Generalized Random-phase Approximation Research Articles

Excitonic collective modes in Weyl semimetals

Weyl semi-metals are three dimensional generalizations of graphene with point-like Fermi surfaces. Their linear electronic dispersion leads to a window in the particle-hole excitation spectrum which allows for undamped propagation of collective excitations. We argue that interactions in Weyl semi-metals generically lead to well-defined exciton modes. However, using a minimal model for interactions, we show that the exciton binding energy is exponentially small for weak interactions. This is due to effective two-dimensional character in the space of particle-hole pairs that are available for bound state formation. This is ultimately a consequence of linear electronic dispersion in three dimensions. Nevertheless, intermediate interaction strengths can lead to sharp spin-carrying excitonic resonances. We demonstrate this in a model Weyl semi-metal with broken time-reversal symmetry and Hubbard interactions, using GRPA (generalized random phase approximation) analysis. Excitons in Weyl semi-metals have evoked interest as their condensation could lead to an axionic charge density wave order. However, we find that the leading instability corresponds to intra-valley spin density wave order which shifts the Weyl points without opening a gap. Our results suggest interesting directions for experimental studies of three dimensional Dirac systems.

Plasmon-phonon coupling in a valley-spin-polarized two-dimensional electron system: A theoretical study on monolayer silicene

We study the hybrid excitations due to the coupling between surface optical phonons of a polar insulator substrate and plasmons in the valley-spin-polarized metal phase of silicene under an exchange field. We perform the calculations within the generalized random-phase approximation where the plasmon-phonon coupling is taken into account by the long-range Fr$\ddot{\mathrm{o}}$hlich interaction. Our investigation on two hybridized plasmon branches in different spin and valley subbands shows distinct behavior compared to the uncoupled case. Interestingly, in one valley, it is found that while the high energy hybrid branch is totally damped in the spin-up state, it can be well-defined in the the spin-down state. Moreover, we show that the electron-phonon coupling is stronger in both spin-down subbands, regardless of valley index, due to their higher electron densities. In addition, we study the effects of electron-phonon coupling on the quasiparticle scattering rate of four distinct spin-valley locked subbands. The results of our calculations predict a general enhancement in the scattering rate for all subbands, and a jump in the case of spin-down states. This sharp increase associated to the damping of hybrid plasmon modes is almost absent in the uncoupled case. The results suggest an effective way for manipulating collective modes of valley-spin-polarized silicene which may become useful in future valleytronic and spintronic applications.

Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC crossover region

We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla \theta({\bf r})$ (where $\theta({\bf r})$ is the phase of the condensate) in the BCS regime, both leading to dynamical instabilities of an exciton-BEC. Our result suggests that substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.

Many electron correlations in stage-1 graphene intercalation compounds

Many electron correlations in stage-1 graphene intercalation compounds are studied in generalized random-phase approximation. With this approximation, we are able to study short-range exchange and correlation effects in graphene intercalation compounds. These exchange correlations lead to BCS superconducting states in which one electron correlates with another via its correlation hole to form a stable pair of electrons known as Cooper pair. Cooper pair energies are calculated as the excitations in S(q ,ω) following a method similar to exciton energy calculations. Short-range effects governing local field correction G(q ,ω) are studied for all wave vectors and frequencies. We have found a reasonable agreement between our results and the earlier reported theoretical results.

Rashba Spin–Orbit-Coupled Atomic Fermi Gases in a Two-Dimensional Optical Lattice

The collective-mode excitation energy of a population-imbalanced spin–orbit-coupled atomic Fermi gas loaded in a two-dimensional optical lattice at zero temperature is calculated within the Gaussian approximation, and from the Bethe–Salpeter equation in the generalized random-phase approximation assuming the existence of a Sarma superfluid state. It is found that the Gaussian approximation overestimates the speed of sound of the Goldstone mode. More interestingly, the Gaussian approximation fails to reproduce the roton-like structure of the collective-mode dispersion which appears after the linear part of the dispersion in the Bethe–Salpeter approach. We investigate the speed of sound of a balanced spin–orbit-coupled atomic Fermi gas near the boundary of the topological phase transition driven by an out-of-plane Zeeman field. It is shown that the minimum of the speed of sound is located at the topological phase transition boundary, and this fact can be used to confirm the existence of a topological phase transition.

Collective Excitation and Stability of Flowing Gapless Fermi Superfluids

We study the collective excitation and stability of superfluid Fermi gases flowing with a constant velocity in three-dimensional free space. In particular, we investigate a possible gapless superfluid state induced by the superflow using the mean-field theory and the generalized random-phase approximation (GRPA). For weak attractive interactions, we find that the mean-field superfluid order parameter can take a nonzero value even after the superflow velocity exceeds the threshold for the onset of Bogoliubov quasiparticle excitations. Since the Cooper pairs are only partially broken by the quasiparticle excitations, a gapless superfluid state can be formed over a certain range of superflow velocity above the pair-breaking onset. In addition to the usual quasiparticle-pair continuum and the Anderson-Bogoliubov collective mode, the GRPA excitation spectrum of the gapless superfluid state has a quasiparticle-quasihole continuum and a second collective mode. We find that the long-wavelength excitations of the second collective mode eventually cause dynamical instability of the system when the superflow velocity increases. However, the gapless superfluid state still remains stable in a narrow but finite range of superflow velocity.

