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).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:1010.3207Physical Review LettersDec 30, 2010140 citations

One-Dimensional Polarons and Bipolarons in the Strong-Coupling Limit

P. R. Vansant

Jan 1, 19941 citation

Discontinuous polaron transition in a two-band model

Mirko M. Möller, Mona Berciu

We present exact diagonalization and momentum average approximation (MA) results for the single-polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a sharp transition in which the polaron ground state momentum jumps discontinuously from $k=\ensuremath{\pi}$ to $k=0$ . The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multiband nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multiband models in higher dimensions.We present exact diagonalization and momentum average approximation (MA) results for the single-polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a sharp transition in which the polaron ground state momentum jumps discontinuously from $k=\ensuremath{\pi}$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multiband nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multiband models in higher dimensions.

arXiv:1611.04543Physical review. B./Physical review. BJan 22, 201621 citations

Polarons in the strong coupling limit

V. I. Mel'Nikov, Григорий Ефимович Воловик

Journal of Experimental and Theoretical PhysicsApr 1, 19744 citations

Investigating Polaron Transitions with Polar Molecules

Felipe Herrera, Kirk W. Madison, Roman V. Krems +1 more

We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. We then show that ultracold molecules trapped in optical lattices can be used as a quantum simulator to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields. The parameters of current experiments place them in the region where one of the transitions occurs. We also propose a scheme to measure the polaron dispersion using stimulated Raman spectroscopy.We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. We then show that ultracold molecules trapped in optical lattices can be used as a quantum simulator to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields. The parameters of current experiments place them in the region where one of the transitions occurs. We also propose a scheme to measure the polaron dispersion using stimulated Raman spectroscopy.

arXiv:1212.6212Physical Review LettersMay 29, 201355 citations

k=0

. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multiband nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multiband models in higher dimensions.