Anomalous Behavior of the $$E_{u}^{1}$$ Infrared-active Phonon Mode in Bi2 – xSrxSe3 Crystal

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“…The strongest absorption peak for both MBT and MBST is located at ∼1.5 THz, and can be identified as the IR active phonon mode E u , which is in agreement with the theoretical estimation from first principle DFT calculations [25]. The E u phonon mode displays two significant temperature dependent features: (i) the phonon peak undergoes a blue-shift (∼ 0.1 THz for MBT and ∼ 0.2 THz for MBST ) upon increasing the sample temperature (from 7K to 250K), which is an anomalous behaviour [35][36][37] The black continuous line represents the corresponding fit using Eq. ( 1).…”

“…Also, the thermal behaviour of lattices are generally expansive in nature (positive thermal coefficient) and therefore it decreases phonon frequency with increasing temperature unlike here [44,57]. For electron phonon coupling in TIs, phonons mostly couple with surface electron transitions [21,35] creating an electron-hole pair [52]. As discussed before, in case of MBT, the Fermi level is much above the Dirac-node of the surface state, and hence the probability of such transitions is extremely low, causing negligible electron-phonon coupling strength [54].…”

“…This unusual behavior has also been attributed to arise from the coupling between the phonons and other degrees of freedom such as charge or spin [49,50]. However in case of TIs, the coupling between surface state electrons and the bulk phonons was identified as the cause of the anomalous softening of the corresponding phonon modes [35,45]. Exact reason for this anomalous phonon behavior and the influence of surface electron-bulk phonon coupling on it, will be discussed further below, followed by discussing the Fano asymmetry which is related to the electron-phonon coupling strength.…”

“…1(b)), which causes substantial filling of surface states and prevents excitation of surface electrons. Whereas, Fermi level gets shifted towards the valence band and comes closer to the Dirac node in MBST, which increases the availability of vacant states for the surface electron transitions significantly [54], (ii) Doping MBT with the lighter atom Sb can increase the penetration depth of the wavefunction of TSS into the bulk via modulating spin orbit coupling and bulk bandgap [21,38], similar to In [21,38] and Sr [35] atom substitution in Bi 2 Se 3 . Therefore, MBST can host a larger spatial overlap between TSS and bulk, which causes stronger Fano interference [21,35] and results in much higher value of |1/q| compared to MBT.…”

Feasibility of Correlated Extensive Air Shower Detection with a Distributed Cosmic-Ray Network

“…Besides the GZ effect, a large class of theorized physical mechanisms exist in literature that motivate wavefronts of UHECR particles and nuclei arriving at Earth simultaneously. A comprehensive list includes relativistic dust grains (Spitzer 1949;Wickramasinghe 1972Wickramasinghe , 1974Epstein1980); cosmic electromagnetic cascades from ultrahigh-energy gamma-ray pair-production (preshowers; Nikishov 1962;Goldreich & Morrison 1964;Jelley 1966;Gould & Schréder 1967;Stecker 1969); super-GZK neutrinos (the Z-Burst scenario; Berezinsky & Zatsepin 1969;Weiler 1982;Roulet 1993;Fargion et al 1999); extradimensions and localized gravity (the Gravi-Burst scenario; Davoudiasl et al 2002); and lastly a collection of so-called top-down exotics that result in Standard Model particles through radiation, annihilation, or collapse processes (Kibble 1976;Hill 1983;Vilenkin 1985;Hill et al 1987;Bhattacharjee 1989;Bhattacharjee & Rana 1990;Brandenberger 1994;Bhattacharjee & Sigl 1995;Hindmarsh & Kibble 1995;Berezinsky & Vilenkin 1997;Chung et al 1998;Masperi & Silva 1998;Masperi & Orsaria 2002;Dave & Taboada 2019).…”