Excitonic Insulator Research Articles

Pressure-driven metal-insulator transition in La- and Tm-doped SmS by exciton condensation

In analogy with well-known intermediate-valent TmTeSe alloys, Sm 1− x La x S, with x = (0.10, 0.25, 0.35), and Sm 1− y Tm y S, with y = (0.10, 0.15), have also turned out as excitonic insulators under high pressure and low temperatures. The condensation of excitons results from strong Coulomb attraction between 4f holes and 5d conduction electrons, which is enhanced by external hydrostatic pressure. By hybridization in the intermediate-valent ground state, a narrow 4f band forms and lends the holes a high effective mass. Thus, the mobility of the excitons is reduced, and low temperature prevents their thermal dissociation. A sufficient exciton density triggers a Bose condensation. In the cryogenic range, the electrical resistivity of the pressurized samples indicates a gap of meV magnitude, corresponding to the activation energy of the excitons. Further pressure being applied closes the gap continuously, since more and more valence electrons pass into the conduction band and screen the Coulomb interaction. Finally, the integer-valent metallic phase is reached.

Electron-hole system revisited: A variational quantum Monte Carlo study.

Properties of a model electron-hole system are studied with a variational Monte Carlo method. Energies of both the two-component plasma phase and the excitonic insulating phase are calculated. The excitonic insulating phase is stable for all densities studied, exhibiting a strong pairing state even near ${\mathit{r}}_{\mathit{s}}$=2.0, the density where the two-component plasma phase has its minimum energy. Analysis of the pair correlation functions reveals that the stabilization of the excitonic insulator traces to enhanced short range electron-hole correlations which are partially offset by reduced electron-electron correlations. In the two-component plasma phase, significant electron-hole correlation effects remain up to high density, e.g., ${\mathit{r}}_{\mathit{s}}$=0.5. \textcopyright{} 1996 The American Physical Society.

Possibilities for exciton condensation in semiconductor quantum-well structures

Recent progress in understanding the behavior of condensed excitonic systems is reviewed. The Bose-Einstein condensed excitonic insulator is studied numerically within the mean-field pairing approximation. In particular, we examine in some detail a system of spatially separated, two-dimensional (2D) electrons and holes, as a candidate system for study in semiconductor heterostructures. Based on these calculations, we suggest that it may be possible to create a droplet of high density exciton condensate fluid in semiconductor quantum-well structures. In heterostructures, the recombination of electrons and holes is dipole-allowed, which presents both difficulties and opportunities. The excitonic insulator state should be superradiant, which provides a direct measure of the coherence of the ground state. Additionally there is a gap between the absorption and emission spectrum, and collective modes lying within this quasiparticle gap. Coupling of the condensate to radiative modes of an optical cavity may offer an opportunity to manipulate the condensate and its optical response.

Excitons in spatially separated electron–hole systems: A quantum Monte Carlo study

Variational and diffusion quantum Monte Carlo simulations of excitons in the type-II semiconductor quantum well system In1−xGaxAs/GaSb1−yAsy are performed for a wide range of composition (0,0)≤(x,y)≤(0.62,0.64) and well width 25 Å ≤L≤200 Å. The exciton binding energy is found to increase with the decrease of the layer thickness and with the increase of the composition. The calculated results suggest that a novel semiconductor–excitonic insulator (Bose condensate)–semimetal transition should be observable in this system.

The discovery of excitonium

The long-predicted existence of an excitonic condensed phase—i.e. the excitonic insulator—has been verified experimentally under pressure and low temperature on the intermediate valent system TmSe 0.45Te 0.55 and TmSe 0.32Te 0.68 by Neuenschwander and Wachter and Bucher, Steiner and Wachter. Now additional compounds such as Sm 0.75La 0.25S and YbO and YbS have been shown to fall under pressure into the category of excitonic insulators. The problem of whether magnetism plays a role in the condensation will be discussed.

Pressure-driven metal-insulator transition in La-doped SmS: Excitonic condensation.

