Showing papers on "Brillouin zone published in 2015"

Distributions of phonon lifetimes in Brillouin zones

Abstract: A collaboration of researchers from Japan and France present a comprehensive study of phonon lifetimes and thermal conductivity for 33 zincblende- and wurtzite compounds using linearized phonon Boltzmann equation and first-principles anharmonic phonon calculations. The software that the authors created for this study will be released as an open source package and should be of help in the search of new materials for thermoelectric applications.

Experimental observation of Weyl points

Abstract: The massless solutions to the Dirac equation are described by the so-called Weyl Hamiltonian. The Weyl equation requires a particle to have linear dispersion in all three dimensions while being doubly degenerate at a single momentum point. These Weyl points are topological monopoles of quantized Berry flux exhibiting numerous unusual properties. We performed angle-resolved microwave transmission measurements through a double-gyroid photonic crystal with inversion-breaking where Weyl points have been theoretically predicted to occur. The excited bulk states show two linear dispersion bands touching at four isolated points in the three-dimensional Brillouin zone, indicating the observation of Weyl points. This work paves the way to a variety of photonic topological phenomena in three dimensions.

k · p theory for two-dimensional transition metal dichalcogenide semiconductors

Abstract: We present k.p Hamiltonians parametrized by ab initio density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K , Q , Γ , and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides (TMDCs). We discuss the parametrization of the essential parts of the k.p[ Hamiltonians for MoS2 , MoSe2 , MoTe2 , WS2 , WSe2 , and WTe2 , including the spin-splitting and spin-polarization of the bands, and we briefly review the vibrational properties of these materials. We then use k.p theory to analyse optical transitions in two-dimensional TMDCs over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualization of scanning tunnelling microscopy maps.

Exciton Binding Energy of Monolayer WS2

Abstract: The optical properties of monolayer transition metal dichalcogenides (TMDC) feature prominent excitonic natures. Here we report an experimental approach to measuring the exciton binding energy of monolayer WS2 with linear differential transmission spectroscopy and two-photon photoluminescence excitation spectroscopy (TP-PLE). TP-PLE measurements show the exciton binding energy of 0.71 ± 0.01 eV around K valley in the Brillouin zone.

Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides

Abstract: The band-edge optical response of transition metal dichalcogenides, an emerging class of atomically thin semiconductors, is dominated by tightly bound excitons localized at the corners of the Brillouin zone (valley excitons). A fundamental yet unknown property of valley excitons in these materials is the intrinsic homogeneous linewidth, which reflects irreversible quantum dissipation arising from system (exciton) and bath (vacuum and other quasiparticles) interactions and determines the timescale during which excitons can be coherently manipulated. Here we use optical two-dimensional Fourier transform spectroscopy to measure the exciton homogeneous linewidth in monolayer tungsten diselenide (WSe2). The homogeneous linewidth is found to be nearly two orders of magnitude narrower than the inhomogeneous width at low temperatures. We evaluate quantitatively the role of exciton-exciton and exciton-phonon interactions and population relaxation as linewidth broadening mechanisms. The key insights reported here—strong many-body effects and intrinsically rapid radiative recombination—are expected to be ubiquitous in atomically thin semiconductors.

Experimental Evidence for Dark Excitons in Monolayer WSe 2

Abstract: Transition metal dichalcogenides in the class MX_{2} (M=Mo, W; X=S, Se) have been identified as direct-gap semiconductors in the monolayer limit. Here, we examine light emission of monolayer WSe_{2} using temperature-dependent photoluminescence and time-resolved photoluminescence spectroscopy. We present experimental evidence for the existence of an optically forbidden dark state of the band-gap exciton that lies tens of meV below the optically bright state. The presence of the dark state is manifest in the strong quenching of light emission observed at reduced temperatures. The experimental findings are consistent with theoretical predictions of spin-polarized conduction and valence bands at the K point of the Brillouin zone, with the minimum gap occurring between bands of opposite electron spin.

Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy

Abstract: Current measurements of the biomechanical properties of cells require physical contact with cells or lack subcellular resolution. Here we developed a label-free microscopy technique based on Brillouin light scattering that is capable of measuring an intracellular longitudinal modulus with optical resolution. The 3D Brillouin maps we obtained of cells in 2D and 3D microenvironments revealed mechanical changes due to cytoskeletal modulation and cell-volume regulation.

Brillouin-scattering-induced transparency and non-reciprocal light storage

Abstract: Stimulated Brillouin scattering is a non-linear interaction that allows light to be stored as coherent acoustic waves. Here, the authors report on Brillouin scattering-induced transparency in an optical microresonator whose high quality allows for long-lifetime non-reciprocal light storage.

Thickness dependence of the interfacial Dzyaloshinskii–Moriya interaction in inversion symmetry broken systems

Abstract: In magnetic multilayer systems, a large spin-orbit coupling at the interface between heavy metals and ferromagnets can lead to intriguing phenomena such as the perpendicular magnetic anisotropy, the spin Hall effect, the Rashba effect, and especially the interfacial Dzyaloshinskii–Moriya (IDM) interaction. This interfacial nature of the IDM interaction has been recently revisited because of its scientific and technological potential. Here we demonstrate an experimental technique to straightforwardly observe the IDM interaction, namely Brillouin light scattering. The non-reciprocal spin wave dispersions, systematically measured by Brillouin light scattering, allow not only the determination of the IDM energy densities beyond the regime of perpendicular magnetization but also the revelation of the inverse proportionality with the thickness of the magnetic layer, which is a clear signature of the interfacial nature. Altogether, our experimental and theoretical approaches involving double time Green's function methods open up possibilities for exploring magnetic hybrid structures for engineering the IDM interaction.

Optical transitions in hybrid perovskite solar cells: Ellipsometry, density functional theory, and quantum efficiency analyses for CH3NH3PbI3

Abstract: We report artifact-free CH3NH3PbI3 optical constants extracted from ultra-smooth perovskite layers without air exposure and assign all the optical transitions in the visible/ultraviolet region unambiguously based on density functional theory (DFT) analysis that assumes a simple pseudo-cubic crystal structure. From the self-consistent spectroscopic ellipsometry analysis of the ultra-smooth CH3NH3PbI3 layers, we find that the absorption coefficients of CH3NH3PbI3 (alpha = 3.8 x 10^4 cm-1 at 2.0 eV) are comparable to those of CuInGaSe2 and CdTe, and high alpha values reported in earlier studies are overestimated seriously by extensive surface roughness of CH3NH3PbI3 layers. The polarization-dependent DFT calculations show that CH3NH3+ interacts strongly with the PbI3- cage, modifying the CH3NH3PbI3 dielectric function in the visible region rather significantly. When the effect of CH3NH3+ on the optical transition is eliminated in the DFT calculation, CH3NH3PbI3 dielectric function deduced from DFT shows excellent agreement with the experimental result. As a result, distinct optical transitions observed at E0 (Eg) = 1.61 eV, E1 = 2.53 eV, and E2 = 3.24 eV in CH3NH3PbI3 are attributed to the direct semiconductor-type transitions at the R, M, and X points in the pseudo-cubic Brillouin zone, respectively. We further perform the quantum efficiency (QE) analysis for a standard hybrid-perovskite solar cell incorporating a mesoporous TiO2 layer and demonstrate that the QE spectrum can be reproduced almost perfectly when the revised CH3NH3PbI3 optical constants are employed. Depth-resolved QE simulations confirm that Jsc is limited by the material's longer wavelength response and indicate the importance of optical confinement and long carrier diffusion lengths in hybrid perovskite solar cells.

Brillouin zone and band structure of β‐Ga2O3

Abstract: Gallium oxide is increasingly used in a variety of applications, but confusion reigns over the Brillouin zone and the band structure of monoclinic β-Ga2O3. We present a detailed study of the shape of the Brillouin zone and the location of high-symmetry points. Combined with a study of electronic structure based on hybrid density functional theory, this allows us to derive an accurate band structure. We discuss the nature of the band gap and the location of the band extrema.

