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physica status solidi (b)

Phase Transition of Fröhlich Polarons, in the Feynman Approximation, Subjected to a Magnetic Field

François Maria Peeters, J. T. Devreese

Published Apr 1, 1982• 15 citations
Publisher

Abstract

Abstract It is shown that the Fröhlich polaron in a magnetic field (calculated in the Feynman approximation) exhibits a first‐order phase transition if the electron‐phonon coupling constant α is larger than 4.2. For α = 4.2 the transition is of second order. The phase transition manifests itself as a discontinuity in the magnetization, the susceptibility, and the polaron mass for a critical value of the magnetic field. It is found that at the transition point the phonon cloud surrounding the polaron cannot follow the electron in its motion in the magnetic field.

DOI
10.1002/pssb.2221100232

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Journal of Physics Condensed Matter•Mar 25, 1996•10 citations

A new variational ansatz in the polaron theory

J. Röseler

Abstract A new translational invariant variational statement is given, which is exact to the order α2 for weak coupling and which is in the limiting case of strong coupling regarding the polaron self‐energy not poorer as‐0.105 α2 h ω. In the limiting case of weak coupling the polaron mass, the contributions to the self‐energy due to the individual components of Fröhlich's Hamiltonian, and up to the order α2 the mean value of virtual phonons in the ground state are exactly calculated.

physica status solidi (b)•Jan 1, 1968•68 citations
Abstract It is shown that the Fröhlich polaron in a magnetic field (calculated in the Feynman approximation) exhibits a first‐order phase transition if the electron‐phonon coupling constant α is larger than 4.2. For α = 4.2 the transition is of second order. The phase transition manifests itself as a discontinuity in the magnetization, the susceptibility, and the polaron mass for a critical value of the magnetic field. It is found that at the transition point the phonon cloud surrounding the polaron cannot follow the electron in its motion in the magnetic field.
Abstract New results for the free polaron ground state energy are presented, based on a non‐perturbative Fock approximation mean field theory. From variational calculations a new energy upper bound for all couplings is obtained, whose newness lies in its cylindrical symmetry, thu sbreaking the spherical symmetry of the Fröhlich Hamiltonian. For α (the electron–phonon coupling constant)≦3 a translational invariant state is found, for 3 ≦ α ⪅ 3.8 a two‐dimensional localized state while for α ⪆ 3.8, a three‐dimensional cylindrical localized state is obtained. By linking the variational approach to a dynamical approximation of the Fröhlich Hamiltonian, the possibility is suggested of second‐order phase transitions for the structure of the polaron, in the framework of the Fock approximation.
A detailed numerical analysis is made of the analytic results presented in paper I. Numerical results are presented for the mass of the Feynman polaron, parallel (${M}_{\ensuremath{\parallel}}$) and perpendicular (${M}_{\ensuremath{\perp}}$) to the magnetic field, and for the following thermodynamic quantities: the magnetization, the susceptibility, the internal energy, the entropy, and the specific heat. Those quantities are studied for different values of the electron-phonon coupling ($\ensuremath{\alpha}$), temperature (TTT), and magnetic field strength (H\mathcal{H}H). We found that an ideal gas of polarons undergoes a phase transition. In the physical parameter space ($\frac{1}{\ensuremath{\alpha}},\frac{1}{\mathcal{H}},T$) the points of first-order phase transition define a two-dimensional surface which is circumscribed by a line of second-order phase transitions. At the transition point the polaron transforms in the direction perpendicular to the magnetic field, and with increasing magnetic field strength, from a polaron state (${M}_{\ensuremath{\parallel}}\ensuremath{\approx}{M}_{\ensuremath{\perp}}$) to an almost free Landau state (${M}_{\ensuremath{\parallel}}>>{M}_{\ensuremath{\perp}}\ensuremath{\sim}1$). This transition can be viewed as a magnetic-field-induced two-dimensional stripping of the polaron. The experimental consequences of this phase transition on the thermodynamic quantities and the magneto-optical absorption spectrum are discussed.
The ground-state energy of an acoustical bipolaron in three dimensions (3D) is studied within the Feynman path integral method. The acoustical polaron exhibits a transition from the quasi-free state to the self-trapped state. Depending on the value of the Debye cut-off in phonon wavevector space this transition can be continuous or discontinuous. If two electrons are present a second transition becomes possible: the transition to the bipolaron state in which the two electrons are self-trapped around the same position. The corresponding phase diagram is calculated as function of the cut-off , the electron - phonon coupling strength , and the repulsion (U) between the electrons. We found that: (i) the bipolaron transition is a first-order transition; (ii) it is also possible between two polarons which are in the quasi-free state, i.e. are not self-trapped; and (iii) the effective particle mass increases substantially at the transition point.
Abstract A new translational invariant variational statement is given, which is exact to the order α2 for weak coupling and which is in the limiting case of strong coupling regarding the polaron self‐energy not poorer as‐0.105 α2 h ω. In the limiting case of weak coupling the polaron mass, the contributions to the self‐energy due to the individual components of Fröhlich's Hamiltonian, and up to the order α2 the mean value of virtual phonons in the ground state are exactly calculated.