Bare Dispersion Research Articles

Marginal Fermi liquid behavior at the onset of 2kF density wave order in two-dimensional metals with flat hot spots

We analyze quantum fluctuation effects at the onset of incommensurate 2kF charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to |kt|α with α>2. We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

We study the thermodynamic properties of dimerized spin-gapped quantum magnets with and without exchange anisotropy (EA) and Dzyaloshinsky and Moriya (DM) anisotropies within the mean-field approximation (MFA). For this purpose we obtain the thermodynamic potential Ω of a triplon gas taking into account the strength of DM interaction up to second order. The minimization of Ω with respect to self-energies Σn and Σan yields the equation for X1,2=Σn±Σan−μ, which define the dispersion of quasiparticles Ek=ϵk+X1ϵk+X2 where ϵk is the bare dispersion of triplons. The minimization of Ω with respect to the magnitude ρ0 and the phase Θ of triplon condensate leads to coupled equations for ρ0 and Θ. We discuss the restrictions on ρ0 and Θ imposed by these equations for systems with and without anisotropy. The requirement of dynamical stability conditions (X1>0,X2>0) in equilibrium, as well as the Hugenholtz–Pines theorem, particularly for isotropic Bose condensate, impose certain conditions to the physical solutions of these equations. It is shown that the phase angle of a purely homogenous Bose–Einstein condensate (BEC) without any anisotropy may only take values Θ=πn (n=0, ±1,±2...) while that of BEC with even a tiny DM interaction results in Θ=π∕2+2πn. In contrast to the widely used Hartree–Fock–Popov approximation, which allows arbitrary phase angle, our approach predicts that the phase angle may have only discrete values, while the phase of the wave function of the whole system remains arbitrary as expected. The consequences of this phase locking for interference of two Bose condensates and to their possible Josephson junction is studied. In such quantum magnets the emergence of a triplon condensate leads to a finite staggered magnetization M⊥, whose direction in the xy-plane is related to the condensate phase Θ. We also discuss the possible Kibble–Zurek mechanism in dimerized magnets and its influence on M⊥.

Seeking to Develop Global SYK-Ness

Inspired by the recent interest in the Sachdev–Ye–Kitaev (SYK) model, we study a class of multi-flavored one- and two-band fermion systems with no bare dispersion. In contrast to the previous work on the SYK model that would routinely assume spatial locality, thus unequivocally arriving at the so-called ‘locally-critical’ scenario, we seek to attain a spatially-dispersing ‘globally-SYK’ behavior. To that end, a variety of the Lorentz-(non)invariant space-and/or-time dependent algebraically decaying interaction functions is considered and some of the thermodynamic and transport properties of such systems are discussed.

TRILEX and GW +EDMFT approach to d -wave superconductivity in the Hubbard model

We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a $d$-wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture $d$-wave pairing using only a single-site effective impurity model. We also systematically explore the dependence of the superconducting temperature on the bare dispersion at weak coupling, which shows a clear link between strong antiferromagnetic (AF) correlations and the onset of superconductivity. We identify a combination of hopping amplitudes particularly favorable to superconductivity at intermediate doping. Finally, we study within $GW$+EDMFT the low-temperature $d$-wave superconducting phase at strong coupling in a region of parameter space with reduced AF fluctuations.

Quantifying Many-Body Effects by High-Resolution Fourier Transform Scanning Tunneling Spectroscopy

High-resolution Fourier transform scanning tunneling spectroscopy (FT-STS) is used to study many-body effects on the surface state of Ag(111). Our results reveal a kink in the otherwise parabolic band dispersion of the surface electrons and an increase in the quasiparticle lifetime near the Fermi energy Ef. The experimental data are accurately modeled with the T-matrix formalism for scattering from a single impurity, assuming that the surface electrons are dressed by the electron-electron and electron-phonon interactions. We confirm the latter as the interaction responsible for the deviations from bare dispersion. We further show how FT-STS can be used to simultaneously extract real and imaginary parts of the self-energy for both occupied and unoccupied states with a momentum and energy resolution competitive with angle-resolved photoemission spectroscopy. From our quantitative analysis of the data we extract a Debye energy of ℏΩD=14±1 meV and an electron-phonon coupling strength of λ=0.13±0.02, consistent with previous results. This proof-of-principle measurement advances FT-STS as a method for probing many body effects, which give rise to a rich array of material properties.

