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We introduce an 𝓛₂-type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed on the basis of the pairwise distance covariance and it accounts for the non-linear and non-monotone dependences among the data, which cannot be fully captured by the existing tests based on either Pearson correlation or rank correlation. Our test can be conveniently implemented in practice as the limiting null distribution of the test statistic is shown to be standard normal. It exhibits excellent finite sample performance in our simulation studies even when the sample size is small albeit the dimension is high and is shown to identify non-linear dependence in empirical data analysis successfully. On the theory side, asymptotic normality of our test statistic is shown under quite mild moment assumptions and with little restriction on the growth rate of the dimension as a function of sample size. As a demonstration of good power properties for our distance-covariance-based test, we further show that an infeasible version of our test statistic has the rate optimality in the class of Gaussian distributions with equal correlation.

Recent works have demonstrated that the Floquet-Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energy-like quantity that defines the spectrum of a periodically-driven system. Here we develop a new paradigm for the topological classification of Floquet-Bloch bands, based on the time-dependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologically-protected degeneracies at intermediate times, which control the topology of the Floquet bands of the full driving cycle. This approach provides a natural framework for incorporating the role of symmetries, enabling a unified and complete classification of Floquet-Bloch bands and yielding new insight into the topological features that distinguish driven and non-driven systems.

The recently discovered intrinsic magnetic topological insulatorMnBi2Te4has been met with unusual success in hosting emergent phenomena such as the quantum anomalous Hall effect and the axion insulator states. However, the surface-bulk correspondence of the Mn-Bi-Te family, composed by the superlatticelikeMnBi2Te4/(Bi2Te3)n(n=0,1,2,3…) layered structure, remains intriguing but elusive. Here, by using scanning tunneling microscopy and angle-resolved photoemission spectroscopy techniques, we unambiguously assign the two distinct surface states ofMnBi4Te7(n=1) to the quintuple-layer (QL)Bi2Te3termination and the septuple-layer (SL)MnBi2Te4termination, respectively. A comparison of the experimental observations with theoretical calculations reveals diverging topological behaviors, especially the hybridization effect between the QL and SL, on the two terminations. We identify a gap on the QL termination, originating from the hybridization between the topological surface states of the QL and the bands of the SL beneath, and a gapless Dirac-cone band structure on the SL termination with time-reversal symmetry. The quasiparticle interference patterns further confirm the topological nature of the surface states for both terminations, continuing far above the Fermi energy. The QL termination carries a spin-helical Dirac state with hexagonal warping, while at the SL termination, a strongly canted helical state from the surface lies between a pair of Rashba-like splitting bands from its neighboring layer. Our work elucidates an unprecedented hybridization effect between the building blocks of the topological surface states and also reveals the termination-dependent time-reversal symmetry breaking in a magnetic topological insulator.

The observation of 1/B-periodic behavior in Kondo insulators and semiconductor quantum wells challenges the conventional wisdom that quantum oscillations (QOs) necessarily arise from Fermi surfaces in metals.We revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure.We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast to metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations arising from occupied Landau levels occur at the same frequency that would exist in the unhybridized case.The LE-DOS oscillations in a disorder-free system are dominated by gap-edge states and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder-induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the amplitude and phase of the magnetization and DOS oscillations are also qualitatively different and show marked deviations fromthe Lifshitz—Kosevich form well known inmetals.We also compute transport to ensure that we are probing a regime with insulating upturns in the direct current (DC) resistivity.