High-energy damping by particle-hole excitations in the spin-wave spectrum of iron-based superconductors

Using a degenerate double-exchange model, we investigate the spin excitation spectra of iron pnictides. The model consists of local spin moments on each Fe site, as well as itinerant electrons from the degenerate $d_{xz}$ and $d_{yz}$ orbitals. The local moments interact with each other through antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg interactions, and they couple to the itinerant electrons through a ferromagnetic Hund coupling. We employ the fermionic spinon representation for the local moments and perform a generalized random-phase approximation calculation on both spinons and itinerant electrons. We find that in the $\left(\pi,0\right)$ magnetically-ordered state, the spin-wave excitation at $\left(\pi,\pi\right)$ is pushed to a higher energy due to the presence of itinerant electrons, which is consistent with a previous study using the Holstein-Primakoff transformation. In the paramagnetic state, the particle-hole continuum keeps the collective spin excitation near $\left(\pi,\pi\right)$ at a higher energy even without any $C_{4}$ symmetry breaking. The implications for recent high temperature neutron scattering measurements will be discussed.

Collective excitations of a trapped Fermi gas at finite temperature

We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov--de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid--superfluid phase-transition temperature: Higgs mode--like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.

Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body $T$-matrix approximation. We assess these approximations with respect to the transition temperature ${T}_{\mathrm{c}}$, the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long-standing problem in cold atom physics, our results would be useful for this important challenge.

Ba 5s photoionization in the region of the second Cooper minimum

We investigate the 5s angular distribution parameter and partial photoionization cross section of atomic Ba in the region of the second Cooper minimum covering a photon energy region from 120 to 260 eV. We observe a strong drop in the Ba 5s β value from 2.0, reaching a minimum of 1.57 ± 0.07 at a photon energy of 150 eV. The β value then slowly rises back towards its nominal value of 2.0 at photon energies beyond the minimum. Our measured 5s partial cross section also shows a pronounced dip around 170 eV due to interchannel coupling with the Ba 4d photoelectrons. After combining our measurements with previous experimental values at lower photon energies, we obtain a consistent data set spanning the photon energy range prior to the onset of the partial cross section maximum and through the cross section minimum. We also calculate the 5s partial cross section under several different levels of approximation. We find that the generalized random-phase approximation with exchange calculation models the shape and position of the combined experimental cross section data set rather well after incorporating experimental ionization energies and a shift in the photon energy scale.

Unified description of collective modes in superconductors and semiconductors with an exciton condensed phase

It is shown that the Bethe-Salpeter approach, the Bardeen, Cooper, and Schrieffer (BCS) based vertex method, and a generalized random-phase approximation (GRPA) to the many-electron problem in the presence of a condensed quantum phase yield the same theoretical excitation spectrum ω(Q) to collective modes. This spectrum reveals a secondary peak in optical absorption in semiconductors that can be understood as signaling the existence of an excitonic Bose-Einstein condensate (BEC). The analysis shows as well that there is an additional, non-trivial linearly-dispersive moving Cooper-pair solution for superconductors in both weak and strong coupling.

Instability of superfluid Fermi gases induced by a rotonlike density mode in optical lattices

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS--Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green's function formalism developed by C\^ot\'e and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair-breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.

Collective modes and superflow instabilities of strongly correlated Fermi superfluids

We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated s-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin-wave analysis of the appropriate strong-coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms--depairing, Landau instabilities or dynamical instabilities--depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii)more » an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.« less

Non-perturbative treatment of the attractive Hubbard model

We have used a Hubbard–Stratonovich transformation to convert the quartic Hubbard problem of interacting electrons into more tractable quadratic problem of non-interacting electrons coupled to a Bose field. The Dyson and the Bethe-Salpeter (BS) equations for the corresponding Green functions are derived by applying a functional derivative technique combined with the method of Legendre transform. This approach allows us to obtain exact relations between single- and two-particle quantities. We have compared the self-consistent relationship between mass operator and two-particle Green function with the similar relationship in the two-particle self-consistent (TPSC) approximation, and came up with the conclusion that the accuracy of the TPSC approximation is questionable because: (i) if equal-time pair-correlation function is set to one, the mass operator in TPSC approximation differs significantly from the exact mass operator; and (ii) the TPSC approximation does not take into account the Hartree part of the mass operator. The latter results in missing exchange interaction in the BS equation. A generalized random-phase approximation is applied to demonstrate the important role of the exchange interaction when BS equation is used to study collective excitation spectrum of the attractive Hubbard model.

