Structures of quantum 2D electron-hole plasmas

📝 Abstract

We investigate structures of 2D quantum electron-hole (e-h) plasmas by the direct path integral Monte Carlo method (PIMC) in a wide range of temperature, density and hole-to-electron mass ratio. Our simulation includes a region of appearance and decay of the bound states (excitons and biexcitons), the Mott transition from the neutral e-h plasma to metallic-like clusters, formation from clusters the hexatic-like liquid and formation of the crystal-like lattice.

💡 Analysis

We investigate structures of 2D quantum electron-hole (e-h) plasmas by the direct path integral Monte Carlo method (PIMC) in a wide range of temperature, density and hole-to-electron mass ratio. Our simulation includes a region of appearance and decay of the bound states (excitons and biexcitons), the Mott transition from the neutral e-h plasma to metallic-like clusters, formation from clusters the hexatic-like liquid and formation of the crystal-like lattice.

📄 Content

arXiv:0810.2709v1 [physics.plasm-ph] 15 Oct 2008 Structures of quantum 2D electron–hole plasmas V S Filinov1, M Bonitz2, H Fehske3, P R Levashov1, V E Fortov1 1Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13 bldg 2, Moscow 125412, Russia 2Christian-Albrechts-Universit¨at zu Kiel, Institut f¨ur Theoretische Physik und Astrophysik, Leibnizstrasse 15, 24098 Kiel, Germany 3Institut f¨ur Physik, Ernst-Moritz-Arndt-Universit¨at Greifswald, Felix-Hausdorff–Str. 6, D-17489 Greifswald, Germany Abstract. We investigate structures of 2D quantum electron–hole (e-h) plasmas by the direct path integral Monte Carlo method (PIMC) in a wide range of temperature, density and hole-to-electron mass ratio. Our simulation includes a region of appearance and decay of the bound states (excitons and biexcitons), the Mott transition from the neutral e-h plasma to metallic–like clusters, formation from clusters the hexatic-like liquid and formation of the crystal-like lattice. PACS numbers: 71.23.An, 71.55.Jv, 52.65.Pp

1. Introduction Strongly correlated two-dimensional quantum Coulomb systems are the subject of intensive discussions. In particular, it is known that the competition between electrostatic and kinetic energy in an electron gas may be the reason of an unusual phase diagram of a 2D system of electrons. The liquid state of such system is stable when the kinetic energy dominates while the electrostatically favored “Wigner” triangular crystal is stable in the opposite case. If there is a strong competition between these two kinds of energy, different situations are possible. The question under discussion is the existence of the intermediate anisotropic liquid phase (hexatic) under melting of crystal into isotropic liquid. Moreover, the physical mechanism of melting can be influenced by the interaction with substrate and defects. Currently all mentioned phenomena can be extensively investigated by a consistent first-principle numerical simulation, and in this brief paper we present the most interesting results of our numerical experiments by the direct PIMC method.
2. Path integral Monte Carlo approach Let us consider a two-component neutral e-h plasma. Thermodynamic properties of such plasma are defined by the partition function Z, which for the case of Ne electrons and Nh holes (Ne = Nh), is given by Z(Ne, Nh, V, β) = Q(Ne, Nh, β)/Ne!Nh, with Q(Ne, Nh, β) = P σ R V dr dq ρ(q, r, σ; β), where β = 1/kBT , σ = (σe, σh), r, σe denotes the space and spin electron coordinates, while q, σh denotes the space and spin hole coordinates. These expressions are valid for 1D, 2D and 3D cases. The Structures of quantum 2D electron–hole plasmas 2 pair distribution functions for a binary mixture of quantum electrons and holes can be written in the form gab(R1 −R2) = gab(R1, R2) = P σ R V dq dr δ(R1 −Qa

1. δ(R2 − Qb 2)ρ(q, r, σ, β)/Q(Ne, Nh, β), where a and b label the particle species, i.e. a, b = e (electrons), h (holes) and Q, R denote the two-dimensional vectors of coordinates, Qe 1,2 = r1,2 and Qh 1,2 = q1,2. The exact density matrix ρ(q, r, σ, β) of a quantum system for low temperature and high density is in general not known but can be constructed using a path integral representation [1, 3]. Thus we take into account interaction, exchange (through permutation operators) and spin effects both for electrons and holes. This procedure gives the expression for the density matrix as a multiple integral which is well suited for efficient numerical evaluation by Monte Carlo techniques, e.g. [1]. We mention here that for all obtained results, the maximum statistical and systematic errors is not more than 5%.

3. Simulation results We are interested in strong Coulomb correlation effects such as bound state (excitons, bi-excitons, many particle clusters), their transformation by the surrounding plasma and their eventual breakup at high densities (Mott effect). Beyond the Mott density, we expect the possibility of the hole crystallization if the hole mass is sufficiently large [2]. Below, the density of the two-component plasma is characterized by the Brueckner parameter rs defined as the ratio of the mean distance between particles d = [1/π(ne + nh)]1/2 and the 3D exciton Bohr radius aB, where ne and nh are the electron and hole 2D densities. The dimensionless temperature will be presented as a ratio of the temperature and the 3D electron-hole binding energy (Rydberg), which includes the reduced effective mass and dielectric constant. We analyze some spacial distribution functions and related spin-resolved typical “snapshots” of the e-h state in the simulation box for different particle densities, temperatures and hole-to-electron mass ratios M. According to the path integral representation of the density matrix, each electron and hole is represented by several tens of points (“beads”). The spatial distribution of the beads of each quantum particle is proportional to its spatial probability distribution. Figure 1 shows that,

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