electronic properties and electron correlations of the bipolaron formed with the participation of electron-hole excitations in the presence of Yukawa-type coupling (between nonrelativistic fermions) in three spatial dimension. The electron-hole excitation, which is necessary to the formation of bipolaron, leads to imaginary particle-hole channel order parameter, and provide finite boson field mass to the single-polaron dispersion in a broken-symmetry phase. We found that the bipolaron exhibits fermi-liquid features as long as the long-range strong interaction is suppressed, and it behave differently compared to the single-polaron. The bosonic momentum determines the mass of boson field propagator and the gap function, and it also related to the self-energies and the single-particle Green’s functions. The Thouless criterion is also used during the calculation of gap equation at critical temperature (which becomes lower in weak-coupling regime), which corresponds to the pole (instability) of the pair propagator in zero center-of-mass freamwork. The mean field term and the bosonic fluctuation-induced contribution to free energy in Aslamazov-Larkin-type bipolaron diagram are also studied.

Topological properties of Josephson current between two s- and p-wave superconducting nanowires with Majorana fermions

Josephson current between two one-dimensional nanowires with proximity induced either s-wave or p-wave pairing and separated by a narrow dielectric barrier is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal Zeeman magnetic fields. We show that Andreev retro-tunneling is realized by means of two channels. The main contribution to the Josephson current in junction of s- or p-wave superconductors is shown to give Andreev scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters’ phase differences φ and oscillates with fractional 4π period. Nevertheless Andreev bound state energy in second anomalous particle-hole channel, corresponding to the reflection of an incident electron-like quasiparticle to a hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field, and oscillates with 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. The magnetic fields destroy also the particle-hole symmetry of the mid-gap states around Fermi level.

Efficient one-loop-renormalized vertex expansions with connected determinant diagrammatic Monte Carlo

We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scaling of the algorithm as a function of perturbation order leads to a polynomial scaling of the approximation error with computational time for a convergent series. To assess the performance of our approach, we apply it to the non-perturbative regime of the square-lattice fermionic Hubbard model away from half-filling and report, as compared to the bare interaction expansion algorithm, significant improvements of the Monte Carlo variance as well as the convergence properties of the resulting perturbative series.

Interplay between superconductivity and non-Fermi liquid behavior at a quantum critical point in a metal. III. The γ model and its phase diagram across γ=1

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction $V(\Omega_m) \propto 1/|\Omega_m|^\gamma$ (the $\gamma$-model). We analyze both the original model and its extension, in which we introduce an extra parameter $N$ to account for non-equal interactions in the particle-hole and particle-particle channel. In two previous papers(arXiv:2004.13220 and arXiv:2006.02968), we considered the case $0 < \gamma <1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions, $\Delta_n (\omega_m)$, all with the same spatial symmetry, and (ii) each $\Delta_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper, we analyze how the system behavior changes between $\gamma <1$ and $\gamma >1$, both at $T=0$ and a finite $T$. The limit $\gamma \to 1$ is singular due to infra-red divergence of $\int d \omega_m V(\Omega_m)$, and the system behavior is highly sensitive to how this limit is taken. We show that for $N =1$, the divergencies in the gap equation cancel out, and $\Delta_n (\omega_m)$ gradually evolve through $\gamma=1$ both at $T=0$ and a finite $T$. For $N \neq 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $\gamma >1$. Namely, the form of $\Delta_n (\omega_m)$ changes qualitatively, and the spectrum of condensation energies, $E_{c,n}$ becomes continuous at $T=0$. We introduce different extension of the model, which is free from singularities for $\gamma >1$.

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading inter-valley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong coupling approaches, indicating that this order is robust. The other is a mixed state with $120^\circ$ complex spin order and orthogonal complex charge order. In addition, we find a weaker, but still attractive interaction in nematic channels, and discuss the type of a nematic order.