An Aharonov-Bohm interferometer for determining Bloch band topology

Abstract: The geometric structure of a single-particle energy band in a solid is fundamental for a wide range of many-body phenomena and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. We realize an atomic interferometer to measure Berry flux in momentum space, in analogy to an Aharonov-Bohm interferometer that measures magnetic flux in real space. We demonstrate the interferometer for a graphene-type hexagonal optical lattice loaded with bosonic atoms. By detecting the singular π Berry flux localized at each Dirac point, we establish the high momentum resolution of this interferometric technique. Our work forms the basis for a general framework to fully characterize topological band structures.

Quantum Oscillations, Thermoelectric Coefficients, and the Fermi Surface of Semimetallic WTe2.

Abstract: We present a study of angle-resolved quantum oscillations of electric and thermoelectric transport coefficients in semimetallic WTe2, which has the particularity of displaying a large B(2) magnetoresistance. The Fermi surface consists of two pairs of electronlike and holelike pockets of equal volumes in a "Russian doll" structure. The carrier density, Fermi energy, mobility, and the mean-free path of the system are quantified. An additional frequency is observed above a threshold field and attributed to the magnetic breakdown across two orbits. In contrast to all other dilute metals, the Nernst signal remains linear in the magnetic field even in the high-field (ωcτ≫1) regime. Surprisingly, none of the pockets extend across the c axis of the first Brillouin zone, making the system a three-dimensional metal with moderate anisotropy in Fermi velocity, yet a large anisotropy in the mean-free path.

Signature of Strong Spin-Orbital Coupling in the Large Nonsaturating Magnetoresistance Material WTe2.

Abstract: We report the detailed electronic structure of WTe2 by high resolution angle-resolved photoemission spectroscopy. We resolved a rather complicated Fermi surface of WTe2. Specifically, there are in total nine Fermi pockets, including one hole pocket at the Brillouin zone center Γ, and two hole pockets and two electron pockets on each side of Γ along the Γ-X direction. Remarkably, we have observed circular dichroism in our photoemission spectra, which suggests that the orbital angular momentum exhibits a rich texture at various sections of the Fermi surface. This is further confirmed by our density-functional-theory calculations, where the spin texture is qualitatively reproduced as the conjugate consequence of spin-orbital coupling. Since the spin texture would forbid backscatterings that are directly involved in the resistivity, our data suggest that the spin-orbit coupling and the related spin and orbital angular momentum textures may play an important role in the anomalously large magnetoresistance of WTe2. Furthermore, the large differences among spin textures calculated for magnetic fields along the in-plane and out-of-plane directions also provide a natural explanation of the large field-direction dependence on the magnetoresistance.

Probing Critical Point Energies of Transition Metal Dichalcogenides: Surprising Indirect Gap of Single Layer WSe2

Abstract: By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasi-particle electronic structures in transition metal dichalcogenides, including the quasi-particle gaps, critical point energy locations, and their origins in the Brillouin zones. We show that single layer WSe2 surprisingly has an indirect quasi-particle gap with the conduction band minimum located at the Q-point (instead of K), albeit the two states are nearly degenerate. We have further observed rich quasi-particle electronic structures of transition metal dichalcogenides as a function of atomic structures and spin-orbit couplings. Such a local probe for detailed electronic structures in conduction and valence bands will be ideal to investigate how electronic structures of transition metal dichalcogenides are influenced by variations of local environment.

Modulation of electronic and mechanical properties of phosphorene through strain

Abstract: We report a first-principles study on the elastic, vibrational, and electronic properties of the recently synthesized phosphorene. By calculating the Gr\"uneisen parameters, we evaluate the frequency shift of the Raman and infrared active modes via symmetric biaxial strain. We also study a strain-induced semiconductor-metal transition, the gap size, and the effective mass of carriers in various strain configurations. Furthermore, we unfold the emergence of a peculiar Dirac-shaped dispersion for specific strain conditions including the zigzag-oriented tensile strain. The observed linear energy spectrum has distinct velocities corresponding to each of its linear branches and is limited to the $\ensuremath{\Gamma}\text{\ensuremath{-}}X$ direction in the first Brillouin zone.

