Driven or non-equilibrium Dirac materials (DMs) offer a new platform for investigation of collective instabilities. Pump-probe photoemmission experiments on Dirac states in graphene have demonstrated the existence of a broadband population inversion, a situation when highly excited electrons and holes form two independent Fermi-Dirac distributions with separate chemical potentials. The lifetime of population inversion in graphene is of the order of 100 fs. Population inversion has also been demonstrated in three-dimensional topological insulators (3D TIs) with much longer lifetimes, ranging from few picoseconds (ps) to hundreds of ps. Much less is known about the dynamics of photoexcited carriers in 3D DMs such as Dirac and Weyl semimetals. However, examples of pump-probe experiments similar to those done on graphene and 3D TIs have already appeared in the literature.
Motivated by these experiments, we proposed to search for transient excitonic instability in optically-excited DMs with population inversion. Given the Dirac nature of the spectrum, the inverted population allows the optical tunability of the density of states (DOS) of the electrons and holes, effectively offering control of the strength of the Coulomb interaction. In 2D, this tunability is unique to DMs and is not available in metals or semiconductors which possess a constant DOS at low energies. In a pumped DM with population inversion, electrons and holes at the two Fermi surfaces experience a mutual Coulomb attraction and can form electron-hole pairs. At low temperatures such electron-hole pairs condense to form a superfluid phase known as an excitonic insulator. Due to the non-equilibrium nature of electron and hole populations in pumped systems, we refer to this collective state as a transient excitonic condensate.
Previous work considered excitonic condensates in various systems and setups, e.g. in narrow-gap semiconductors, electron-hole bilayers which are realizable in semiconductor heterostructures, graphene bilayers in the quantum Hall regime, and in optically excited semiconductirs. Optically-pumped DMs offer a unique platform for transient excitonic condensate because of the tunability of the effective coupling strength. As a result, the condensate can potentially occur at temperatures that are orders of magnitude larger than in systems studied previously.
We showed that the critical temperature and the size of the excitonic gap in optically-pumped DMs is controlled by the interplay between the enhanced DOS at the non-equilibrium chemical potentials and metallic screening which grows with the chemical potentials, the value of the coupling constant and the Dirac cone degeneracy. Based on this we derive a set of criteria to identify the best material candidates for observing the transient collective states. We also propose the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements.
Among the existing DMs, we predict the largest effect, a gap on the order of 10meV and a critical temperature of 70K, in undoped suspended graphene in which optical pumping is realized selectively on a single valley, e.g. using circularly polarized light. Such gap sizes are large enough to be detected by angle-resolved photoemission spectroscopy (ARPES). We also find that 3D TIs with a single Dirac cone and long-lived photoexcited states are promising candidates, leading to gap sizes of the order of few eV and critical temperatures of tens of K. By tuning the material properties, large gaps and critical temperature could be found in new 3D DMs.
- Excitonic gap formation in pumped Dirac materials
C. Triola, A. Pertsova, R. S. Markiewicz, and A. V. Balatsky,
Phys. Rev. B, 95 205410 (2017)
- Excitonic instability in optically pumped three-dimensional Dirac materials
A. Pertsova and A. V. Balatsky
Phys. Rev. B 97, 075109 (2018)