Probing the thermal atoms of a Bose gas through Raman transition

We explore the many body physics of a Bose condensed atom gas at finite temperature through the Raman transition between two hyperfine levels. Unlike the Bragg scattering where the phonon-like nature of the collective excitations has been observed, a different branch of thermal atom excitation is found theoretically in the Raman scattering. This excitation is predicted in the generalized random phase approximation (GRPA) and has a gapped and parabolic dispersion relation. The gap energy results from the exchange interaction and is released during the Raman transition. The scattering rate is determined versus the transition frequency $\omega$ and the transferred momentum $\vc{q}$ and shows the corresponding resonance around this gap. Nevertheless, the Raman scattering process is attenuated by the superfluid part of the gas. The macroscopic wave function of the condensate deforms its shape in order to screen locally the external potential displayed by the Raman light beams. This screening is total for a condensed atom transition in order to prevent the condensate from incoherent scattering. The experimental observation of this result would explain some of the reasons why a superfluid condensate moves coherently without any friction with its surrounding.

Manifestation of a gap due to the exchange energy in a spinor condensate

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between the results obtained in the Bogoliubov–Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We verify that, contrary to the BPA, the GRPA preserves the S U ( 2 ) symmetry and the f -sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.

Dynamical matrix of two-dimensional electron crystals

In a quantizing magnetic field, the two-dimensional electron gas has a rich phase diagram with broken translational symmetry phases such as Wigner, bubble, and stripe crystals. In this paper, we derive a method to obtain the dynamical matrix of these crystals from a calculation of the density response function performed in the generalized random-phase approximation (GRPA). We discuss the validity of our method by comparing the dynamical matrix calculated from the GRPA with that obtained from standard elasticity theory with the elastic coefficients obtained from a calculation of the deformation energy of the crystal.

Collective modes ofCP3skyrmion crystals in quantum Hall ferromagnets

The two-dimensional electron gas (2DEG) in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor $\ensuremath{\nu}=1$ even in the absence of tunneling between the layers. This system, which can be described as a quantum Hall pseudospin ferromagnet, has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor $\ensuremath{\nu}=1$, a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling $({\ensuremath{\Delta}}_{SAS})$, Zeeman coupling $({\ensuremath{\Delta}}_{Z})$, or electrical bias $({\ensuremath{\Delta}}_{b})$, these textured crystal states can involve spin, pseudospin, or both intertwined. This last case is a ``$C{P}^{3}$ skyrmion crystal.'' In this paper, we present a comprehensive numerical study of the collective excitations of these textured crystals using the generalized random-phase approximation. For the pure spin case, at finite Zeeman coupling the state is a skyrmion crystal with a gapless phonon mode and a separate goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent skyrmions break up, and the resulting state is a meron crystal with four gapless modes. In contrast, a pure pseudospin-skyrme crystal at finite tunneling has only the phonon mode. For ${\ensuremath{\Delta}}_{SAS}\ensuremath{\rightarrow}0$, the state evolves into a meron crystal and supports an extra gapless [U(1)] mode in addition to the phonon. For a $C{P}^{3}$ skyrmion crystal, we find a U(1) gapless mode in the presence of nonvanishing symmetry-breaking fields ${\ensuremath{\Delta}}_{SAS}$, ${\ensuremath{\Delta}}_{Z}$, and ${\ensuremath{\Delta}}_{b}$. In addition, a second mode with a very small gap is present in the spectrum. We present dispersion relations for the different low-energy modes of these various crystals as well as their physical interpretations.

Kinetic theory and dynamic structure factor of a condensate in the random phase approximation

We present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature \cite{condenson}. In this approach, the condensate influences the binary collisional process between the two normal atoms, in the sense that their interaction force results from the mediation of a Bogoliubov collective excitation traveling throughout the condensate. Furthermore, as long as the Bose gas is stable, no collision happens between condensed and normal atoms. In this paper, we show how the kinetic theory in the GRPA allows to calculate the dynamic structure factor at finite temperature and when the normal and superfluid are in a relative motion. The obtained spectrum for this factor provides a prediction which, compared to the experimental results, allows to validate the GRPA. PACS numbers:03.75.Hh, 03.75.Kk, 05.30.-d

Intra-Landau-level polarization effect for a striped Hall gas

We calculate the polarization function including only intra-Landau level correlation effects of striped Hall gas. Using the polarization function, the dielectric function, the dispersion of the plasmon and the correlation energy are computed in a random phase approximation (RPA) and generalized random phase approximation (GRPA). The plasmon becomes anisotropic and gapless owing to the anisotropy of the striped Hall gas and two dimensionality of the quantum Hall system. The plasmon approximately agrees with the phonon derived before by the single mode approximation. The (G)RPA correlation energy is compared with other numerical calculations.