Recent experiments, combing ultrafast strong-field irradiation of surfaces with time- and angle-resolved photoemission spectroscopy, allow for monitoring the time-dependent charge carrier dynamics and the build-up of transient sidebands due to the radiation pulses. While these structures are reminiscent of Floquet–Bloch bands, standard Floquet theory is not applicable since it requires a strictly time-periodic driving field. To study the emergence and formation of such sidebands, i.e. to provide a link between common Floquet physics and dynamical mechanisms underlying short driving pulses, we consider a generalization of Floquet theory, the so-called t − t ′ formalism. This approach naturally extents Floquet theory to driving field amplitudes with a superimposed envelope shape. Motivated by experiments we study 2D Dirac Hamiltonians subject to linearly and circularly polarised light waves with a Gaussian field envelope of a few cycles. For these Floquet–Bloch Hamiltonians we study the evolution of their Floquet–Bloch spectra, accompanied by a systematic analysis of the time-dependent (sideband) transitions. We show that sideband occupation requires circularly polarized light for linear Dirac systems such as graphene, while for Dirac models with trigonal warping, describing surface states of topological insulators such as Bi 2 Se 3 , both linearly and circularly polarised pulses induce sideband excitations.

Analogous to the condensation of Cooper pairs in superconductors, the Bose–Einstein condensation (BEC) of electron–hole pairs in semiconductors and semimetals leads to an emergence of an exotic ground state — the excitonic insulator state. In this paper, we study the electronic structure of 1 T -TiSe 2 utilizing angle-resolved photoemission spectroscopy and alkali-metal deposition. Alkali-metal adatoms are deposited in-situ on the sample surface, doping the system with electrons. The conduction bands of 1 T -TiSe 2 are thereby pushed down below the Fermi energy, which enables us to characterize its temperature dependence with precision. We found that the formation of the charge density wave (CDW) in 1 T -TiSe 2 at ~ 205 K is accompanied by a significant increase of the band gap, supporting the existence of excitonic pairing in the CDW state of 1 T -TiSe 2 . More importantly, by analyzing the linewidth of the single-particle excitation spectrum, we unveiled an incoherence-to-coherence crossover at 165 K, which could be attributed to a possible exciton condensation that occurs beneath the CDW transition in 1 T -TiSe 2 . Our results not only explain the exotic transport properties of 1 T -TiSe 2 , but also highlight the possible existence of an excitonic condensate in this semiconducting material. Excitonic insulators remain a topic of great interest in condensed matter physics. Here, the authors provide spectroscopic evidence of increased electronic coherence in the charge-density-wave state of semiconducting 1 T -TiSe 2 .

Among the families of transition metal dichalcogenides (TMDs), Pd-based TMDs have been one of the less explored materials. In this study, we investigate the electronic properties of PdX2 (X = S, Se, or Te) bulk and thin films. The analysis of structural stability shows that the bulk and thin film (1 to 5 layers) structures of PdS2 exhibit pyrite, while PdTe2 exhibits 1T. Furthermore, PdSe2 exhibits pyrite in bulk and thin films down to the bilayer. Most surprisingly, PdSe2 monolayer transits to 1T phase. For the electronic properties of the stable bulk configurations, pyrite PdS2 and PdSe2, and 1T PdTe2, demonstrate semi-metallic features. For monolayer, on the other hand, the stable pyrite PdS2 and 1T PdSe2 monolayers are insulating with band gaps of 1.399 eV and 0.778 eV, respectively, while 1T PdTe2 monolayer remains to be semi-metallic. The band structures of all the materials demonstrate a decreasing or closing of indirect band gap with increasing thickness. Moreover, the stable monolayer band structures of PdS2 and PdSe2 exhibit flat bands and diverging density of states near the Fermi level, indicating the presence of van Hove singularity. Our results show the sensitivity and tunability of the electronic properties of PdX2 for various potential applications.

Strong electron-electron interaction can induce Mott insulating state, which is believed to host unusual correlated phenomena such as quantum spin liquid when quantum fluctuation dominates and unconventional superconductivity through doping. Transition metal compounds as correlated materials provide a versatile platform to engineer the Mott insulating state. Previous studies mostly focused on the controlling of the repulsive interaction and bandwidth of the electrons by gating or doping. Here, we performed angle-resolved photoemission spectroscopy (ARPES) on monolayer 1T phase NbSe 2 , TaSe 2 , and TaS 2 and directly observed their band structures with characteristic lower Hubbard bands. By systematically investigating the orbital textures and temperature dependence of the energy gap of the materials in this family, we discovered that hybridization of the chalcogen p states with lower Hubbard band stabilizes the Mott phase via tuning of the bandwidth, as shown by a significant increase of the transition temperature ( T C ) at a stronger hybridization strength. Our findings reveal a mechanism for realizing a robust Mott insulating phase and establish monolayer 1T phase transition metal dichalcogenide family as a promising platform for exploring correlated electron problems. Transition metal compounds provide a versatile platform for tailoring Mott physics. Here, the authors reveal that hybridization between the lower Hubbard band and the chalcogen band stabilizes the Mott state through bandwidth tuning in the 1T-MX 2 (M = Nb, Ta; X = S, Se) family.

