Topological insulators (TIs) are characterized by possessing metallic (gapless) surface states and a finite band-gap state in the bulk. As the thickness of a TI layer decreases down to a few nanometers, hybridization between the top and bottom surfaces takes place due to quantum tunneling, consequently at a critical thickness a crossover from a 3D-TI to a 2D insulator occurs. Although such a crossover is generally accessible by scanning tunneling microscopy, or by angle-resolved photoemission spectroscopy, such measurements require clean surfaces. Here, we demonstrate that a cascading nonlinear magneto-optical effect induced via strong spin-orbit coupling can examine such crossovers. The helicity dependence of the time-resolved Kerr rotation exhibits a robust change in periodicity at a critical thickness, from which it is possible to predict the formation of a Dirac cone in a film several quintuple layers thick. This method enables prediction of a Dirac cone using a fundamental nonlinear optical effect that can be applied to a wide range of TIs and related 2D materials.

We study a specific type of lifetime broadening resulting in the well-known exponential "Urbach tail" density of states within the energy gap of an insulator. After establishing the frequency and temperature dependence of the Urbach edge in GaAs quantum wells, we show that the broadening due to the zero-point optical phonons is the fundamental limit to the Urbach slope in high-quality samples. In rough analogy with Welton's heuristic interpretation of the Lamb shift, the zero-temperature contribution to the Urbach slope can be thought of as arising from the electric field of the zero-point longitudinal-optical phonons. The value of this electric field is experimentally measured to be 3  kV cm-1, in excellent agreement with the theoretical estimate.

Chalcogenide superlattices (SLs), formed by the alternate stacking of GeTe and SbTe layers, also referred to as interfacial phase-change memory (iPCM), are a leading candidate for spin-based memory device applications. Theoretically, the iPCM structure has been predicted to form a three-dimensional topological insulator or Dirac semimetal phase depending on the constituent layer thicknesses. Here, we experimentally investigate the topological insulating nature of chalcogenide SLs using a helicity-dependent time-resolved Kerr measurement. The helicity-dependent Kerr signal is observed to exhibit a four-cycle oscillation with π/2 periodicity, suggesting the existence of a Dirac-like cone in some chalcogenide SLs. Furthermore, we found that increasing the thickness of the GeTe layer dramatically changed the periodicity, indicating a phase transition from a Dirac semimetal into a trivial insulator. Our results demonstrate that thickness-tuned chalcogenide SLs can play an important role in the manipulation of topological states, which may open up new possibilities for spintronic devices based on chalcogenide SLs.

State-filling dynamics in self-assembled InAs/GaAs quantum dots (QDs) is studied through their steady-state photoluminescence (PL) using a variant of picosecond excitation-correlation (EC) spectroscopy. Steady-state PL showed an interesting transition from bimolecular recombination at low-excitation fluence to excitonic recombination at higher fluence. As for the EC signal, while the ground-state response is always snubbed when the two excitation pulses are temporally nearly coincident, the excited-state response can either be enhanced or reduced, depending on the excitation fluence. The time evolution of this response is studied for the first three levels in a QD ensemble. A minimal theoretical model, which combines carrier loss kinetics with the principle of detailed balance and the Pauli exclusion principle, quantitatively reproduces the observations.

We explore the ultrafast reflectivity response from photo-generated coupled phonon-surface Dirac plasmons in Sb2Te3 topological insulators several quintuple layers thick. The transient coherent phonon spectra obtained at different time frames exhibit a Fano-like asymmetric line shape of the A 2 1g mode, which is attributed to quantum interference between continuum-like coherent Diracplasmons and phonons. By analyzing the time-dependent asymmetric line shape using the twotemperature model (TTM), it was determined that a Fano-like resonance persisted up to ≈1 ps after photo-excitation with a relaxation profile dominated by Gaussian decay at ≤200 fs. The asymmetry parameter could be well described by the TTM for ≥200 fs, therefore suggesting the coherence time of the Dirac plasmon is ≈200 fs. PACS numbers: 78.47.jg, 63.20.kd Coherent states in condensed media are quantum mechanically described in terms of the annihilation operator, as described by Glauber 1,2 . The concept of coherent states has succeeded in producing the laser 3 . In the last two decades, moreover, the importance of coherent states in solid state physics has greatly increased and new physical effects, such as Bose-Einstein condensation have been discovered 4 . In addition, spin relaxation in quantum spin Hall (QSH) systems 5 has been often studied coupled with the recent discovery of topological insulators 5,6 , and the loss of coherence exhibited by its Gaussian relaxation behavior 7,8 , a characteristic significantly different from exponential relaxation. Thus, Gaussian relaxation is often referred to as a signature of a coherent state.A topological insulator (TI) 6 is a quantum electronic material, which is characterized by an insulating gap in the bulk, while gapless surface states (SSs) exist at the interface with the vacuum or other dielectric materials. The metallic surface states are characterized by massless Dirac quasiparticles, whose scattering is prohibited by time reversal symmetry 9 . Exploiting the birth and decay of quasiparticles on the surface of TIs provides a novel paradigm for future application of TIs to quantum computation 10 , spin electronics 11 , and optical devices 12 . The dynamics of the quasiparticles on a TI surface, however, have been exclusively investigated by means of time-and angle-resolved photoemission spectroscopy under vacuum conditions and only limited information has been obtained 13 .Recently Dirac plasmons have been observed on the surface of TIs in the form of a polariton wave using metamaterials (MMs) 14 . Without the help of MMs, in general, optical techniques are unable to characterize the dynamics of Dirac plasmon-polaritons on the surface of TIs, since momentum conservation requires large wavevectors for the plasmon wave to couple to a photon. Instead of using MMs, one can excite Dirac plasmons by direct coupling using a ≈1.5 eV photon to access the TI surface states 15 . In this alternative case, a film thinner than ∼15 nm for a Bi 2 Se 3 TI is required. Under the conditions that both the Dirac ...