The long-predicted excitonic condensed phase, the excitonic insulator, has been verified once more. After the discovery of two intermediate valent ${\mathrm{TmSe}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Te}}_{\mathit{x}}$ alloys a few years ago, for which the excitonic phase has been verified under pressure at low temperatures, another rare-earth chalcogenide alloy system, namely, ${\mathrm{Sm}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$S, has now turned out to be also an excitonic insulator under pressure at low temperatures. The effect is caused by Coulomb interaction of electron and holes in an intermediate valent state when pressure is decreasing the interaction volume and low temperature is preventing the ionization of the condensed phase.

Excitonic instability and origin of the mid-gap states

In the framework of the two-band model of a doped semiconductor the self-consistent equations describing the transition into the excitonic insulator state are obtained for the 2D case. It is found that due to the exciton-electron interactions the excitonic phase may arise with doping in a semiconductor stable initially with respect to excitonic transition in the absence of doping. The effects of the strong interactions between electron (hole) Fermi-liquid (FL) and excitonic subsystems can lead to the appearance of the states lying in the middle of the insulating gap.

Intermediate valence and the possibility of a magnetic excitonic insulator

The long predicted existence of an excitonic condensed phase-i.e. the excitonic insulator-has first been verified experimentally under pressure and low temperature on the intermediate valent system TmSe/sub 0.45/Te/sub 0.55/ and TmSe/sub 0.32/Te/sub 0.68/ by Neuenschwander and Wachter (1990) and Bucher, Steiner and Wachter (1991). Now additional compounds such as Sm/sub 0.75/La/sub 0.25/S and YbO and YbS have been shown to fall under pressure into the category of excitonic insulators. The problem whether magnetism plays a role in the condensation will be discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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: 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.

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.

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.

Precursors of the excitonic insulator in excited quantum wells

The theory of the magnetooptical properties of highly excited quantum wells is reviewed with emphasis on recent experimental work in a collaboration led by the Chernogolovka group. Realistic numerical calculations strongly support the interpretation of the experimental magnetoluminescence spectra in terms of bound electron-hole pairs, but at the experimental plasma temperatures of ~40-50 K phase coherence and thus observation of the excitonic insulator state is not yet achieved. Important screening effects beyond the Hartree-Fock approximation exist even at magnetic fields of ~10T. At lower densities, evidence of dynamical screening of the electron-hole interaction is found.

Excitonic insulator phase in TmSe0.45Te0.55.

We measured the Hall constant, resistivity, and magnetoresistance of the narrow-band-gap semiconductor ${\mathrm{TmSe}}_{0.45}$${\mathrm{Te}}_{0.55}$ at pressures up to 17 kbar and down to 4 K. As the band gap can be closed with pressure, a semiconductor-metal transition occurs. Above 5 kbar, when the gap is partially closed, a transition to a more insulating phase is detected. The Hall effect at low temperature and high pressure reveals that the resistivity increase is caused by a condensation of free carriers, which strongly supports this as the first observation of the excitonic insulator ground state of condensed matter.

Electron-hole pairing and anomalous properties of layered high-Tc compounds.

Band-structure pictures for layered high-{ital T}{sub {ital c}} materials available in the literature show that, besides the dispersive broad band responsible for metallic properties, there are at least two additional bands having minima and maxima near the Fermi surface. These additional bands belong to different planes (for example, CuO planes and BiO planes in Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8}) or to planes and chains (in YBa{sub 2}Cu{sub 3}O{sub 7}). Provided the Coulomb repulsion is not very weak, pairing of electrons and holes belonging to these additional bands in different planes or planes and chains is possible. It is shown that, if this possibility is realized, a transition in the additional bands into a state of an excitonic dielectric occurs. The spin of an electron-hole pair can be both 0 and 1. Due to the fact that the electron and the hole of the pair belong to different planes, there are no charge- or spin-density waves. This excitonic insulator can serve as a polarizing substance and give a strong attraction between electrons of the metallic band even if the bare interaction is repulsive. It is also shown that some interesting gapless excitations exist. Provided there are impurities in the system thatmore » scatter from plane to plane, these excitations are coupled to the electrons of the metallic band. This effective interaction can be described in terms of an effective mode {ital P}({omega}) with Im{ital P}({omega}){similar to}{minus}sgn{omega}. As a result, one can obtain such properties of the normal state as a linear dependence of the resistivity on temperature, linear dependence of the density of states on energy, constant background in the Raman-scattering intensity, large nuclear relaxation rate, etc., which are very well known from experiments.« less

