Dynamical Birefringence: Electron-Hole Recollisions as Probes of Berry Curvature

Abstract

The direct measurement of Berry phases is still a great challenge in condensed-matter systems. The bottleneck has been the ability to adiabatically drive an electron coherently across a large portion of the Brillouin zone in a solid where the scattering is strong and complicated. We break through this bottleneck and show that high-order sideband generation (HSG) in semiconductors is intimately affected by Berry phases. Electron-hole recollisions and HSG occur when a near-band-gap laser beam excites a semiconductor that is driven by sufficiently strong terahertz-frequency electric fields. We carry out experimental and theoretical studies of HSG from three GaAs=AlGaAs quantum wells. The observed HSG spectra contain sidebands up to the 90th order, to our knowledge the highest-order optical nonlinearity reported in solids. The highest-order sidebands are associated with electron-hole pairs driven coherently across roughly 10% of the Brillouin zone around the Γ point. The principal experimental claim is a dynamical birefringence: the intensity and polarization of the sidebands depend on the relative polarization of the exciting near-infrared (NIR) and the THz electric fields, as well as on the relative orientation of the laser fields with the crystal. We explain dynamical birefringence by generalizing the three-step model for highorder harmonic generation. The hole accumulates Berry phases due to variation of its internal state as the quasimomentum changes under the THz field. Dynamical birefringence arises from quantum interference between time-reversed pairs of electron-hole recollision pathways. We propose a method to use dynamical birefringence to measure Berry curvature in solids.

Imperfect Recollisions in High-Harmonic Generation in Solids

“…electron correlation. We predict that eh-PER should be ubiquitous in a large range of extreme nonlinear phenomena of current interest, such as HHG with elliptical drivers [1,3,4,8,27,35,56,57] and systems with large Berry curvatures [58], as well as high-order sideband generation [59][60][61][62]. The identification of eh-PER and its effect on the harmonic emission profiles, as well as the formulation of the ERM, provides new insights into the HHG process in solids and could potentially stimulate new experiments.…”

Strongly Enhanced Berry Dipole at Topological Phase Transitions in BiTeI

“…A crucial property of BiTeI is the absence of inversion symmetry, which endows the Bloch states with a nonzero Berry curvature. This opens the possibility to analyze the transitions between the topologically distinct electronic phases by means of response functions that are particularly sensitive to the geometry of the Bloch states [9][10][11][12][13][14][15][16]. Recent experiments [17,18] have reported the observation of the time reversal invariant nonlinear Hall effect [9] in two-dimensional transition metal dichalcogenides [19][20][21][22].…”

Optical frequency combs from high-order sideband generation

“…A thin film of ITO was deposited on the backside of the sapphire to create a strong THz cavity to enhance the field in the QWs, see Fig. 1 and [20] for details. The second sample contained 20× 5 nm GaAs/Al 0.3 Ga 0.7 As and was processed in the same fashion.…”

“…The NIR excitation wavelength was kept at 798.3 nm for the 10nm QWs, and 764.1 nm for the 5nm QWs, which correspond to the heavy-hole exciton resonance in each sample. The NIR power was fixed at 50 mW (∼ 250 V/cm), and the polarization was fixed at 90 • relative to the THz polarization to minimize effects due to dynamical birefringence [20]. Reported THz field strengths are those in the QWs, including dielectric screening, and have an error of ±1 kV/cm.…”

“…In HSG, a weak near-infrared (NIR) laser tuned near resonance with the exciton energy in a semiconductor is incident on a sample that is driven by a strong THz field. Similar to the atomic phenomenon of high-order harmonic generation (HHG) [17], a three-step model [18] can be used to describe the following dynamics [19,20]; the NIR laser creates an electron and hole in the semiconductor which the THz field (i) ionizes, (ii) accelerates away from and then back towards each other and (iii) causes to recollide, emitting a sideband photon with higher energy than the NIR laser. Recent time-resolved experiments have observed a delay between electron-hole pair creation and sideband emission [21], which supports this recollision model in solids.…”