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1.
We study the interactions among phonons and the phonon lifetime in a pair‐condensed Fermi gas in the BEC‐BCS crossover in the collisionless regime. To compute the phonon‐phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC‐BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev‐Landau process 2 phonons ? 1 phonon while, when the concavity is downwards, it is the Landau‐Khalatnikov process 2 phonons ? 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF 19 , 637 (1949)] for the 2?2 processes in the downward concavity case. In the upward concavity case, for the Beliaev 1? 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number q including the first correction proportional to q 7 to the q 5 hydrodynamic prediction, which was never done before in a systematic way. 相似文献
2.
We extend the well-known Cooper’s problem beyond one pair and study how this dilute limit is connected to the many-pair Bardeen-Cooper-Schrieffer
(BCS) condensate. We find that, all over from the dilute to the dense regime of pairs, Pauli blocking induces the same “moth-eaten
effect” as the one existing for composite boson excitons. This effect makes the average pair binding energy decrease linearly
with pair number, bringing it, in the standard BCS configuration, to half the single-pair value. This proves that, at odds
with popular understanding, the BCS gap is far larger than the broken pair energy. The increase comes from Pauli blocking
between broken and unbroken pairs. Possible link between our result and the crossover between the Bose-Einstein condensate
and BCS condensate is also discussed. 相似文献
3.
Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of . In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically. 相似文献
4.
我们利用解析和数值的方法,研究从Bardeen-Cooper-Schrieffer(BCS)超流到玻色-爱因斯坦凝聚(BEC)渡越的过程里超流费米气体中两维(2D)孤子的形成和演化.基于超流流体力学方程,在准二维和长波近似下,推导描述弱非线性激发带正色散项的Kadomtsev-Petviashvili方程;给出整个BCS-BEC渡越的2D孤子解,以及数值求解孤子在囚禁势中的演化.数值结果显示由于Snake(横向)不稳定性,大振幅的暗孤子会衰变为大量涡旋-反涡旋对,并且这个不稳定性在不同超流区域不同. 相似文献
5.
The energy bands and the global density of states are computed for
superconductor / normal-metal superlattices in the clean limit.
Dispersion relations are derived for the general case of insulating
interfaces, including the mismatch of Fermi velocities and effective
band masses. We focus on the influence of finite interface
transparency and compare our results with those for transparent
superlattices and trilayers. Analogously to the rapid
variation on the atomic scale of the energy dispersion with
layer thicknesses in transparent superlattices, we find strong
oscillations of the almost flat energy bands (transmission
resonances) in the case of finite transparency. In small-period
transparent superlattices the BCS coherence peak disappears and a
similar subgap peak is formed due to the Andreev process. With
decreasing interface transparency the characteristic double peak
structure in the global density of states develops towards a gapless
BCS-like result in the tunnel limit. This effect can be
used as a reliable STM probe for interface transparency. 相似文献
6.
利用扩展的 Brueckner- Hartree- Fock理论与推广的 BCS方法研究了自能的色散效应和基态关联对中子物质中超流性和能隙的影响 .研究结果表明 ,自能的色散效应使中子物质中能隙减小;考虑基态关联后 ,超流性将进一步减弱. The effects of the dispersion and ground state correlation of the single particle self-energy on neutron matter superfluidity have been investigated in the framework of the Extended Brueckner-Hartree-Fock and the generalized BCS approaches. A sizable reduction of the energy gap is found due to the energy dependence of the self-energy. And the inclusion of the ground state correlations in the self-energy suppresses further the neutron matter superfluidity. 相似文献
7.
We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-de Gennes (BdG) equations for the density of states rho(E) with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior rho(E) approximately |E|(alpha) with nonuniversal alpha over an energy scale comparable to the single-impurity resonance energy Omega(0). We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution. 相似文献
8.
Zhang W Liu G Meng J Zhao L Liu H Dong X Lu W Wen JS Xu ZJ Gu GD Sasagawa T Wang G Zhu Y Zhang H Zhou Y Wang X Zhao Z Chen C Xu Z Zhou XJ 《Physical review letters》2008,101(1):017002
Laser-based angle-resolved photoemission spectroscopy measurements have been carried out on the high energy electron dynamics in Bi2Sr2CaCu2O8 high temperature superconductor. Our superhigh resolution data, momentum-dependent measurements, and complete analysis provide important information to judge the nature of the high energy dispersion and kink. Our results rule out the possibility that the high energy dispersion from the momentum distribution curve (MDC) may represent the true bare band as believed in previous studies. We also rule out the possibility that the high energy kink represents electron coupling with some high energy modes as proposed before. Through detailed MDC and energy distribution curve analyses, we propose that the high energy MDC dispersion may not represent intrinsic band structure. 相似文献
9.
We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller (“moth-eaten effect”). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizable fraction of the number of states available for pairing. As a result, in BEC–BCS crossover of 3D systems, the condensation energy per pair first increases and then decreases with pair number while in 2D, it always is controlled by the “moth-eaten effect” and thus simply decreases. 相似文献
10.
