Accessing the Anisotropic Nonthermal Phonon Populations in Black Phosphorus

Abstract

We combine ultrafast electron diffuse scattering experiments and first-principles calculations of the coupled electron–phonon dynamics to provide a detailed momentum-resolved picture of lattice thermalization in black phosphorus. The measurements reveal the emergence of highly anisotropic nonthermal phonon populations persisting for several picoseconds after exciting the electrons with a light pulse. Ultrafast dynamics simulations based on the time-dependent Boltzmann formalism are supplemented by calculations of the structure factor, defining an approach to reproduce the experimental signatures of nonequilibrium structural dynamics. The combination of experiments and theory enables us to identify highly anisotropic electron–phonon scattering processes as the primary driving force of the nonequilibrium lattice dynamics in black phosphorus. Our approach paves the way toward unravelling and controlling microscopic energy flows in two-dimensional materials and van der Waals heterostructures, and may be extended to other nonequilibrium phenomena involving coupled electron–phonon dynamics such as superconductivity, phase transitions, or polaron physics.

Nonequilibrium Lattice Dynamics in Monolayer MoS2

“…30,31 These manifest themselves through the emergence of hot-spots in the FEDS intensity, which indicates local enhancement of the phonon population at selected high-symmetry points and directions in the Brillouin zone. 28,[31][32][33]33,34 A quantitative understanding of these phenomena is challenging owing to the combined influence of valley degrees of freedom, lattice anharmonicities, and anisotropies of the electron-phonon interaction on the lattice dynamics. Despite providing valuable insight into the carrier dynamics of two-dimensional and layered materials, [35][36][37] the concept of hot phonon -whereby the hot-carrier relaxation is assumed to be dominated by a few stronglycoupled phonon modes [38][39][40][41][42] -is unsuitable for the description of these phenomena, since it inherently lacks a momentum-resolved description of the lattice dynamics.…”

Properties and challenges of hot-phonon physics in metals: MgB$_2$ and other compounds

“…Equations ( 2)- (7) [and hence Eqs. ( 9)-( 10)] form a closed set of integrodifferential equations which can be solved explicitly via conventional timepropagation algorithms to investigate the non-equilibrium dynamics of electronic and vibrational degrees of freedom [124][125][126]. In 3D metallic compounds, the solution of the Boltzmann equation is computationally very demanding due to the need of extremely dense meshes to sample phonon-assisted particlehole transitions in a sufficiently wide region of reciprocal space (see Fig.…”

“…The presence and an active role of hot phonons is also commonly revealed in the analysis of the time dependence of electronic properties upon nonequilibrium conditions. Given the plethora of ultrafast pump-probe experiments nowadays accessible, the physical properties under investigation can vary in a wide range, from optical probes (transmission [77,84,85,87,150,151], reflectivity [13,89,[110][111][112][152][153][154], absorption [91,[155][156][157][158]) to non-linear optics [86], time-resolved photoelectron spectroscopy [108,132,133,[159][160][161][162], photoluminescence [83,163], time-dependent Raman probes [164], ultrafast diffraction [6,44,109,126,[165][166][167][168][169][170][171].…”

Fingerprints of hot-phonon physics in time-resolved correlated quantum lattice dynamics

“…However, the thermalization process of some materials can be hindered by the so-called phonon bottleneck [2,3,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] that quenches the energy transfer between electron and lattice degrees of freedom. Such a physical phenomenon is usually encountered in semiconductors and semimetals where the pump-driven particle-hole excitations are restricted to few single points (valleys) in the Brillouin zone.…”

“…As related to the analysis of time-independent quantities, our proposal is not affected by the limitations of uncertainty principle. Note that the present analysis, here applied to the paradigmatic case of MgB 2 , does not rely on specific properties of this material but it can be employed as well in other compounds, such as single-layer and multi-layer graphene [47,48], transition metal dichalcogenides [49], black phosphorous [34,50], and hole-doped diamond [51,52], where el-ph coupling plays a major role.…”