Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1411.3635 · Physical Review B

BLF-SSH polarons coupled to acoustic phonons in the adiabatic limit

Carl J. Chandler, F. Marsiglio

Published Dec 31, 2014• 4 citations
arXivHTMLPDF

Abstract

We survey polaron formation in the Barisi\ifmmode \acute{c}\else \'{c}\fi{}-Labb\'e-Friedel and Su-Schrieffer-Heeger (BLF-SSH) model using acoustic phonons in the adiabatic limit. Multiple different numerical optimization routines and strong-coupling analytical calculations are used to find a robust ground-state energy for a wide range of coupling strengths. The electronic configuration and accompanying ionic distortions of the polaron were determined, as well as a nonzero critical coupling strength for polaron formation in two and three dimensions.

DOI
10.1103/physrevb.90.245149

Related papers

Numerical study of the crossover from free electrons to small polarons

Zhou Li

The electron-phonon interaction is one of the fundamental interactions in almost all condensed matter materials. In conventional superconductors, the electron-phonon interaction is the glue that attracts two electrons to one another to form a pair. A strong electron-phonon interaction leads to the concept of a polaron, which is an electron with lattice distortions around it. The small polaron is a polaron with spatial extent comparable to an interatomic dimension of the solid. Evidence for polarons has been identified in many experiments in superconductors and semiconductors. In this thesis we present exact calculations of the polaron. Specifically we have refined Trugman's method to solve the ground state of an electron-phonon coupled system in the whole parameter regime, and we also generalized this method to treat spin-orbit coupled systems. The most difficult regimes, which is the strong-coupling regime and the small phonon frequency limit, have been solved by these refinements. There are three representative kinds of electron-phonon interaction, the Holstein model, the Fr"ohlich model and the BLF-SSH model. In this thesis we have addressed the first and the third one. The second one, the Fr"ohlich model, is very similar to the Holstein model but the interaction is nonlocal. For the Holstein model we have observed the expected smooth crossover from free electrons to small polarons, while for the BLF-SSH model, we have studied the weak coupling regime with perturbation theory and derived a new analytical result for the one-dimensional problem.

•Jan 1, 2012•0 citations

Dual coupling effective band model for polarons

D. J. J. Marchand, Philip C. E. Stamp, Mona Berciu

Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the $k=0$ effective mass diverges, now becomes a transition line in the coupling constant plane---the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No ``self-trapping transition'' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.

arXiv:1609.03096•Physical review. B./Physical review. B•Jan 11, 2017•31 citations

Sharp Transition for Single Polarons in the One-Dimensional Su-Schrieffer-Heeger Model

D. J. J. Marchand, G. De Filippis, V. Cataudella +5 more

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).

arXiv:1010.3207•Physical Review Letters•Dec 30, 2010•140 citations

REALISTIC MODELS FOR POLARONS

Carl J. Chandler

Electrons interacting with the ions in a solid, or polarons, are some of the most basic condensed matter quasi-particles. They influence the electric conductivity in normal metals, but perhaps most fascinatingly, they mediate the formation of Cooper pairs in low temperature superconductors. The details of this phonon mediation are poorly understood at the level of a microscopic Hamiltonian. The Hamiltonian for basic polaron models has only recently been solved for the single electron, and seems to predict that the polarons in low temperature superconductors would have very large effective masses. This is at odds with the measured small effective masses of many low temperature superconductors in the normal state. In this thesis we examine extensions to the basic Holstein polaron Hamiltonian that provide a more realistic model of what happens in real materials. We also look at the BLF-SSH model, which is the appropriate Hamiltonian for superconductors without optical phonons such as the elemental superconductors. We found that extending the Holstein model to include next nearest neighbour electron hopping and nearest neighbour electron-phonon interactions changed the effective mass slightly, but nowhere near enough to account for the low effective masses that must be present in real materials. The BLF-SSH model was examined in the adiabatic limit and with weak-coupling perturbation theory, but an exact solution was not found. It seems likely that the effective mass for this model is also very large, but an improved algorithm is necessary to prove this. A potential path forward is presented in the appendix.

•Jan 1, 2016•0 citations

Comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models

Andy Tanjaroon Ly, Benjamin Cohen-Stead, Sohan Malkaruge Costa +1 more

Su-Schrieffer-Heeger (SSH) electron-phonon ($e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$) interactions have been theorized to play critical roles in several novel states of matter, ranging from nontrivial topological states to high-temperature bipolaronic superconductivity. This work compares the superconducting and competing charge and bond correlations of the two-dimensional Holstein and optical (SSH) models. The authors find that near half-filling, light SSH (bi)polarons support superconductivity to larger values of $e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$ coupling compared to the Holstein polaron. These results are essential for identifying and engineering bipolaronic superconductivity in quantum materials.

