Excitonic Insulator Phase Research Articles

Peierls distortion in hexagonal YH3.

A pseudopotential local-density calculation is performed for ${\mathrm{YH}}_{3}$ to study the unusual hydrogen displacements previously found in neutron diffraction. These displacements are Peierls distortions associated with (hydrogen) lattice instability in this 3D system. The wave vector of these displacements is close to the vector connecting the electron and hole pockets in the undistorted system. With other electron and hole pockets at \ensuremath{\Gamma} that still overlap after distortion, the possibility of the existence of an excitonic insulator phase will be discussed.

The dipolar Frenkel excitonic insulator phase of an impurity in a liquid solvent: theory

A theory of the dipolar Frenkel excitonic insulator (EI) phase developed in an earlier paper is extended to spatially disordered systems. Using the Hartree approximation studied previously, the authors derive, for a given atomic centre-of-mass configuration, a self-consistency equation for the atomic dipole moments, a non-zero solution to which indicates an EI phase. They obtain as a special case the microscopic Yvon-Kirkwood equations of classical dielectric theory. For the experimentally relevant case of an impurity at infinite dilution in a solvent or disordered matrix, they derive an explicit expression for the impurity dipole moment. To take into account the ensemble of atomic configurations a mean field approximation is developed, numerical results for which, within the class of linear approximations of classical liquid state theory, will be given in a subsequent paper. The authors also examine the dynamic response of the impurity system to an oscillating electric field. They locate the lowest excited state of the system in both the normal insulating and dipolar EI phases, and show that it is degenerate with the ground state at the EI transition, thus making contact with exciton theories of the EI phase.

The dipolar Frenkel excitonic insulator phase of an impurity in a liquid solvent: results

In a previous paper the authors have developed a mean field theory for the dipolar Frenkel excitonic insulator (EI) phase of an impurity at infinite dilution in a liquid solvent or disordered matrix, a situation of experimental relevance. Based on this, they here present numerical results for the location of the EI transition, and the impurity dipole moment in the dipolar EI phase, using linear classical liquid state theories. For a non-polar polarizable solvent, the authors consider impurity and solvent atoms of (i) identical hard-sphere diameter, and (ii) differing hard-sphere diameter. They also generalize the previously studied model to allow for dipolar polarizable solvent molecules, and present example results. The authors consider in particular the case of alkali metal atoms dissolved in methylamine, and conclude that a dipolar EI phase is possible for Li and Cs.

On the formation and nature of a dipolar Frenkel excitonic insulator

Recently, experiments on expanded fluid mercury, and simulations of alkali metals in liquid ammonia and in molten alkali halides, have motivated interest in the possibility of a Frenkel excitonic insulator (EI) phase. In this paper, the authors discuss several aspects of a model for describing such a phase. They choose a model Hamiltonian which is the asymptotically exact low-density form for a system of atoms each possessing an sp3 basis, and present two methods of analysis. The pairing theory centres on the broadening of the S to P atomic transition into exciton bands, which, as is known, may lead to the formation of a Frenkel EI phase. They analyse two corrections to the traditional exciton picture: (i) double-excitation processes, which are responsible for the van der Waals stabilization energy, are shown to halve the density predicted for the transition to an EI phase; (ii) correct incorporation of non-boson statistics for the exciton operators is argued to drive the transition from first order to second order. The authors also analyse the model Hamiltonian via a Hartree approximation, which proves to be the more tractable method, and further allows an explicit description of the EI phase itself. The validity of the Hartree approximation is justified by comparison with the pairing theory.

Excitonic modes in a Bose-condensed electron-hole gas in the pairing approximation.

In studying the low-temperature state of an electron-hole gas in an optically pumped semiconductor there has been increasing realization that the pair approximation (similar to the Gor'kov approximation for BCS superfluids) can deal with both the low-density phase of excitons in a Bose-condensed state as well as the high-density excitonic insulator phase. Using functional differentiation techniques, we use this pair approximation to give a systematic derivation of the two-particle Green's function and the associated collective modes. Our equations of motion give what is often called the generalized random-phase approximation (GRPA). The collective modes are shown to correspond to the solution of the standard electron-hole ladder and bubble diagram sum, but with 2\ifmmode\times\else\texttimes\fi{}2 matrix propagators. Our model calculations are for a simple two-band direct-band-gap semiconductor with parabolic bands and a positive band gap (the semiconductor limit as opposed to the semimetal limit) and thus might be appropriate for optically pumped ${\mathrm{Cu}}_{2}$O. In the appropriate limits, our formalism leads to the phonon modes discussed (in the late 1960s) by Maksimov and Kozlov in the excitonic insulator and by Keldysh and Kozlov in the Bose-condensed state of excitons. In the low-density limit, the excitation of these collective modes is crucial in understanding how the Bose condensate is depleted at higher temperatures. Besides the excitonic modes, our equations of motion allow a systematic study of the complete spectrum of collective modes in the GRPA, including plasmons. Throughout, we emphasize the formal similarity with the theory of collective modes and excited Cooper-pair states in BCS superfluids.

Is Expanded Fluid Mercury a Ferroelectric Excitonic Insulator?

We relate the metal-nonmetal transition in expanded liquid mercury to the dielectric transition in dense mercury vapor. Condensation of Frenkel excitons into an excitonic-insulator phase is shown to occur at the dielectric transition. The excitons unbind at the associated (Mott) metal-nonmetal transition. The permanent dipole moments of the condensed excitons are estimated to order as a ferroelectric phase; the critical exponents of the liquid-gas transition therefore become classical.

Excitonic Clusters and the Phase Transitions in Fluid Mercury

AbstractWe review the metal‐nonmetal transition in expanded liquid mercury and the dielectric transition in dense mercury vapor. Previous explanations for these transitions are found to be deficient. We propose that the high‐temperature, high‐pressure fluid is an excitonic insulator phase. The condensation instability of the Frenkel excitons is shown to result from improved coordination within the fluid. The phase diagram for the excitonic insulator naturally explains both the metal‐nonmetal and the dielectric transitions.

The nature of the phase transitions in fluid mercury

We review the metal-nonmetal transition in expanded liquid mercury and the dielectric transition in dense mercury vapor. Previous explanations for these transitions are found to be deficient. We propose that the high-temperature, high-pressure fluid is an excitonic insulator phase. The phase diagram for the excitonic insulator naturally explains both the metal-non-metal and the dielectric transitions.

An electronic band structure model for the metal-semiconductor transition in cerium-group hydrides

An excitonic insulator model is proposed for early rare earth hydrides in an attempt to explain the metal-semiconductor transition. Band structure calculations for the trihydrides of lanthanum and cerium demonstrate the reason for such a model. Two possible types of electron-hole coupling in these systems are discussed. It is shown that in the first case a dielectric state occurs. In the second case a semimetallic state remains but a supercell with twice the periodicity along one of the principal directions 〈111〉 together with rhombohedral distortion appears. The experimental results were analysed on the basis of an excitonic insulator phase diagram. The first type of electron-hole coupling is realized.

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the “overlap-gap” |G|≲1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain “threshold” (30–40 kOe). It is inferred that the EI energy gapΔ increases with the magnetic field. The maximum gap observed in fields of ∼70 kOe turns out to beΔ00∼7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureTc is related to the EI gapΔ by the expressionTc⋍0.7Δ. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.