Second plasmon and collective modes in binary Coulomb systems

Abstract

In a system consisting of two different charged species we identify the excitation of a second, low frequency plasmon. At strong coupling the doublet of high frequency (first) and low frequency (second) plasmons replaces the single plasmon excitation that prevails at weak coupling. We observe the formation of the second plasmon from the acoustic Goldstone type mode associated with short range interaction as the range is extended to infinity. The existence of plasmons in many body systems interacting through a Coulomb potential (plasmas, electron gases, etc.) with a characteristic oscillation frequency, the plasma frequency(with the symbols having their usual meaning) has been known for a long time [1]. The identification of this phenomenon as a collective excitation -in fact, the very introduction of the idea of collective excitations and the notion of collective coordinates -is due to the pioneering series of works by Bohm, Gross and Pines [2][3][4]. It was also Bohm and Gross [2] (BG) who determined the eponymous k-dependent positive dispersion of the plasmon, caused by the random motion of the particles. Soon, however, it became clear that the BG dispersion and the underlying theoretical approach (which later was reformulated in many differ guises [3,5] and has commonly become known as the Random Phase Approximation (RPA)) are appropriate for weak coupling only. The coupling strength is conveniently defined as the ratio of the potential energy of the particles to their kinetic energy. The appropriate parameters that characterize the coupling strength for classical systems are Γ = Z 2 e 2 /ak B T and for quantum systems r s = a/a B (a is the Wigner-Seitz radius, a B the Bohr radius and T the temperature). Motivated by the case of the electron gas in metals where the condition r s < 1 is mildly violated, it was Singwi and collaborators [6] who have made the first serious attempts to study the effect of strong coupling on the properties of the plasmon. However, the first systematic and reliable analysis of this problem, primarily through molecular dynamics (MD) computer simulation was done by Hansen and collaborators [7,8]; in particular Hansen [8] verified the change of the BG behavior to a negative dispersion, the hallmark phenomenon of strong coupling, which was predicted and investigated by a number of workers [9,10] around the same time. A different theoretical approach, the Quasilocalized Charge Approximation (QLCA), geared for the study of strongly coupled Coulomb systems was introduced by Kalman and Golden [11,12] and combined with advanced MD computer simulations has led to a thorough investigation of the plasmon dispersion. Experimentally, the plasmon dispersion of the electron gas has been mapped directly and indirectly in various condensed matter situations at low or moderate coupling values; with the advent of complex (dusty) plasma experiments, the way to directly observing strongly coupled plasmon behavior in the laboratory has opened up.Looking at the problem from a more general point of view, w...

Elastic properties of binary crystals in neutron stars and white dwarfs

“…Our analysis of the phonon spectrum shows that the fc2 lattice is stable at 0.66 ≤ α ≤ 1.36 (step over α equals 0.02; see Kozhberov 2018, for details). This result agrees with the limits of stability of the fc2 lattice obtained independently by Kalman et al (2014): 0.661 ≤ α ≤ 1.368. For this range of α, the µ lm,fc2 eff /µ fc2 eff ratio always ranges between 1 and 1.002.…”

“…The results of Igarashi & Iyetomi (2003) are labeled as c dis 44 . Igarashi & Iyetomi (2003) investigated lattices with α ≤ 13 while we restrict ourselves to α = 3 because (as shown by Kozhberov & Baiko 2012) the sc2 lattice is stable with respect to the small oscillations of ions around their equilibrium positions at α < 3.6 (similar result was obtained latter in Kalman et al (2014) from molecular dynamics).…”

Electrostatic properties and stability of Coulomb crystals

“…Similar limits 1/3.596 < < 3.596 were recently found (but later than paper 14 was published) from molecular dynamics simulations in Ref. 38 The stability of the deformed sc2 lattice can be studied as a function of the direction and magnitude of the deformation, as well as parameter . Among all deformed sc2 lattices, we consider only a binary sc2 lattice stretched along one of the edges of its elementary cell,c 1 is the relative stretch in units of a l (similarly to the fcob lattice from paragraph 4).…”

Resonant and anti‐resonant modes of the dilute, spin‐inbalanced, two‐dimensional electron liquid including correlations

“…However, accounting for correlation effects lowers the spin-plasmon dispersion, implying that it enters the strong damping continuum at much lower wave vectors. [14] Similar situations are known for the acoustic modes in other binary Coulomb systems, such as ionic mixtures, [15] electron bilayers, [16] semiconductor double wells, [17] or the interface 2DEL of perovskites coupled to graphene [18] (the list being far from complete; note also recent work on static many-body correlations in graphene and the linear mode in the graphene-related MoS 2 [19] ). The transverse counterpart of the spin-plasmon, i.e.…”