Nonlinear optical probe of tunable surface electrons on a topological insulator

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi$_2$Se$_3$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi$_2$Se$_3$. Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces

Semimetal to semimetal charge density wave transition in 1T-TiSe2_2

We report an infrared study on 1$T$-TiSe$_2$, the parent compound of the newly discovered superconductor Cu$_x$TiSe$_2$. Previous studies of this compound have not conclusively resolved whether it is a semimetal or a semiconductor: information that is important in determining the origin of its unconventional CDW transition. Here we present optical spectroscopy results that clearly reveal that the compound is metallic in both the high-temperature normal phase and the low-temperature CDW phase. The carrier scattering rate is dramatically different in the normal and CDW phases and the carrier density is found to change with temperature. We conclude that the observed properties can be explained within the scenario of an Overhauser-type CDW mechanism.Comment: 4 pages, 4 page

Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape

An estimate is derived for the volume fraction of a subset $C_{\epsilon}^{P} = \{U : ||grad J(U)|\leq {\epsilon}\}\subset\mathrm{U}(N)$ in the neighborhood of the critical set $C^{P}\simeq\mathrm{U}(\mathbf{n})P\mathrm{U}(\mathbf{m})$ of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O), where $U$ represents the unitary time evolution operator, {\rho} is the initial density matrix of the ensemble, and O is an observable operator. This estimate is based on the Hilbert-Schmidt geometry for the unitary group and a first-order approximation of $||grad J(U)||^2$. An upper bound on these near-critical volumes is conjectured and supported by numerical simulation, leading to an asymptotic analysis as the dimension $N$ of the quantum system rises in which the volume fractions of these "near-critical" sets decrease to zero as $N$ increases. This result helps explain the apparent lack of influence exerted by the many saddles of $J$ over the gradient flow.Comment: 27 pages, 1 figur

Anomalous metallic state of Cu0.07_{0.07}TiSe2_2: an optical spectroscopy study

We report an optical spectroscopy study on the newly discovered superconductor Cu$_{0.07}$TiSe$_2$. Consistent with the development from a semimetal or semiconductor with a very small indirect energy gap upon doping TiSe$_2$, it is found that the compound has a low carrier density. Most remarkably, the study reveals a substantial shift of the "screened" plasma edge in reflectance towards high energy with decreasing temperature. This phenomenon, rarely seen in metals, indicates either a sizeable increase of the conducting carrier concentration or/and a decrease of the effective mass of carriers with reducing temperature. We attribute the shift primarily to the later effect.Comment: 4 figures, 4+ page

Nonlinear and time-resolved optical study of the 112-type iron-based superconductor parent Ca_(1−x)La_xFeAs_2 across its structural phase transition

The newly discovered 112-type ferropnictide superconductors contain chains of As atoms that break the tetragonal symmetry between the ɑ and b axes. This feature eliminates the need for uniaxial strain that is usually required to stabilize large single domains in the electronic nematic state that exists in the vicinity of magnetic order in the iron-based superconductors. We report detailed structural symmetry measurements of 112-type Ca_(0.73)La_(0.27)FeAs_2 using rotational anisotropy optical second-harmonic generation. This technique is complementary to diffraction experiments and enables a precise determination of the point-group symmetry of a crystal. By combining our measurements with density functional theory calculations, we uncover a strong optical second-harmonic response of bulk electric dipole origin from the Fe and Ca 3d-derived states that enables us to assign C_2 as the crystallographic point group. This makes the 112-type materials high-temperature superconductors without a center of inversion, allowing for the possible mixing of singlet and triplet Cooper pairs in the superconducting state. We also perform pump-probe transient reflectivity experiments that reveal a 4.6-THz phonon mode associated with the out-of-plane motion of As atoms in the FeAs layers. We do not observe any suppression of the optical second-harmonic response or shift in the phonon frequency upon cooling through the reported monoclinic-to-triclinic transition at 58 K. This allows us to identify C_1 as the low-temperature crystallographic point group but suggests that structural changes induced by long-range magnetic order are subtle and do not significantly affect electronic states near the Fermi level