The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on Cs2CuCl4, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems and remains similarly accurate in the two-dimensional model corresponding to Cs2CuCl4, thus representing a good ansatz for describing spin fractionalization in two dimensions. 相似文献
11.
The effect of hybridization of conduction electrons and f-level on superconductivity (SC) and antiferromagnetism (AFM) in
the coexistent phase of rare-earth nickel borocarbide superconductors (RNi2B2C) is reported. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the
single-particle Green functions. It is assumed that superconductivity arises due to BCS pairing mechanism in the presence
of antiferromagnetism in nickel lattices of Ni2B2 plane. The expressions for superconducting and antiferromagnetic order parameters are derived using double time electron
Green functions. The quasiparticle energy bands are plotted and the nature of band dispersion of the quasiparticles is studied. 相似文献
12.
The equation of state (EOS) of a Fermi superfluid is investigated in the BCS-BEC crossover at zero temperature. We discuss the EOS based on Monte Carlo (MC) data and asymptotic expansions and the EOS derived from the extended BCS (EBCS) mean-field theory. Then we introduce a time-dependent density functional, based on the bulk EOS and Landau’s superfluid hydrodynamics with a von Weizsäcker-type correction, to study the free expansion of the Fermi superfluid. We calculate the aspect ratio and the released energy of the expanding Fermi cloud showing that MC EOS and EBCS EOS are both compatible with the available experimental data of 6Li atoms. We find that the released energy satisfies and approximate analytical formula that is quite accurate in the BEC regime. For an anisotropic droplet, our numerical simulations show an initially faster reversal of anisotropy in the BCS regime, later suppressed by the BEC fluid. 相似文献
13.
J.-P. Gallinar 《Solid State Communications》1975,17(4):493-495
We calculate for an almost half-filled tight-binding band, the mean field ground state energy differences between the charge-density-wave (CDW) and BCS paired states for a truncated model Hamiltonian with zero-range instantaneous electron-electron interactions. The CDW pairing is found to be always unstable vis-à-vis BCS for a static lattice distortion of wave vector Q = (2kF, π, π). 相似文献
14.
In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied two-component Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the cluster-integrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions. 相似文献
15.
We describe a new formulation of the functional renormalization group (RG) for
interacting fermions within a Wilsonian momentum-shell approach. We show that
the Luttinger-Ward functional is invariant under the RG transformation, and
derive the infinite hierarchy of flow equations satisfied by
the two-particle-irreducible (2PI) vertices. In the one-loop
approximation, this hierarchy reduces to two equations that determine
the self-energy and the 2PI two-particle vertex Φ(2).
Susceptibilities are calculated from the Bethe-Salpeter equation that relates
them to Φ(2). While the one-loop approximation breaks down at low
energy in one-dimensional
systems (for reasons that we discuss), it reproduces the exact results both in
the normal and ordered phases in single-channel (i.e. mean-field) theories, as
shown on the example of BCS theory. The possibility to continue the RG flow
into broken-symmetry phases is an essential feature of the 2PI RG scheme and
is due to the fact that the 2PI two-particle vertex, contrary to its 1PI
counterpart, is not singular at a phase transition. Moreover, the normal phase
RG equations can be directly used to
derive the Ginzburg-Landau expansion of the thermodynamic potential near a
phase transition. We discuss the implementation of the 2PI RG scheme to
interacting fermion systems beyond the examples (one-dimensional systems and
BCS superconductors) considered in this paper. 相似文献
16.
von Kameke A Huhn F Fernández-García G Muñuzuri AP Pérez-Muñuzuri V 《Physical review letters》2011,107(7):074502
We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles. 相似文献
17.
We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side. 相似文献
18.
R. Kishore S. Lamba 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(2):161-164
An exact analytical expression for the specific heat jump at the critical temperature Tc has been obtained directly from the BCS gap equation for any shape of the energy dependent electronic density of states (DOS).
We consider a model which takes into consideration electron-electron repulsion, formulated in the Hubbard model along with
the electron-electron attraction due to electron-phonon interaction in the BCS formalism. We have analyzed this expression
for constant as well as for the Lorentzian forms of DOS. It is shown that the constant DOS in the simple BCS theory cannot
explain the large values of , found in some superconductors. The specific heat versus temperature curve has been found to have a peak, similar to that of Eliashberg theory of superconductivity. The influence
of repulsive interaction is very small and occurs mainly at higher temperatures.
Received: 26 January 1998 相似文献
19.
García-García AM Urbina JD Yuzbashyan EA Richter K Altshuler BL 《Physical review letters》2008,100(18):187001
We study finite-size effects in superconducting metallic grains and determine the BCS order parameter and the low energy excitation spectrum in terms of the size and shape of the grain. Our approach combines the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements, and corrections to the BCS mean field. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we observe shell effects when, e.g., a small change in the electron number leads to large changes in the energy gap. 相似文献