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Chinese Physics Letters

The phase transition-like behaviour of the bulk polaron

Wang N. Wang, Pan Jin-Sheng

Published Jun 1, 1985• 1 citation
Publisher

Abstract

The phase transition-like behaviour of bulk polaron is investigated. We find that there exists a certain critical temperature T c and the phase transition behaviour below T c is different from that above T c .
DOI
10.1088/0256-307x/2/6/009

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In recent literature it was frequently claimed that free polarons should undergo a (formal) phase transition from a mobile to a localized state, if the electron-phonon coupling constant \ensuremath{\alpha} exceeds some critical value ${\ensuremath{\alpha}}_{c}$. For \ensuremath{\alpha}=${\ensuremath{\alpha}}_{c}$, the formal free energy should be nonanalytic in \ensuremath{\alpha}. In this paper we prove that for optical polarons no such transition exists for finite temperatures. To do so, we use functional-integration techniques and discuss perturbation theory in \ensuremath{\alpha} to infinite order.
In recent literature it was frequently claimed that free polarons should undergo a (formal) phase transition from a mobile to a localized state, if the electron-phonon coupling parameter \ensuremath{\alpha} exceeds some critical value ${\ensuremath{\alpha}}_{c}$. For \ensuremath{\alpha}=${\ensuremath{\alpha}}_{c}$, the formal free energy should be nonanalytic in \ensuremath{\alpha}. In this paper we prove that for nonoptical polarons no such transition exists for finite temperatures. Our results can be generalized to the case of lower spatial dimensions as well as to polarons in homogeneous electromagnetic fields. We include some comments on related problems; in particular, the partition function of an electron moving in a Gaussian random potential is considered.
In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d -wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.
One of the most striking aspects of critical behaviour is that of the crucial role played by the geometry of the System. Critical exponents depend in a non-trivial manner on the dimensionality d . The very existence of a phase transition depends on the way in which the infinite volume limit is taken, as discussed in Section 4.4. This happens because the critical fluctuations, which determine the universal properties, occur at long wavelengths and are therefore very sensitive to the large scale geometry. By contrast, the non-critical properties of a system are sensitive to fluctuations on the scale of the correlation length and are therefore much less influenced. This line of reasoning also suggests that not all points in a system are equivalent in the way the local degrees of freedom couple to these critical fluctuations. So far, we have considered the behaviour of scaling operators only at points deep inside the bulk of a system. Near a boundary, however, the local environment of a given degree of freedom is different, and we might expect to find different critical properties there. In general, such differences should extend into the bulk only over distances of the order of the bulk correlation length. However, at a continuous bulk phase transition, this distance diverges, and we should expect the influence of boundaries to be more pronounced. The simplest modification of the bulk geometry to consider is that of a ( d − 1)-dimensional hyperplane bounding a semi-infinite d -dimensional system.