T. M. Rice

The Excitonic State at the Semiconductor-Semimetal Transition

Publisher Summary Some years ago, Mott considered the role of the Coulomb attraction for a semimetal with small numbers of electrons and holes and observed that under certain conditions the electrons and holes could bind to form a nonconducting phase. Knox remarked that the ordinary Bloch wave groundstate of the crystal could become unstable against the spontaneous formation of excitons if the exciton binding energy exceeded the energy grip. The exciton instability leads to a second-order transition to a new state having a “condensate” of excitons and in which the translational periodicity of the original lattice is broken by a new “long-range order” in the electronic states. This new state is variously referred to as the “excitonic state” or as the “distorted state,” whereas the normal Bloch-wave state is referred to as the “undistorted state.” This chapter gives a brief review of the previous work on the excitonic state. The bulk of the chapter is devoted to an attempt to elucidate further the physical significance of the distorted state, and to examine more carefully than previously the question of the existence of such a state, and of the location and nature of the transition points.

The Electron-Hole Liquid in Semiconductors: Theoretical Aspects

Publisher Summary The chapter presents a discussion on the theoretical aspects of the electron-hole liquid in semiconductors. In an intrinsic semiconductor such as germanium or silicon, there are essentially no free carriers at very low temperatures. However, high densities of positive (hole) and negative (electron) charge carriers can be generated in these crystals by photoexcitation with a photon energy greater than the forbidden gap. In recent years, experiments in Ge and Si have revealed that optically pumped electrons and holes at high densities can undergo a phase transition at liquid helium temperatures into a metallic, liquid state. This condensate represents a state of matter particularly unique in nature because the electrons and holes, by reason of their small masses, are simultaneously in the quantum limit. This chapter presents a discussion on the collective behavior of electrons and holes at low temperatures and high densities. The chapter presents an historical introduction, mentions a few of the important early experiments performed, and presents a comparison of theory and experiment. Semiconductors can be divided into two classes. Those in which the conduction band minimum and valence band maximum occur at the same value of the wavevector are known as direct gap semiconductors, while those in which they are separated in k space are known as indirect gap semiconductors. The chapter discusses the latter.

Antiferromagnetism in Chromium and its Alloys

Recent experimental and theoretical work on itinerant antiferromagnetism in Cr and its alloys is reviewed with particular emphasis on optical and pressure effects. At low temperatures, a peak appears in the infrared conductivity of Cr which is attributed to excitation of electrons across the antiferromagnetic energy gap. The maximum in absorption occurs at photon energy 5.1kTN, at low temperatures, which is substantially higher than the value 3.5kTN predicted by the simplest models. Both the position and shape of the absorption can be explained if the effects of electron‐phonon scattering are incorporated in the model. The pressure dependence of the Neel temperature of Cr and alloys with Mo and V is described. The role of band structure is discussed, particularly its effect on the vanishing of antiferromagnetism under pressure.

Critical Pressure for the Metal‐Semiconductor Transition in V2O3

The metal‐semiconductor transition is found to be suppressed at Pc=25.8±1.0 and 23.0±1.0 kbar for increasing and decreasing pressure. The temperature and volume dependence of the resistivity of the metallic phase is anomalous. The resistivity varies as BT2 at low temperature and rises more slowly at high temperatures. The data are analogous to Sr and Yb in the region where the band overlap approaches zero with increasing pressure. We propose that the metal‐semiconductor transition in V2O3 may be driven by the Coulomb attraction between electrons and holes and may be an example of an excitonic phase change.