Su–Schrieffer–Heeger model

Su–Schrieffer–Heeger model
Name	Su–Schrieffer–Heeger model
Field	Condensed matter physics
Introduced	1979
Creators	Alan J. Heeger; John R. Schrieffer; William P. Su

Su–Schrieffer–Heeger model The Su–Schrieffer–Heeger model is a one-dimensional tight-binding model introduced in 1979 that describes polyacetylene and exemplifies a symmetry-protected topological insulator, connecting concepts from Alan J. Heeger, John R. Schrieffer, William P. Su, Peierls transition, polyacetylene, and Jackiw–Rebbi model in condensed matter physics and quantum field theory. It provides a minimal setting for studying topological phases, domain walls, fractionalization, and zero-energy modes that link to work by Charles H. Townes, Philip W. Anderson, Nobel Prize in Physics, and later developments in topological insulator research including links to Kane–Mele model and Haldane model.

Introduction

The model arose from attempts to explain conductivity and soliton excitations in polyacetylene and was formalized by William P. Su, John R. Schrieffer, and Alan J. Heeger, who connected the electronic structure of one-dimensional polymers to the Peierls transition and to midgap electronic states analogous to the Jackiw–Rebbi model, the latter being influential in quantum field theory and in studies by Gerard 't Hooft and Alexander Polyakov. Its influence extends to research by Charles L. Kane, Eugene Mele, F. Duncan M. Haldane, and groups at institutions such as IBM and Bell Labs, motivating experimental realizations linked to cold atom, photonic crystal, and molecular electronics platforms.

Model Definition and Hamiltonian

The Hamiltonian is a one-dimensional, nearest-neighbor tight-binding model with alternating hopping amplitudes, formulated by William P. Su alongside collaborators and analyzed using techniques related to those employed by P. W. Anderson and Philip Anderson in disordered systems; the canonical form uses intracell hopping t1 and intercell hopping t2 and can be written using creation and annihilation operators as in lattice models studied at Bell Labs and in textbooks by authors like Philip M. Chaikin and T. C. Lubensky. The model's chiral (sublattice) symmetry parallels symmetry discussions in works by Eugene Wigner and Hermann Weyl, and the two-site unit cell connects to Bloch theory described by Felix Bloch and band-structure methods used at Los Alamos National Laboratory and CERN.

Bulk Band Structure and Topological Invariants

Band structure analysis yields two bands separated by a gap except at critical points, a situation analyzed with Bloch Hamiltonians and winding numbers similar to topological invariants studied by M. V. Berry, Simon Donaldson, and Michael Atiyah in mathematical physics; the winding number of the SSH Bloch map is the prototypical example of a one-dimensional topological invariant influential in the work of Charles L. Kane and F. Duncan M. Haldane. The bulk-boundary correspondence that relates this winding number to edge phenomena draws on principles developed in studies by David Thouless, J. Michael Kosterlitz, and Vadim Berezinskii and is foundational for later classifications such as the tenfold way associated with A. Altland and M. R. Zirnbauer.

Edge States and Solitons

Open chains in the topological phase host exponentially localized zero-energy edge states, a manifestation of topologically protected boundary modes that echo domain-wall solutions in the Jackiw–Rebbi model and soliton concepts familiar from the work of N. J. Zabusky and Martin Kruskal; these midgap states are associated with fractional charge phenomena discussed by Frank Wilczek and studied in polyacetylene experiments at Bell Labs. The soliton solutions connect to kink excitations in field-theory models studied by Alexander Polyakov and Gerard 't Hooft and have pedagogical parallels to localized modes in systems explored at MIT and Stanford University laboratories.

Variants and Extensions

Extensions include staggered on-site potentials linking to the Rice–Mele model, spinful generalizations connecting to the Kane–Mele model and Bernevig–Hughes–Zhang model, interactions treated in Hubbard-like SSH-Hubbard models pursued in work by Philip W. Anderson and James Hubbard, long-range hopping studied in cold-atom experiments by groups at Max Planck Society and ETH Zurich, and non-Hermitian generalizations motivated by research at California Institute of Technology and Harvard University that relate to the non-Hermitian skin effect and studies by Carl Bender and Nicolò M. G. L. Brissaud. Multi-band, higher-dimensional, and crystalline-symmetry variants connect to work by F. D. M. Haldane and J. E. Moore.

Experimental Realizations and Applications

Realizations have appeared in polyacetylene chemistry performed by groups at Bell Labs, photonic waveguide arrays developed at Harvard University and ICFO, cold-atom optical lattices in experiments at MIT and Max Planck Institute of Quantum Optics, and mechanical metamaterials engineered by teams at University of Pennsylvania and University of California, Berkeley; applications inform designs in molecular electronics, quantum simulation platforms promoted by Google (company) and Microsoft Research, and topological photonics pursued at EPFL and Imperial College London. Measurement techniques involve angle-resolved experiments influenced by Zhi-Xun Shen and scanning probes used in condensed matter labs like Argonne National Laboratory and Brookhaven National Laboratory.

Mathematical Methods and Solvable Limits

Analysis employs Bloch theory from Felix Bloch, Green's function methods popularized by Julian Schwinger, index theorems inspired by Michael Atiyah and Isadore Singer, and continuum field-theory mappings to the Dirac equation akin to treatments by Gerard 't Hooft and Roman Jackiw, while integrable or noninteracting limits permit exact diagonalization and transfer-matrix techniques used in statistical mechanics by Lars Onsager and Rudolf Peierls. Computational studies draw on algorithms developed at Los Alamos National Laboratory and methodologies from Lawrence Livermore National Laboratory and National Institute of Standards and Technology.

Category:Condensed matter physics