Clustered fluid a novel state of charged quantum fluid mixtures H. Nykänen, T. Taipaleenmäki and M. Saarela, University of Oulu, Finland F. V. Kusmartsev Loughborough University, U.K. E. Krotscheck Johannes Keppler Universität, Linz, Austria

Mixture of electrons and holes  Electron- hole liquid  and excitons. What is the structure of the system at densities between the liquid and gas? Positrons embedded into metals and semiconductors. What happens at the Mott’s metal-insulator transition? Mixture of electrons and protons  Liquid metallic hydrogen and atomic crystal. Does the crystal melt into clustered liquid? Mixture of charged particles

Electrons and holes At high densities they condensate into electron-hole liquid, if the degeneracy is high enough. At low densities they bind together into excitons, trions, bi-excitons and perhaps polyexcitons and form a gas. Is there a stable phase in between the liquid and gas?

Phase diagram of the mixture of electrons and holes in Silicon Smith and Wolfe, Phys. Rev. B (1995) Kulakovskii, Kukushkin and Timofeev, Sov. Phys. JETP 51, 191 (1980)

Total energy per electron in Germanium and Silicon Total energy/exciton as a function of r s from the present theory. Results for the stressed and fully isotropic, non-degenerate bands are also shown. The location of the minimum agrees well with experiments.

Instability indicating charged electron-hole clusters At the critical density the sound velocity drops sharply. The electron-electron component of the distribution function grows a peak near the critical density

EHL in narrow Si/SiO 2 channels Experiments by Pauc, Calvo, Eymery, Fournel and Magnea, PRL (2004)

Phase diagram of electrons mixed with positively charged particles at T=0

and is the Slater determinant to insure the Fermionic nature. Variational theory of quantum fluids The Hamiltonian of the mixture of N a + N b =N particles with the two-body interaction V  (|r i – r j |) and masses m  of the particles in the mixture. The variational wave function is based on the Jastrow type correlations.

Optimal correlations Diagrammatic hypernetted summations are needed to calculate distribution functions and we use the single loop approximation to include the Fermionic character. Search for the optimal correlation function by minimizing the expectation value

Euler equation for mixtures S is the structure function H 1 is the free particle kinetic energy S F is the free Fermion structure function, which contains degeneracy factors and anisotropy V p-h is the particle-hole interaction between pairs of particles, which is the self-consistent result of the many-body calculation. This leads to a 2x2 matrix equation for the static structure function

Over-screened Coulomb interaction in the simple one impurity limit The electron-hole interaction for a single hole impurity in excitonic units The effective interaction between two hole impurities

Effective interactions in the electron-hole mixture in the electron-electron and electron-hole channels

Positrons Annihilation rates in the metallic region V. Apaja, S. Denk and E. Krotscheck; Phys. Rev. B (2003) Radial distribution functions for r s =1,2,…9 The system becomes unstable when r s ≈9.4 Positrons are embedded into metals and semiconductors. From the annihilation one can study the electronic structure of the system.

Mott instability In the charged Bose gas we find the bound state by studying the that the scattering phase shift. Correlation energies by Apaja, Denk, Krotscheck. Red curve, present work with bosonic electrons.

Protons and electrons At low densities and room temperatures they form a molecular gas, which solidifies at zero temperature into an insulating, molecular crystal. By increasing the pressure (or density) molecular crystal undergoes a series of phase transitions and may even melt into clustered liquid before it forms an atomic crystal. Even further increase of the pressure melts the atomic crystal into the liquid metallic hydrogen.

Simulations by Bonev, Schwegler, Ogitsu and Galli, Nature 431 (2004) Melt curve of hydrogen predicted from first principles MD. The filled circles are experimental data and the open squares are measurements from Phys. Rev. Lett. 90, (2003). Triangles indicate two-phase simulations where solidification (up) or melting (down) have been observed, and bracketed melting temperatures (Tm) are presented by open circles. Snapshots from two-phase MD simulations at P=130 GPa and temperatures. below and above the melting temperature. Molecules are coloured according to the arrangement of their nearest neighbours, representing configurations uniquely characteristic of the h.c.p. solid and liquid

The phase diagram of the proton electron mixture in the temperature pressure plane. The phase diagram of the proton electron mixture in the pressure - temperature plane The phase diagram of the proton electron mixture in the temperature pressure plane Log P [GPa] Log T [K] Electron Proton Plasma Electron Proton Liquid Molecular Liquid Molecular Solid Proton Solid Clustered liquid

Liquid-solid instability in the liquid metallic hydrogen The proton-proton component of the distribution and structure functions in the liquid metallic hydrogen.

Conclusions Positron binds a cluster of electrons at the Mott transition. A new kind of clustered liquid phase appears in the electron-hole mixture Electron-proton clusters with weakly metallic properties can appear at low temperatures and high densities.

From The interior of Jupiter by Guillot, Stevenson, Hubbard and Saumon