Excitonic instability in optically pumped three-dimensional Dirac materials

Abstract

Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in opticallypumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by nonequilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. The competition between screening effects and the increase of the density of states with optical pumping results in a reach phase diagram for the transient excitonic condensate. Based on the static theory of screening, we find that under certain conditions for the value of the dimensionless coupling constant screening in 3D DMs can be weaker than in 2D DMs. Furthermore, we identify the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs.

Pump-driven normal-to-excitonic insulator transition: Josephson oscillations and signatures of BEC-BCS crossover in time-resolved ARPES

“…The last decade has seen a renewed interest in systems which are semimetals [30,31] or insulators [32][33][34][35][36][37][38] in the ground state but exhibit an EI phase in some (possibly pumpinduced) nonequilibrium (NEQ) excited state. The optical properties of a NEQ-EI have been calculated by several authors in the past [39][40][41][42].…”

Dynamically Induced Excitonic Instability in Pumped Dirac Materials

“…The Hamiltonian in Equation (1) can be formally derived by diagonalizing the interacting Dirac Hamiltonian H for a 2D or 3D DM and by including the finite chemical potential for electron and hole bands (the procedure is demonstrated in ref. [16] for the case of a DSM/WSM). Thus the electron and hole Hamiltonians are essentially the linearly-dispersing conduction and valence band of the DM, modified by optical pumping…”

“…This finding suggests that prolonged population inversion can be established at least in some 3D DMs. The possibility of achieving an inverted population of electrons and holes by optical pumping, makes optically excited DMs a promising system for realizing a transient excitonic instability …”

“…Such states can be induced by interaction with a timedependent drive such as electromagnetic-fields or coherent lattice vibrations. Prominent recent examples include novel dynamical states in periodically driven systems, such as Floquet topological DOI: 10.1002/andp.201900549 insulators [1][2][3][4][5][6] and time crystals, [7][8][9][10] nonlinear optical and transport effects in graphene and related materials, [11] phonon-driven Floquet states, [12] lightinduced superconductivity, [13,14] and transient, or non-equilibrium, exciton condensate in pumped semimetals [15,16] and semiconductors. [17][18][19] Another example is intrinsically dynamical orders such as odd-frequency, or Berezinskii, superconducting pairing, [20,21] which involves correlations non-local in time and naturally manifests in the time domain, see also related paper in this volume.…”

“…The possibility of achieving an inverted population of electrons and holes by optical pumping, makes optically excited DMs a promising system for realizing a transient excitonic instability. [15,16] Prof. Balatsky's focus lies on Dirac materials and their dynamics, as well as on materials informatics in quantum materials. In these materials strong quantum correlations lead to entangled and resonating orders that often are hidden from conventional observations.…”