Evidence of Topological Surface State in Three-Dimensional Dirac Semimetal Cd3As2

Abstract: The three-dimensional topological semimetals represent a new quantum state of matter. Distinct from the surface state in the topological insulators that exhibits linear dispersion in two-dimensional momentum plane, the three-dimensional semimetals host bulk band dispersions linearly along all directions. In addition to the gapless points in the bulk, the three-dimensional Weyl/Dirac semimetals are also characterized by “topologically protected” surface state with Fermi arcs on their surface. While Cd3As2 is proposed to be a viable candidate of a Dirac semimetal, more investigations are necessary to pin down its nature. In particular, the topological surface state, the hallmark of the three-dimensional semimetal, has not been observed in Cd3As2. Here we report the electronic structure of Cd3As2 investigated by angle-resolved photoemission measurements on the (112) crystal surface and detailed band structure calculations. The measured Fermi surface and band structure show a good agreement with the band structure calculations with two bulk Dirac-like bands approaching the Fermi level and forming Dirac points near the Brillouin zone center. Moreover, the topological surface state with a linear dispersion approaching the Fermi level is identified for the first time. These results provide experimental indications on the nature of topologically non-trivial three-dimensional Dirac cones in Cd3As2.

Impact of rattlers on thermal conductivity of a thermoelectric clathrate: a first-principles study.

Abstract: We investigate the role of rattling guest atoms on the lattice thermal conductivity of a type-I clathrate ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ by first-principles lattice dynamics. Comparing phonon properties of filled and empty clathrates, we show that rattlers cause tenfold reductions in the relaxation time of phonons by increasing the phonon-phonon scattering probability. Contrary to the resonant scattering scenario, the reduction in the relaxation time occurs in a wide frequency range, which is crucial for explaining the unusually low thermal conductivities of clathrates. We also find that the impact of rattlers on the group velocity of phonons is secondary because the flattening of phonon dispersion occurs only in a limited phase space in the Brillouin zone.

Theory of strain in single-layer transition metal dichalcogenides

Abstract: Strain engineering has emerged as a powerful tool to modify the optical and electronic properties of two-dimensional crystals. Here we perform a systematic study of strained semiconducting transition metal dichalcogenides. The effect of strain is considered within a full Slater-Koster tight-binding model, which provides us with the band structure in the whole Brillouin zone (BZ). From this, we derive an effective low-energy model valid around the $K$ point of the BZ, which includes terms up to second order in momentum and strain. For a generic profile of strain, we show that the solutions for this model can be expressed in terms of the harmonic oscillator and double quantum well models, for the valence and conduction bands respectively. We further study the shift of the position of the electron and hole band edges due to uniform strain. Finally, we discuss the importance of spin-strain coupling in these 2D semiconducting materials.

Exciton band structure in layered MoSe2: from a monolayer to the bulk limit

Abstract: We present the micro-photoluminescence (μPL) and micro-reflectance contrast (μRC) spectroscopy studies on thin films of MoSe2 with layer thicknesses ranging from a monolayer (1L) up to 5L. The thickness dependent evolution of the ground and excited state excitonic transitions taking place at various points of the Brillouin zone is determined. Temperature activated energy shifts and linewidth broadenings of the excitonic resonances in 1L, 2L and 3L flakes are accounted for by using standard formalisms previously developed for semiconductors. A peculiar shape of the optical response of the ground state (A) exciton in monolayer MoSe2 is tentatively attributed to the appearance of a Fano-type resonance. Rather trivial and clearly decaying PL spectra of monolayer MoSe2 with temperature confirm that the ground state exciton in this material is optically bright in contrast to a dark exciton ground state in monolayer WSe2.

