Search

Quantifying electron-phonon interactions for the surface states of topological materials can provide key insights into surface-state transport, topological superconductivity, and potentially how to manipulate the surface state using a structural degree of freedom. We perform time-resolved x-ray diffraction (XRD) and angle-resolved photoemission (ARPES) measurements on Bi$_2$Te$_3$ and Bi$_2$Se$_3$, following the excitation of coherent A$_{1g}$ optical phonons. We extract and compare the deformation potentials coupling the surface electronic states to local A$_{1g}$-like displacements in these two materials using the experimentally determined atomic displacements from XRD and electron band shifts from ARPES.We find the coupling in Bi$_2$Te$_3$ and Bi$_2$Se$_3$ to be similar and in general in agreement with expectations from density functional theory. We establish a methodology that quantifies the mode-specific electron-phonon coupling experimentally, allowing detailed comparison to theory. Our results shed light on fundamental processes in topological insulators involving electron-phonon coupling.

We investigate coupled electron-lattice dynamics in the topological insulator Bi2Te3 with time-resolved photoemission and time-resolved x-ray diffraction. It is well established that coherent phonons can be launched by optical excitation, but selection rules generally restrict these modes to zone-center wavevectors and Raman-active branches. We find that the topological surface state couples to additional modes, including a continuum of surface-projected bulk modes from both Raman- and infrared-branches, with possible contributions from surface-localized modes when they exist. Our calculations show that this surface vibrational spectrum occurs naturally as a consequence of the translational and inversion symmetries broken at the surface, without requiring the splitting-off of surface-localized phonon modes. The generality of this result suggests that coherent phonon spectra are useful by providing unique fingerprints for identifying surface states in more controversial materials. These effects may also expand the phase space for tailoring surface state wavefunctions via ultrafast optical excitation.

We report the observation of a novel nonlinear optical response from the prototypical three-dimensional topological insulator Bi$_2$Se$_3$ through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. Our study reveals a new platform for chiral strong-field physics and presents a novel, contact-free, all-optical approach for the spectroscopy of topological insulators. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation., Comment: 21 pages, 5 figures

We determine experimentally the excited-state interatomic forces in photoexcited bismuth. The forces are obtained by a constrained least-squares fit of the excited-state dispersion obtained by femtosecond time-resolved x-ray diffuse scattering to a fifteen-nearest neighbor Born-von Karman model. We find that the observed softening of the zone-center $A_{1g}$ optical mode and transverse acoustic modes with photoexcitation are primarily due to a weakening of three nearest neighbor forces along the bonding direction. This provides a more complete picture of what drives the partial reversal of the Peierls distortion previously observed in photoexcited bismuth., Comment: 6 pages, 3 figures, plus 3 pages, 3 figures of supplemental information

We observe anharmonic decay of the photoexcited coherent A1g phonon in bismuth to points in the Brillouin zone where conservation of momentum and energy are satisfied for three-phonon scattering. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This results in energy transfer through resonant squeezing of the target modes. Using ultrafast diffuse x-ray scattering, we observe build up of coherent oscillations in the target modes driven by this parametric resonance over a wide range of the Brillouin zone. We compare the extracted anharmonic coupling constant to first principles calculations for a representative decay channel., Comment: 5 pages, 6 figures

One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistic problems, infrastructure difficulties and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast, due to the use of the integrated nested Laplace approximation (INLA). The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and Severe Acute Respiratory Illness (SARI) data in Paran\'a state, Brazil.

Uncertainty of decisions in safety-critical engineering applications can be estimated on the basis of the Bayesian Markov Chain Monte Carlo (MCMC) technique of averaging over decision models. The use of decision tree (DT) models assists experts to interpret causal relations and find factors of the uncertainty. Bayesian averaging also allows experts to estimate the uncertainty accurately when a priori information on the favored structure of DTs is available. Then an expert can select a single DT model, typically the Maximum a Posteriori model, for interpretation purposes. Unfortunately, a priori information on favored structure of DTs is not always available. For this reason, we suggest a new prior on DTs for the Bayesian MCMC technique. We also suggest a new procedure of selecting a single DT and describe an application scenario. In our experiments on the Short-Term Conflict Alert data our technique outperforms the existing Bayesian techniques in predictive accuracy of the selected single DTs.

Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes that is of crucial importance for safety critical applications. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the classifier diversity and the required performance. The interpretability of MCSs can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models for experts. The required diversity of MCSs exploiting such classification models can be achieved by using two techniques, the Bayesian model averaging and the randomised DT ensemble. Both techniques have revealed promising results when applied to real-world problems. In this paper we experimentally compare the classification uncertainty of the Bayesian model averaging with a restarting strategy and the randomised DT ensemble on a synthetic dataset and some domain problems commonly used in the machine learning community. To make the Bayesian DT averaging feasible, we use a Markov Chain Monte Carlo technique. The classification uncertainty is evaluated within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. Exploring a full posterior distribution, this technique produces realistic estimates which can be easily interpreted in statistical terms. In our experiments we found out that the Bayesian DTs are superior to the randomised DT ensembles within the Uncertainty Envelope technique.

Bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be estimated. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the diversity of a classifier ensemble and the required performance. The interpretability of classification models can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models. The required diversity of the DT ensemble can be achieved by using the Bayesian model averaging all possible DTs. In practice, the Bayesian approach can be implemented on the base of a Markov Chain Monte Carlo (MCMC) technique of random sampling from the posterior distribution. For sampling large DTs, the MCMC method is extended by Reversible Jump technique which allows inducing DTs under given priors. For the case when the prior information on the DT size is unavailable, the sweeping technique defining the prior implicitly reveals a better performance. Within this Chapter we explore the classification uncertainty of the Bayesian MCMC techniques on some datasets from the StatLog Repository and real financial data. The classification uncertainty is compared within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. This technique provides realistic estimates of the classification uncertainty which can be easily interpreted in statistical terms with the aim of risk evaluation.