Optical phonons and the soft mode in 2H-NbSe2

We present an investigation of the lattice dynamics of the charge density wave (CDW) compound 2$H$-NbSe${}_{2}$. We analyze the precise nature of the wave vector-dependent electron-phonon coupling (EPC) and derive the bare dispersion of the CDW soft phonon mode using inelastic x-ray scattering combined with ab initio calculations. Experimentally, phonon modes along the \ensuremath{\Gamma}\ensuremath{-}$M$ line, i.e., q $=$ ($h$,0,0), with 0 \ensuremath{\le} $h$ \ensuremath{\le} 0.5 and the same longitudinal symmetry (${\ensuremath{\Sigma}}_{1}$) as the CDW soft mode, were investigated up to 32 meV. In agreement with our calculations, we observe significant EPC in the optic modes at $h$ \ensuremath{\le} 0.2. We analyze the EPC in the optic, as well as acoustic, mode and show that the q dependences stem from scattering processes between two bands at the Fermi surface that both have a Nb 4$d$ character. Finally, we demonstrate that the soft mode dispersion at $T$ $=$ 33 K (=${T}_{\mathrm{CDW}}$) can be well described on the basis of a strongly q-dependent EPC matrix element and an acousticlike bare phonon dispersion in agreement with observations near room temperature.

Dynamically induced Fermi arcs and pockets: A model for the pseudogap in underdoped cuprates

We investigate the effects of the dynamic bosonic fluctuations on the Fermi surface reconstruction in two dimensions as a model for the pseudogap in underdoped cuprates. At energies larger than the boson energy ωb, the dynamic nature of the fluctuations is not important and the quasi-particle dispersion exhibits the shadow feature like that induced by a static long range order. At lower energies, however, the shadow feature is pushed away by the finite ωb. The detailed low energy features are determined by the bare dispersion and the coupling of quasi-particles to the dynamic fluctuations. We present how these factors truncate the Fermi surface to produce the Fermi arcs or the Fermi pockets, or their coexistence. Our principal result is that the dynamic nature of the fluctuations, without invoking a yet-to-be-established translational symmetry breaking hidden order, can produce the Fermi arc or Fermi pocket centered away from the (π/2, π/2) towards the zone center. This is discussed in comparison with the experimental observations.

Dynamically induced Fermi arcs and Fermi pockets in two dimensions: A model for underdoped cuprates

We investigate the effects of the dynamic bosonic fluctuations on the Fermi surface reconstruction in two dimensions as a model for the underdoped cuprates. At energies larger than the boson energy $\omega_b$, the dynamic nature of the fluctuations is not important and the quasi-particle dispersion exhibits the shadow feature like that induced by a static long range order. At lower energies, however, the shadow feature is pushed away by the finite $\omega_b$. The detailed low energy features are determined by the bare dispersion and the coupling of quasi-particles to the dynamic fluctuations. We present how these factors reconstruct the Fermi surface to produce the Fermi arcs or the Fermi pockets, or their coexistence. Our principal result is that the dynamic nature of the fluctuations, without invoking a yet-to-be-established translational symmetry breaking hidden order, can produce the Fermi pocket centered away from the $(\pi/2,\pi/2)$ towards the zone center which may coexist with the Fermi arcs. This is discussed in comparison with the experimental observations.

Brueckner–Goldstone perturbation theory for the half-filled Hubbard model in infinitedimensions

We use Brueckner–Goldstone perturbation theory to calculate the ground-state energy ofthe half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbardinteraction. We obtain the momentum distribution as a functional derivative of theground-state energy with respect to the bare dispersion relation. The resultingexpressions agree with those from Rayleigh–Schrödinger perturbation theory. Ourresults for the momentum distribution and the quasi-particle weight agree verywell with those obtained earlier from Feynman–Dyson perturbation theory forthe single-particle self-energy. We give the correct fourth-order coefficient in theground-state energy which was not calculated accurately enough from Feynman–Dysontheory due to the insufficient accuracy of the data for the self-energy, and find agood agreement with recent estimates from quantum Monte Carlo calculations.