Physical review. B./Physical review. B•Nov 1, 2023•22 citations

A comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models

Andy Tanjaroon Ly, Benjamin Cohen-Stead, Sohan Malkaruge Costa +1 more

Theoretical studies suggest that Su-Schrieffer-Heeger-like electron-phonon ($e$-ph) interactions can mediate high-temperature bipolaronic superconductivity that is robust against repulsive electron-electron interactions. Here we present a comparative analysis of the pairing and competing charge/bond correlations in the two-dimensional Holstein and optical Su-Schrieffer-Heeger (SSH) models using numerically exact determinant quantum Monte Carlo. We find that the SSH interactions support light bipolarons and strong superconducting correlations out to relatively large values of the $e$-ph coupling $λ$ and densities near half-filling, while the Holstein interaction does not due to the formation of heavy bipolarons and competing charge-density-wave order. We further find that the Holstein and SSH models have comparable pairing correlations in the weak coupling limit for carrier concentrations $\langle n \rangle \ll 1$, where competing orders and polaronic effects are absent. These results support the proposal that SSH (bi)polarons can support superconductivity to larger values of $λ$ in comparison to the Holstein polaron, but that the resulting $T_\mathrm{c}$ gains are small in the weak coupling limit. We also find that the SSH model's pairing correlations are suppressed after including a weak on-site Hubbard repulsion. These results have important implications for identifying and engineering bipolaronic superconductivity.

arXiv:2307.10809•Jul 20, 2023•0 citations
We survey polaron formation in the Barisi\ifmmode \acute{c}\else '{c}\fi{}-Labb'e-Friedel and Su-Schrieffer-Heeger (BLF-SSH) model using acoustic phonons in the adiabatic limit. Multiple different numerical optimization routines and strong-coupling analytical calculations are used to find a robust ground-state energy for a wide range of coupling strengths. The electronic configuration and accompanying ionic distortions of the polaron were determined, as well as a nonzero critical coupling strength for polaron formation in two and three dimensions.
The electron-phonon interaction is one of the fundamental interactions in almost all condensed matter materials. In conventional superconductors, the electron-phonon interaction is the glue that attracts two electrons to one another to form a pair. A strong electron-phonon interaction leads to the concept of a polaron, which is an electron with lattice distortions around it. The small polaron is a polaron with spatial extent comparable to an interatomic dimension of the solid. Evidence for polarons has been identified in many experiments in superconductors and semiconductors. In this thesis we present exact calculations of the polaron. Specifically we have refined Trugman's method to solve the ground state of an electron-phonon coupled system in the whole parameter regime, and we also generalized this method to treat spin-orbit coupled systems. The most difficult regimes, which is the strong-coupling regime and the small phonon frequency limit, have been solved by these refinements. There are three representative kinds of electron-phonon interaction, the Holstein model, the Fr"ohlich model and the BLF-SSH model. In this thesis we have addressed the first and the third one. The second one, the Fr"ohlich model, is very similar to the Holstein model but the interaction is nonlocal. For the Holstein model we have observed the expected smooth crossover from free electrons to small polarons, while for the BLF-SSH model, we have studied the weak coupling regime with perturbation theory and derived a new analytical result for the one-dimensional problem.
Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the k=0k=0k=0 effective mass diverges, now becomes a transition line in the coupling constant plane---the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No ``self-trapping transition'' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.
We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).
Electrons interacting with the ions in a solid, or polarons, are some of the most basic condensed matter quasi-particles. They influence the electric conductivity in normal metals, but perhaps most fascinatingly, they mediate the formation of Cooper pairs in low temperature superconductors. The details of this phonon mediation are poorly understood at the level of a microscopic Hamiltonian. The Hamiltonian for basic polaron models has only recently been solved for the single electron, and seems to predict that the polarons in low temperature superconductors would have very large effective masses. This is at odds with the measured small effective masses of many low temperature superconductors in the normal state. In this thesis we examine extensions to the basic Holstein polaron Hamiltonian that provide a more realistic model of what happens in real materials. We also look at the BLF-SSH model, which is the appropriate Hamiltonian for superconductors without optical phonons such as the elemental superconductors. We found that extending the Holstein model to include next nearest neighbour electron hopping and nearest neighbour electron-phonon interactions changed the effective mass slightly, but nowhere near enough to account for the low effective masses that must be present in real materials. The BLF-SSH model was examined in the adiabatic limit and with weak-coupling perturbation theory, but an exact solution was not found. It seems likely that the effective mass for this model is also very large, but an improved algorithm is necessary to prove this. A potential path forward is presented in the appendix.
Su-Schrieffer-Heeger (SSH) electron-phonon ($e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$) interactions have been theorized to play critical roles in several novel states of matter, ranging from nontrivial topological states to high-temperature bipolaronic superconductivity. This work compares the superconducting and competing charge and bond correlations of the two-dimensional Holstein and optical (SSH) models. The authors find that near half-filling, light SSH (bi)polarons support superconductivity to larger values of $e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$ coupling compared to the Holstein polaron. These results are essential for identifying and engineering bipolaronic superconductivity in quantum materials.
Theoretical studies suggest that Su-Schrieffer-Heeger-like electron-phonon (eee-ph) interactions can mediate high-temperature bipolaronic superconductivity that is robust against repulsive electron-electron interactions. Here we present a comparative analysis of the pairing and competing charge/bond correlations in the two-dimensional Holstein and optical Su-Schrieffer-Heeger (SSH) models using numerically exact determinant quantum Monte Carlo. We find that the SSH interactions support light bipolarons and strong superconducting correlations out to relatively large values of the eee-ph coupling λλλ and densities near half-filling, while the Holstein interaction does not due to the formation of heavy bipolarons and competing charge-density-wave order. We further find that the Holstein and SSH models have comparable pairing correlations in the weak coupling limit for carrier concentrations ⟨n⟩≪1\langle n \rangle \ll 1⟨n⟩≪1, where competing orders and polaronic effects are absent. These results support the proposal that SSH (bi)polarons can support superconductivity to larger values of λλλ in comparison to the Holstein polaron, but that the resulting TcT_\mathrm{c}Tc​ gains are small in the weak coupling limit. We also find that the SSH model's pairing correlations are suppressed after including a weak on-site Hubbard repulsion. These results have important implications for identifying and engineering bipolaronic superconductivity.