Pressure-driven semiconductor-metal transition in intermediate-valenceTmSe1−xTexand the concept of an excitonic insulator

This work studies the pressure-induced semiconductor-to-metal transition (SMT) in the TmSe-TmTe alloy system. This SMT is accompanied by a valence instability of the Tm ions. Single-crystalline semiconducting ${\mathrm{TmSe}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Te}}_{\mathit{x}}$ alloys are investigated under high pressure at low temperatures. Measurements of electrical resistivity, magnetic susceptibility, neutron diffraction, and optical properties are presented and discussed. A very unusual peak structure in the resistivity-pressure relation is observed at low temperatures. A discussion of the novel feature involves the concept of an excitonic insulator and f-d hybridization. The magnetic behavior of the compounds is significantly influenced by the SMT. This is thought to be mainly due to the additional coupling between the magnetic moments of Tm via free carriers which are present in the metallic state.

A high pressure low temperature study on rare earth compounds: Semiconductor to metal transition

This work studies the pressure induced semiconductor to metal transition (SMT) in several rare earth compounds. This SMT is accompanied by a valence instability. Single crystalline semiconducting TmSe1−xTex, Tm1−xEuxSe and SmS1−xSex alloys are investigated under high pressure at low temperatures. Measurements of electrical resistivity, magnetic susceptibility, neutron diffraction, volume and optical properties are presented and discussed. A very unusual peak structure in the resistivity-pressure relation of TmSe1−xTex at low temperatures is observed. A discussion of the novel feature involves the concept of the excitonic insulator and f-d hybridization. The magnetic behavior of the Tm and Eu based compounds is significantly influenced by the SMT. This is thought to be mainly due to the additional coupling between the rare earth moments via free carriers which are present in the metallic state. In SmS1−xSex a considerable softening of the lattice is observed before the valence transition occurs. It is speculated that Poisson's ratio might become negative already in the semiconducting state.

The electronic structure of a liquid of interacting hydrogenic atoms: A prototype for expanded liquid metals

The electronic structure of a metal heated above its critical temperature (an ‘‘expanded liquid metal’’) shows dramatic changes as the density is increased. There is some experimental evidence that as one proceeds from insulating to metallic behavior the substance can even go through two separate phase transitions: from an ordinary insulator to a so-called excitonic insulator, and then from an excitonic insulator to a metal. In an effort to study how the metallic phase is approached, we have used discretized-path-integral methods to look at the statistical mechanics and the electronic structure of a model liquid. In the gas phase, the atoms in the model have a single valence electron constrained to occupy one of the s or p orbitals of the valence shell, but at higher densities, the orbitals hybridize, leading to instantaneous dipole–dipole interaction. We show that formulating this electronic structure in terms of occupation numbers allows us to monitor the hybridization evolution via an imaginary-time correlation function—which we calculate from an analytical solution to the mean-spherical approximation for the model. The numerical results strongly suggest that the model has a sudden hybridization transition, suggesting, in turn, that it might be profitable to think of the excitonic insulator transition in this language.

Electron-hole interaction in TmSe1−xTex under pressure

Semiconducting TmSe1−xTex (x=0.55, 0.68) reveals at low temperatures an anomalous peak structure in the resistivity pressure relation followed by a first-order transition into a metallic state. It is believed that the electron-hole interaction plays an important role and speculated that these data show the transition from a normal semiconductor to an excitonic insulator followed by a transition into an electron-hole liquid. Neutron scattering indicates ferromagnetism in pressure-driven metallic TmSe0.45Te0.55 below ∼5 K.

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.