Crystallization in Two-Component Coulomb Systems

Abstract

The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical mass ratio of the two charged components is found which is of the order of 80. Thus, holes in semiconductors with sufficiently flat valence bands are predicted to spontaneously order into a regular lattice. Such hole crystals are intimately related to ion Coulomb crystals in white dwarf and neutron stars as well as to ion crystals produced in the laboratory. A unified phase diagram of two-component Coulomb crystals is presented and is verified by first-principle computer simulations.PACS numbers: 52.27. -h, 52.25.-b Crystallization is one of the most fundamental manyparticle phenomena in charged particle systems. After the prediction of a highly correlated state of the electron gas -the electron Wigner crystal [1] -there has been an active search for this phenomenon in many fields. Crystallization of electrons was observed on the surface of helium droplets [2] and is predicted to occur in semiconductor quantum dots [3]. Moreover, crystals of ions have been observed in traps [4] and storage rings [5], and are expected to occur in layered systems [6]. The necessary condition for the existence of a crystal in these onecomponent plasmas (OCP) is that the mean Coulomb interaction energy, e 2 /r (r denotes the mean inter-particle distance), exceeds the mean kinetic energy (thermal energy 3 2 k B T or Fermi energy E F in classical or quantum plasmas, respectively) by a factor Γ larger than Γ cr which, in a classical OCP is given by 175 [2,7]. In a quantum OCP at zero temperature the coupling strength is measured by the Brueckner parameter, r s ≡r/a B (a B denotes the effective Bohr radius), with a critical value for crystallization of r The vast majority of Coulomb matter in the Universe, however, exists in the form of neutral plasmas, containing (at least) two oppositely charged components (twocomponent plasma, TCP). Coulomb crystallization in a TCP has been observed as well, e.g. in colloidal and dusty plasmas [9,10] and it is predicted to be possible in laser-cooled expanding plasmas [11]. The lattice of heavy particles is immersed into a structureless gas of the light component which does not affect the former. Besides these classical TCP crystals it is expected that in the interior of white dwarf stars and in the crust of neutron stars there exists an entirely different type of TCP crystals [12]: Crystals of highly charged ions (e.g. fully ionized carbon, oxygen, iron) which are embedded into an extremely dense degenerate This Letter aims to answer these questions. We show that, in fact, a common phase diagram of Coulomb crystals in a generic neutral TCP (consisting of electrons and point-like ions [14]) exists which is governed by five parameters -density and temperature (as in the OCP case) and, additionally, by the asymmetry of the heavy (h) and electron (e) components with...

Classical and quantum Coulomb crystals

“…53,55,57 As can be seen in Fig. 5, with increasing M, indeed hole localization becomes more pronounced and, between M = 50 and M = 100, a transition to crystal-like behavior is observed.…”

Bound state formation and the nature of the excitonic insulator phase in the extended Falicov-Kimball model

“…But also on the semiconducting side, the EI instability might be prevented-within this model-by either electron-hole liquid phases 6,7 or, at very large electron-hole mass ratios ( 100), by Coulomb crystallization. 8 The effective-mass Mott-Wannier-type exciton model neglects, however, important band structure effects, intervalley-scattering of excitons, as well as exciton-phonon scattering . Moreover, the excitons in Tm[Se,Te] are rather small-tointermediate sized bound objects (otherwise the experimentally estimated exciton density of about 1.3 × 10 21 cm −3 would lead to a strong overlap of the exciton wave functions, see Refs.…”

Ground states of finite spherical Yukawa crystals

“…Here, the ground state configuration changes from (30,7) to (29,8) at a screening value of κ = 4.2 and back to (30,7) at a screening value of κ = 6.91. The seven particles on the inner shell are not a platonic body and, as one can see from figure 4, it is not a common configuration compared to six or eight particles in the center.…”

“…for N = 35, cf figure 6(a). Here the configuration (28,7) which is the ground state at κ = 5 has in fact two subshells each containing 14 particles which we will denote ( [14,14], 7). The radii of the two subshells differ only slightly, R 2,1 = 0.947 and R 2,2 = 0.875, respectively, whereas the inner shell radius is R 1 = 0.426, clearly distinguishable from the outer shell.…”

“…Coulomb crystallization also occurs in classical and quantum two-component systems, such as electron-ion or electron-hole plasmas [7,8] or laser-cooled expanding plasmas [9], for a recent overview see [10,11]. Of particular recent interest has been crystallization of charged microspheres in complex plasmas in two dimensions [12]- [14], as well as in three dimensions [15] since here the structure and dynamics of the individual particles is directly visible or recordable by standard CCD cameras, e.g.…”