Motohiko Saitoh

Theory of a Polaron at Finite Temperatures

In order to calculate the effective mass and free energy of a polaron at finite temperatures, Feynmans path-integral formalism is generalized in the following two points: (a) the most general quadratic form is used to fully optimize the partition function, and (b) the new definition of the effective mass is introduced such that the effective mass is determined from the acceleration rate against the fictitious driving force which is incorporated in the original Lagrangian. The use of (a) leads to a non-linear integral equation which determines the best trial form. This non-linear integral equation is solved analytically for the Frohlich polaron model to obtain the explicit expressions for the effective mass and free energy at finite temperatures.

Free Energy of a Polaron in a Strong Magnetic Field

New results for the free energy of a polaron in a strong magnetic field are presented. The method used here is the extended version of Feynmans pathintegral formalism in which the most general quadratic form containing an infinite number of variational parameters is employed to simulate the variational trial action. A set of nonlinear integral equations is established to determine the upper bound for the free energy in the entire range of electron-phonon coupling constants, temperatures and magnetic fields. Analytical solutions are provided for some limiting cases of interest, and are compared critically with existing calculations of the ground-state energy at zero temperature. The free energy thus obtained is exact to the lowest order in the coupling constant and provides the good interpolation up to the strong coupling regime.

Theory of a Polaron in Weak Magnetic Fields

Using the generalized Feynman path-integral method developed in the preceding paper, the polaron state at finite temperature in a weak magnetic field is investigated. The Landau zero-point energy and the diamagnetic susceptibility are calculated. The magnetic mass deduced from these coincides with the inertial mass which was calculated previously except for the case of the strong electron-phonon coupling at finite temperature.

Magneto-Conductivity of Ripplonic Polarons in a Wigner Crystal

General formulae for the free energy and the conductivity in the presence of a magnetic field are obtained for the system of electrons in a two-dimensional Wigner crystal on the surface of liquid He when the electrons interact with the surface roughness created by ripplons. The dc magneto-resistance is calculated explicitly and is shown to differ qualitatively from the result for the independent electron system.

Stark Ladders in a Two-Dimensional Tight-Binding Lattice

Electronic states of a two-dimensional tight-binding model in a uniform electric field are studied. Numerical solutions for eigenenergies and eigenfunctions are presented as functions of the angle between the electric field and the symmetry axis of the lattice. When the direction of the electric field is [ M , N ], where M and N are mutually prime each other and M N ≠0, the eigenenergies are shown to be quantized with an interval equal to the potential drop between the nearest neighbor net lines. Though the level separation varies discontinuously with the change of the direction, the density of states is shown to be independent of the direction of the electric field, except for the direction [1 0] where the motions parallel and perpendicular to the electric field directions are separable. Unexpected gaps open near the band edges for appropriate electric fields, the magnitudes and the positions of which are smooth functions of the angle for a fixed electric field. The effects of the system edges are also d...

Ripplonic Polarons in a Wigner Crystal

By the use of the path-integral method, general formula of the free energy and the conductivity of electrons in a two-dimensional Wigner crystal are obtained when both of the electron-electron and the electron-surface interactions are present. The dc conductivity is calculated explicitly for electrons bound on the surface of liquid He in the case of the weak electron-ripplon coupling. Good agreement is obtained between theory and experiment about the density dependence of the collision time.

Two-Dimensional Tight-Binding Electrons in Electric and Magnetic Fields

Electronic states of a two-dimensional tight-binding lattice with finite size in the presence of both uniform electric and magnetic fields are studied. Numerical solutions for eigenenergies are presented. The magnetic subbands at zero electric field known as the Hofstadter butterfly are modified by the electric field and the eigenenergies for high electric fields are represented by the Stark ladder states associated with each of the magnetic subbands. When the electric potential drop across the system becomes comparable to the bandwidth of zero field, the density of states becomes the pyramid shape with steps, the steps being induced by the finiteness of the lattice. The influence on the density of states by the change of the direction of the electric field is also discussed.

Strongly-coupled ripplonic polarons in high magnetic fields

Quasi-two-dimensional electrons on a thin liquid He film, which are strongly coupled to the gravity-capillary waves (ripplonic polarons), are investigated theoretically when a high magnetic field is applied perpendicularly to the surface. The free energy and the absorption line-shape of the cyclotron resonance are calculated with the use of the path-integral method. The expression for the cyclotron mass has the same form as the one for the weak coupling case, and is always smaller than the electron vacuum mass. The line-width has an exponential temperature dependence with a characteristic energy proportional to the coupling constant, and is very narrow. The pre-factor of the line-width is dependent both on the coupling constant and the magnetic field, and is different from that of the inverse DC collision time.

Melting and transport properties of two-dimensional wigner crystals on liquid He

Abstract Electrons on the surface of liquid helium make an almost ideal two-dimensional system. When the electron surface density is increased the system undergoes a gas-solid transition at a critical temperature. Theoretical understanding of the melting and transport properties of this solid-phase will be reviewed in reference to existing experiments.

Diamagnetic susceptibility of a Fröhlich polaron

Abstract Numerical calculations of the diamagnetic susceptibility of a Frohlich polaron are presented on the basis of Feynmans path-integral method with the generalized trial action developed earlier. The results show that the susceptibility deviates from the free-electron value and becomes practically temperature independent as the electron-phonon coupling increases.