Discontinuous polaron transition in a two-band model

Abstract

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 novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=\pi$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-band 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 multi-band models in higher dimensions

Type-II Dirac semimetal stabilized by electron-phonon coupling

“…1 , where we see that the GS moves from M to X for some α ≤ 0.2 (for all values of α , we scanned the whole BZ; the GS is always either at M or X ). This looks, therefore, like the discontinuous sharp GS transition found for the 1D version of this model 36 , coming from a change in the shape of the lowest polaron band. However, the behavior here is more interesting and rich than in the 1D model.…”

“…The odd p − band couples more efficiently to phonons 36 and moves faster toward lower energies with increasing electron–phonon coupling, so that for α ≈ 0.3 the two bands touch at the M point. For even larger α , the p − band becomes the low-energy band near M , and a tilted Dirac point appears where the two bands cross.…”

“… 33 , only smooth crossovers are allowed in such models, suggesting that quasiparticle states never cross each other because the phonon clouds always mediate some degree of level repulsion, so the existence of Dirac cones is impossible. Very recently, true transitions have been found in models where the electron–phonon coupling comes from the modulation of the particle hopping 34 – 36 , however what happens here is that the shape of the polaron band changes with increased coupling, so that the miminum moves from the free-particle ground state (GS) momentum to some other value. This may happen continuously 34 , 35 or discontinuously 36 , but again it is not due to level crossing.…”

“…Very recently, true transitions have been found in models where the electron–phonon coupling comes from the modulation of the particle hopping 34 – 36 , however what happens here is that the shape of the polaron band changes with increased coupling, so that the miminum moves from the free-particle ground state (GS) momentum to some other value. This may happen continuously 34 , 35 or discontinuously 36 , but again it is not due to level crossing. It is thus not a priori clear if sharp level crossings can occur in polaron spectra.…”

Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature

“…As can be seen, the development of the theory of interaction of quasi-particles with phonons was almost always performed on the basis of a single-band model. However, recently there appeared an information which proves that the physics of multi-band models that describe the interacting electronphonon systems is significantly different from single-band models, [29,30].…”