Success Story

Type-II Dirac semimetal stabilized by electron-phonon coupling

Principal Investigators: Mona Berciu, Marcel Franz, and George Sawatzky
HQP: Mirko Möller
Research Theme: Topologically protected quantum states

Understanding the role of topology is a topic of major interest within the condensed matter physics community. To date, researchers have made remarkable progress in classifying topological properties of non-interacting electrons, and on understanding the interplay between topology and electron–electron interactions. We extended such studies to investigate the role of interactions with the lattice, and predicted non-trivial topological effects in infinitely long-lived polaron bands.

First, we proved that a sharp crossing of two polaron bands is indeed possible in a realistic model of electron-phonon coupling. This band crossing is not due to just a trivial renormalization of the bare bands because of coupling to the lattice. Instead, different bands are renormalized differently by the coupling to the lattice and can move past each other. The avoided crossings one would generically expect are prevented along high-symmetry lines due to protection by certain crystal symmetries, opening the way for sharp level crossings. To our knowledge, such crossings had not been explicitly revealed for coherent polaron bands ever before. Moreover, we found that such crossings can lead to a new type of sharp transition in the ground-state properties of the polaron, where the ground-state momentum remains unchanged but a symmetry of its wave function changes discontinuously.

Second, we demonstrated that these crossings lead to the appearance of tilted Dirac points whose location, and even existence, can be controlled through the strength of the electron-phonon coupling. We find that the Dirac points can be stabilized for a wide range of parameters, even those for which the bare bands are far apart, if the electron–phonon coupling is sufficiently large. In practical terms, we envision the use of pump-probe experiments to resonantly excite the relevant phonons and renormalize the strength of their coupling to the carrier. In other words, it may be possible to create Dirac points and to shift their position in the Brillouin zone through optical pumping, opening a new pathway for the realization of topological semimetals.

We studied a 2D Lieb lattice in this work, but it is reasonable to expect that the phenomena described here are not restricted to it. Similar 3D models should stabilize 3D Weyl points, but this is yet to be verified. Ab-initio calculations will be needed to identify suitable candidates for experimental studies.

Recently featured in Nature Communications Editors’ Highlights, the study is important because there are practically no previous studies of topological effects in the polaron bands, in particular, no demonstration that polaron bands can acquire non-trivial topological features as the electron-phonon coupling is tuned.

Second, we demonstrated that these crossings lead to the appearance of tilted Dirac points whose location, and even existence, can be controlled through the strength of the electron-phonon coupling. We find that the Dirac points can be stabilized for a wide range of parameters, even those for which the bare bands are

Polaron spectrum at various electron–phonon couplings (color online). a The infinitely long-lived polaron bands obtained from the spectral function A γ,γ(k, ω). For M → M/2 the symmetry of the bands is indicated in blue for p+ and red for p. Parameters are sp = −1, t pp = −0.49,ϵs = ϵp = 0, Ω = 1 and α = 0.1…0.4. In the bottom panel β = 0.75α, in all other panels β = α/2. (b) The Lieb lattice. Arrows indicate the direction of oscillation of the phonons.

far apart, if the electron–phonon coupling is sufficiently large. In practical terms, we envision the use of pump-probe experiments to resonantly excite the relevant phonons and renormalize the strength of their coupling to the carrier. In other words, it may be possible to create Dirac points and to shift their position in the Brillouin zone through optical pumping, opening a new pathway for the realization of topological semimetals.

We studied a 2D Lieb lattice in this work, but it is reasonable to expect that the phenomena described here are not restricted to it. Similar 3D models should stabilize 3D Weyl points, but this is yet to be verified. Ab-initio calculations will be needed to identify suitable candidates for experimental studies.

Recently featured in Nature Communications Editors’ Highlights, the study is important because there are practically no previous studies of topological effects in the polaron bands, in particular, no demonstration that polaron bands can acquire non-trivial topological features as the electron-phonon coupling is tuned.