Perception and production of music and speech rely on auditory–motor coupling, a mechanism which has been linked to temporally precise oscillatory coupling between auditory and motor regions of the human brain, particularly in the beta frequency band. Recently, brain imaging studies using magnetoencephalography (MEG) have also shown that accurate auditory temporal predictions specifically depend on phase coherence between auditory and motor cortical regions. However, it is not yet clear whether this tight oscillatory phase coupling is an intrinsic feature of the auditory–motor loop, or whether it is only elicited by task demands. Further, we do not know if phase synchrony is uniquely enhanced in the auditory–motor system compared to other sensorimotor modalities, or to which degree it is amplified by musical training. In order to resolve these questions, we measured the degree of phase locking between motor regions and auditory or visual areas in musicians and non‐musicians using resting‐state MEG. We derived phase locking values (PLVs) and phase transfer entropy (PTE) values from 90 healthy young participants. We observed significantly higher PLVs across all auditory–motor pairings compared to all visuomotor pairings in all frequency bands. The pairing with the highest degree of phase synchrony was right primary auditory cortex with right ventral premotor cortex, a connection which has been highlighted in previous literature on auditory–motor coupling. Additionally, we observed that auditory–motor and visuomotor PLVs were significantly higher across all structures in the right hemisphere, and we found the highest differences between auditory and visual PLVs in the theta, alpha, and beta frequency bands. Last, we found that the theta and beta bands exhibited a preference for a motor‐to‐auditory PTE direction and that the alpha and gamma bands exhibited the opposite preference for an auditory‐to‐motor PTE direction. Taken together, these findings confirm our hypotheses that motor phase synchrony is significantly enhanced in auditory compared to visual cortical regions at rest, that these differences are highest across the theta‐beta spectrum of frequencies, and that there exist alternating information flow loops across auditory–motor structures as a function of frequency. In our view, this supports the existence of an intrinsic, time‐based coupling for low‐latency integration of sounds and movements which involves synchronized phasic activity between primary auditory cortex with motor and premotor cortical areas. We provide evidence that human auditory–motor networks show stronger phase coupling than visuomotor networks. Auditory–motor phase‐coupling was greatest in right hemisphere and its strength varied consistently across motor regions. This intrinsic coupling we discovered may underlie the fast integration of sound and movement required for speech and music.

The growing demand for electricity has increased the interest of the researchers towards exploration of energy storing devices (ESDs). With the motif for developing electrochemical energy storage devices, this research work is focussed on the study of MoO 3 nanoparticles and its doping with chromium as an efficient electrode material for energy storage applications. The nanoparticles were synthesized by hydrothermal method and were examined by powder X-ray diffraction, which determined the thermodynamically stable orthorhombic phase of MoO 3 , and their morphologies were examined using scanning electron microscopy displaying flake-like structures. The typical vibrational bands of Mo–O were identified from Infra-red and Raman spectral analysis. The ultra violet diffuse reflectance spectra revealed the decrease in optical band gap after doping with chromium. The temperature dependent AC and DC conductivities were enhanced on doping. Electrochemical behaviour of the nanoparticles was probed by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS) measurements and galvanostatic charge–discharge (GCD) analysis for which specific capacitance ( C sp ) value of 334 Fg −1 was achieved for Cr-doped MoO 3 nanoparticles. The electrochemical performance of the sample was found to be increased after doping with Cr.