Coalescence of exceptional points and phase diagrams for one-dimensional P T -symmetric photonic crystals

Abstract: Non-Hermitian systems with parity-time- ($\mathcal{P}\mathcal{T}$)- symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with $\mathcal{P}\mathcal{T}$-symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of $\mathcal{P}\mathcal{T}$ symmetry transitions are found. One is that a $\mathcal{P}\mathcal{T}$-broken phase can reenter into a $\mathcal{P}\mathcal{T}$-exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some $k$ point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the $\mathcal{P}\mathcal{T}$-exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

Phase stability and transformations in the halide perovskite CsSnI3

Abstract: We employ the quasiharmonic approximation to study the temperature-dependent lattice dynamics of the four different phases of cesium tin iodide $({\mathrm{CsSnI}}_{3})$. Within this framework, we obtain the temperature dependence of a number of structural properties, including the cell volume, bulk modulus, and Gr\"uneisen parameter. The Gibbs free energy of each phase is compared against the temperature-dependent Helmholtz energy obtained from the equilibrium structure within the harmonic approximation. We find that the black tetragonal perovskite phase is not dynamically stable up to at least 500 K, with the phonon dispersion displaying negative optic modes, which pass through all of the high-symmetry wave vectors in the Brillouin zone. The main contributions to the negative modes are found to be motions of the Cs atom inside the perovskite cage. The black cubic perovskite structure shows a zone-boundary instability, indicated by soft modes at the special $\mathbf{q}$ points $M$ and $R$. These modes are present in calculations at the equilibrium (0 K) lattice constant, while at finite temperature additional negative modes develop at the zone center, indicating a ferroelectric instability. The yellow crystal, composed of one-dimensional $({\mathrm{SnI}}_{6}){}_{n}$ double chains, has the same heat of formation as the orthorhombic perovskite phase at 0 K, but becomes less energetically favorable at higher temperatures, due to its higher free energy.

Electronic and thermoelectric properties of van der Waals materials with ring-shaped valence bands

Abstract: The valence band of a variety of few-layer, two-dimensional materials consist of a ring of states in the Brillouin zone. The energy-momentum relation has the form of a “Mexican hat” or a Rashba dispersion. The two-dimensional density of states is singular at or near the band edge, and the band-edge density of modes turns on nearly abruptly as a step function. The large band-edge density of modes enhances the Seebeck coefficient, the power factor, and the thermoelectric figure of merit ZT. Electronic and thermoelectric properties are determined from ab initio calculations for few-layer III–VI materials GaS, GaSe, InS, InSe, for Bi2Se3, for monolayer Bi, and for bilayer graphene as a function of vertical field. The effect of interlayer coupling on these properties in few-layer III–VI materials and Bi2Se3 is described. Analytical models provide insight into the layer dependent trends that are relatively consistent for all of these few-layer materials. Vertically biased bilayer graphene could serve as an experimental test-bed for measuring these effects.

Disorder and Metal-Insulator Transitions in Weyl Semimetals.

Abstract: The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arc surface states. We study the effects of disorder and localization in WSMs and find three novel phase transitions. (i) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional quantum anomalous Hall state. (ii) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (iii) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the novel phase transitions can be realized on a photonic lattice.

Dual Raman-Brillouin Microscope for Chemical and Mechanical Characterization and Imaging

Abstract: We present a unique confocal microscope capable of measuring the Raman and Brillouin spectra simultaneously from a single spatial location. Raman and Brillouin scattering offer complementary information about a material’s chemical and mechanical structure, respectively, and concurrent monitoring of both of these spectra would set a new standard for material characterization. We achieve this by applying recent innovations in Brillouin spectroscopy that reduce the necessary acquisition times to durations comparable to conventional Raman spectroscopy while attaining a high level of spectral accuracy. To demonstrate the potential of the system, we map the Raman and Brillouin spectra of a molded poly(ethylene glycol) diacrylate (PEGDA) hydrogel sample in cyclohexane to create two-dimensional images with high contrast at microscale resolutions. This powerful tool has the potential for very diverse analytical applications in basic science, industry, and medicine.

