Peierls transition
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| Peierls transition | |
|---|---|
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| Name | Peierls transition |
| Field | Condensed matter physics |
| Discovered by | Rudolf Peierls |
| Year | 1955 |
| Phenomena | Electron-phonon coupling, charge-density wave, lattice distortion |
Peierls transition The Peierls transition is a low-dimensional electronic instability in which a one-dimensional metallic system spontaneously develops a periodic lattice distortion that opens an energy gap at the Fermi level, producing an insulating or semiconducting state. First argued by Rudolf Peierls in mid-20th century discussions with contemporaries such as John Bardeen and Lev Landau, the mechanism links electronic band structure to lattice dynamics through electron-phonon coupling and Fermi surface nesting. The phenomenon has informed experiments and theory across platforms studied by groups at institutions like Cavendish Laboratory, Bell Labs, and Max Planck Institute for Solid State Research.
Introduction
The canonical picture of the Peierls transition arises when a uniform one-dimensional chain of atoms with one conduction electron per atom lowers its total energy by doubling the unit cell, a concept elaborated by Rudolf Peierls and later invoked in work by Felix Bloch, Philip Anderson, and Walter Kohn. This instability competes with metallic behavior described in early models developed at University of Cambridge and influenced by research at Massachusetts Institute of Technology and Harvard University. Connections to charge ordering were later explored in experimental programs at IBM Research and theoretical programs at École Normale Supérieure.
Theoretical basis
The theoretical basis rests on electron-phonon coupling as analyzed using tight-binding models pioneered by Felix Bloch and perturbative approaches popularized by Lev Landau and Lars Onsager. Peierls argued that a one-dimensional Fermi surface with perfect nesting at wavevector 2k_F is unstable; similar nesting ideas appear in studies by John Bardeen and Walter Kohn. Formal treatments employ the Su–Schrieffer–Heeger model developed by Alan J. Heeger, Alan G. MacDiarmid, and Hideki Shirakawa in the context of conducting polymers, and the Fröhlich model named for H. Fröhlich. Renormalization group methods introduced by Kenneth Wilson and bosonization techniques due to Sergio Coleman and Sin-Itiro Tomonaga elucidate how fluctuations alter mean-field predictions, while work by P. A. Lee and T. M. Rice addresses imperfect nesting and interchain coupling.
Experimental observations
Experimental detection of Peierls transitions has used transport, optical, X-ray, and neutron probes developed at facilities such as Stanford Synchrotron Radiation Lightsource, European Synchrotron Radiation Facility, and Oak Ridge National Laboratory. Early electrical resistivity signatures were reported in quasi-one-dimensional compounds studied at Bell Labs and Los Alamos National Laboratory, with structural superlattice peaks resolved by teams at Brookhaven National Laboratory and Argonne National Laboratory. Spectroscopic confirmation and gap measurements have come from angle-resolved photoemission spectroscopy at SLAC National Accelerator Laboratory and scanning tunneling microscopy experiments conducted at IBM Research and University of California, Berkeley.
Materials and examples
Canonical materials exhibiting Peierls-like transitions include inorganic chains such as blue bronze studied at University of Geneva and transition-metal trichalcogenides characterized at Max Planck Institute for Solid State Research. Organic charge-transfer salts examined at University of Tokyo and conducting polymers synthesized by teams at University of Pennsylvania provide additional platforms; paradigmatic examples include tetrathiafulvalene-tetracyanoquinodimethane investigated at University of Strasbourg and polyacetylene whose chemistry was developed by Alan G. MacDiarmid and colleagues. Low-dimensional oxides explored at California Institute of Technology and dichalcogenides researched at Columbia University and ETH Zurich also show density-wave order related to the Peierls mechanism.
Consequences and related phenomena
Consequences include the formation of charge-density waves and spin-density waves studied by researchers at University of Cambridge and Princeton University, and soliton excitations identified in conducting polymers by Alan J. Heeger. Competing orders such as superconductivity observed in materials explored at MIT and magnetism investigated at Los Alamos National Laboratory reflect interplay between Peierls instabilities and correlations emphasized by P. W. Anderson and Philip W. Anderson. Related phenomena include Mott transitions discussed by Nevill Mott and Luttinger-liquid behavior formalized by F. Duncan M. Haldane and J. M. Luttinger; experimental crossovers have been observed in studies at University of Chicago and Duke University.
Mathematical models and methods
Mathematical models used to describe Peierls transitions begin with the one-dimensional tight-binding Hamiltonian whose modulation leads to band folding, elaborated in textbooks by Charles Kittel and N. W. Ashcroft. The Su–Schrieffer–Heeger model by Alan J. Heeger captures soliton physics, while the Holstein model, associated with T. Holstein, treats local electron-phonon coupling. Analytical approaches use bosonization techniques introduced by Sergio Coleman and Sin-Itiro Tomonaga, renormalization group frameworks developed by Kenneth Wilson and Leo Kadanoff, and mean-field approximations inspired by Lev Landau and J. Robert Schrieffer. Numerical methods such as density matrix renormalization group pioneered by Steven R. White, quantum Monte Carlo advanced at Argonne National Laboratory, and exact diagonalization employed at Los Alamos National Laboratory allow quantitative comparison with experiments performed at Brookhaven National Laboratory and Stanford University.