Excitonic Phase Transition Research Articles

Quantum renormalization group and excitonic phase transition in a strong magnetic field

The critical behavior of excitonic fluctuations is investigated at low temperatures. The Wilson renormalization group is applied to a generalized free-energy functional of the Landau-Ginzburg-Wilson type, which is derived by coarse-graining a microscopic functional. The quantum mechanical effects give rise to an increase of the effective dimensionality at zero temperature. The values of this increase z are z = 1 for a semiconductor and z = 2 for a semimetal, depending on whether the electronic density of states is zero at the Fermi energy or not, respectively. Quantum-classical crossover phenomena appear at a finite but low temperature. As the phase transition point is approached in a semimetal the critical fluctuations in real space first grow two-dimensionally in the plane perpendicular to the magnetic field and then develop three-dimensionally. It is explicitly shown that the mean field theory breaks down in a semiconductor.

Excitonic Phase and Gas-Liquid Transition of Semimetals in a Strong Magnetic Field

The properties of an electron-hole system in a strong magnetic field is studied. Especially the effect of the excitonic correlation on the gas-liquid type phase transition is studied by a mean field theory. It is shown that the effective mass, number of carriers and Landau quantum number of the relevant Landau subbands have characteristic effects. It is suggested that a semimetal bismuth in a magnetic field of about 100 kOe shows various types of phase transitions at low temperatures (\(T{\lesssim}0.1\) K).

Theory of the excitonic fluctuation in a strong magnetic field. I. Development of the physical picture and a self-consistent Hartree theory

The physical picture of the appearance of the excitonic correlation in a strong magnetic field is developed in an electron-hole system which consists of one conduction band and one valence band. The field is assumed to be sufficiently strong that all the electrons and holes occupy their lowest Landau levels. Kinematical and dynamical aspects of such a truncated system are discussed in detail. The discussion does not deny the possibility of the excitonic phase transition in a strong magnetic field. The essence of the present physics is in the high degeneracy of the single-particle state and the strong shrinking of the electron wave function due to the magnetic field. In order to study the physics explicitly we construct a self-consistent Hartree theory. Further introducing static and local approximations for the excitonic fluctuation. We can determine the quasiparticle state and the fluctuation exactly near the transition point. We present the transition temperature in two limiting cases of the band configuration. We indicate the self-consistent Hartree theory combined with the static and local approximations is an unsatisfactory theory in the light of our physical picture. We also discuss possible improvements of the theory briefly.

Further Study of the Occurrence of the Excitonic Phase Transition in Bismuth under Strong Magnetic Fields by Ultrasonic Attenuation

A previous measurement of the anomalous temperature dependence of the giant quantum attenuation of longitudinal sound waves in bismuth under strong magnetic fields was extended down to 1.06 K, and further evidence for the occurrence of the excitonic phase transition was obtained. The plot of sound attenuation versus temperature in the anomalous case showed a roundish convex curve near a maximum located at a point a little below T c , a temperature parameter to be identified with the phase transition point. This temperature dependence of the attenuation is well explained in terms of the critical fluctuation and a modified form of Maki-Nakanishi's formula of the attenuation of the excitonic state in the absence of field. The transition temperature, the critical exponent and other parameters to specify the anomalous attenuation curve near T c are evaluated for several cases of a parameter related to the energy difference between the hole and electron Landau levels in the normal state.

Further evidence for the occurence of the excitonic phase in Bismuth under strong magnetic fields

When electrons and holes in strong magnetic fields resonantly absorbed ultrasound energy at nearly equal field-strengths, a maximum was observed in plot of attenuation versus temperature (4.2 K ⩾ T ⩾ 1.06 K). This temperature dependence is well explained in terms of the excitonic phase transition.

A New Phenomenon is Sound Attenuation in Bismuth under Very Strong Magnetic Fields

A new phenomenon in sound attenuation in bismuth has been observed at liquid helium temperatures and under very strong magnetic-field conditions such that the electrons and holes in the states with the Landau quantum number n =1 almost simultaneously satisfy resonance when varing the field strength in some suitable field directions. The anomalous part of the attenuation at the resonance field position, Δ α, obeys the law Δ α= A ( T / T c -1) -(0.49±0.06) in a limited region of reduced temperature ( T / T c -1). The values of the parameters T c (\({\lesssim}1.6\) K) and A depend characteristically on the difference between the resonance field strengths for the electrons and holes. The experimental facts suggest that this phenomenon may be related to the fluctuation of electron-hole pairs produced above the excitonic phase transition temperature.