Double resonance Raman modes in monolayer and few-layer MoTe2

Abstract: We study the second-order Raman process of mono- and few-layer ${\mathrm{MoTe}}_{2}$, by combining ab initio density functional perturbation calculations with experimental Raman spectroscopy using 532, 633, and 785 nm excitation lasers. The calculated electronic band structure and the density of states show that the resonance Raman process occurs at the $M$ point in the Brillouin zone, where a strong optical absorption occurs due to a logarithmic Van Hove singularity of the electronic density of states. The double resonance Raman process with intervalley electron-phonon coupling connects two of the three inequivalent $M$ points in the Brillouin zone, giving rise to second-order Raman peaks due to the $M$-point phonons. The calculated vibrational frequencies of the second-order Raman spectra agree with the observed laser-energy-dependent Raman shifts in the experiment.

Zone-Folded Phonons and the Commensurate–Incommensurate Charge-Density-Wave Transition in 1T-TaSe2 Thin Films

Abstract: Bulk 1T-TaSe2 exhibits unusually high charge density wave (CDW) transition temperatures of 600 and 473 K below which the material exists in the incommensurate (I-CDW) and the commensurate (C-CDW) charge-density-wave phases, respectively. The (13)1/2 × (13)1/2 C-CDW reconstruction of the lattice coincides with new Raman peaks resulting from zone-folding of phonon modes from middle regions of the original Brillouin zone back to Γ. The C-CDW transition temperatures as a function of film thickness are determined from the evolution of these new Raman peaks, and they are found to decrease from 473 to 413 K as the film thicknesses decrease from 150 to 35 nm. A comparison of the Raman data with ab initio calculations of both the normal and C-CDW phases gives a consistent picture of the zone-folding of the phonon modes following lattice reconstruction. The Raman peak at ∼154 cm−1 originates from the zone-folded phonons in the C-CDW phase. In the I-CDW phase, the loss of translational symmetry coincides with a stro...

Accidental degeneracy of double Dirac cones in a phononic crystal

Abstract: Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using k·p method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals

Abstract: High harmonic generation in semiconductors is analyzed for high mid-infrared laser intensities for which the electron-hole pair is driven beyond the first Brillouin zone and exhibits Bloch oscillations. We find that even a two-band analysis exhibits second and higher plateaus. Whereas the first plateau is shown to be consistent with high harmonic generation through electron-hole recollision, the higher plateaus arise from dynamic Bloch oscillations; however, the driving process is interband in nature, in contrast to the generally accepted intraband Bloch oscillation mechanism. Energy conservation is fulfilled, as harmonics beyond the first plateau come from a cascaded nonlinearity.

Breakdown of the Migdal approximation at Lifshitz transitions with giant zero-point motion in H3S superconductor

Abstract: While 203 K high temperature superconductivity in H3S has been interpreted by BCS theory in the dirty limit here we focus on the effects of hydrogen zero-point-motion and the multiband electronic structure relevant for multigap superconductivity near Lifshitz transitions. We describe how the topology of the Fermi surfaces evolves with pressure giving different Lifshitz-transitions. A neck-disrupting Lifshitz-transition (type 2) occurs where the van Hove singularity, vHs, crosses the chemical potential at 210 GPa and new small 2D Fermi surface portions appear with slow Fermi velocity where the Migdal-approximation becomes questionable. We show that the neglected hydrogen zero-point motion ZPM, plays a key role at Lifshitz transitions. It induces an energy shift of about 600 meV of the vHs. The other Lifshitz-transition (of type 1) for the appearing of a new Fermi surface occurs at 130 GPa where new Fermi surfaces appear at the Gamma point of the Brillouin zone here the Migdal-approximation breaks down and the zero-point-motion induces large fluctuations. The maximum Tc=203K occurs at 160 GPa where Ef/w0=1 in the small Fermi surface pocket at Gamma point. A Feshbach-like resonance between a possible BEC-BCS condensate at Gamma and the BCS condensate in different k-space spots is proposed.