Superlattice Point Research Articles

Investigation of the phonon dispersion associated with superlattice reflections in the BiS2 -based superconductor LaBiS2O0.5F0.5

The phonon dispersion of a $\mathrm{Bi}{\mathrm{S}}_{2}$-based superconductor $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$ is investigated by first-principles calculations and inelastic x-ray scattering experiments. The origin of superlattice (SL) reflections arising from transverse-type lattice modulation, which were recently reported in [J. Kajitani et al., J. Phys. Soc. Jpn. 90, 103601 (2021)], is discussed in terms of lattice dynamics. Our first-principles calculations of phonon dispersion and the Fermi surfaces (FSs) demonstrate that the phonon mode corresponding to the transverse-type lattice modulation is unstable, and the propagation vector corresponding to the SL reflections is close to the FS nesting vector, which suggests that the phonon softening originates from the FS nesting. Against these calculated expectations, measured phonon dispersion in $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$ along the Z-A direction, where the SL point is located, shows no remarkable temperature dependence, and there are no steeply declining branches accompanied with a softening around the SL point. Based on these results, we discuss the two possibilities for the transverse lattice modulation in $\mathrm{La}\mathrm{Bi}{\mathrm{S}}_{2}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}$: the order-disorder-type structural transition and the displacive structural transition with an overdamped mode, for both of which the local structure distortion or the short-range correlation within the $\mathrm{Bi}{\mathrm{S}}_{2}$ plane would be essential.

Superconductor versus insulator in twisted bilayer graphene

We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. These features are consistent with experimental observations in magic-angle twisted bilayer graphenes despite the distinct microscopic details. We further study the full phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.

Neutron and x-ray scattering study of phonon dispersion and diffuse scattering in (Na,Bi)TiO3−xBaTiO3 single crystals near the morphotropic phase boundary

Neutron and x-ray scattering measurements were performed on $(\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2})\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}x\phantom{\rule{0.28em}{0ex}}\mathrm{at}%\mathrm{BaTi}{\mathrm{O}}_{3}$ (NBT-$x\mathrm{BT}$) single crystals ($x=4$, 5, 6.5, and 7.5) across the morphotropic phase boundary (MPB), as a function of both composition and temperature, and probing both structural and dynamical aspects. In addition to the known diffuse scattering pattern near the $\mathrm{\ensuremath{\Gamma}}$ points, our measurements revealed new, faint superlattice peaks, as well as an extensive diffuse scattering network, revealing a short-range ordering of polar nanoregions (PNR) with a static stacking morphology. In samples with compositions closest to the MPB, our inelastic neutron scattering investigations of the phonon dynamics showed two unusual features in the acoustic phonon branches, between the superlattice points, and between the superlattice points and $\mathrm{\ensuremath{\Gamma}}$ points, respectively. These critical elements are not present in the other compositions away from the MPB, which suggests that these features may be related to the tilt modes coupling behavior near the MPB.

Persistent current in an almost staggered Harper model

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model is different than other one dimensional disordered systems which are always localized, since it is a quasi-periodic system with correlated disorder resulting in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.

Thermal properties of 1T-TaS 2 at the onset of charge density wave states

The crystal lattice plays an essential role in the charge density wave (CDW) phase transition together with the electron system through electron–phonon interactions. The CDW in the layered compound 1T-TaS 2 at low temperatures has a commensurate phase, which causes superlattice points to appear in the Brillouin zone of the undistorted phase. Since the effect of CDWs is to directly modulate the lattice, it is evident that an investigation that looks directly at the phonon frequencies would be most instructive in examining this phenomenon. Hence the Born–von Karman formalism, in which the equilibrium conditions are fulfilled, has been employed for the calculation of phonon frequency distribution curves of 1T-TaS 2 both in the normal and in the commensurate charge density wave (CCDW) phases. A folding technique has been adopted for the calculation in the CCDW phase. The phonon distribution and some dominant phonon frequencies for both the phases have been reported. With these results the thermal properties such as specific heat capacity, Debye Waller factor and thermal conductivity have been worked out, and are compared with the available experimental results.

Fractal dimension in percolating Heisenberg antiferromagnets

We investigated static and dynamical properties in the three-dimensional percolating Heisenberg antiferromagnets, RbMn c Mg 1 - c F 3 , with the magnetic concentration close to the percolation threshold, c P = 0.312 , around the superlattice point well below T N . In neutron diffraction experiment, the wave number dependence of the elastic scattering component was well fitted to q - x . Magnetic fractons were also studied using inelastic neutron scattering, and the observed fractons showed the dispersion relation of q z . The determined exponents, x = 2.43 ± 0.05 and z = 2.5 ± 0.1 , were in good agreement with the fractal dimension ( D f = 2.48 ) .

Fractal structure and critical scattering in the three-dimensional percolating antiferromagnet, [formula omitted

We have performed neutron scattering experiments to investigate the static magnetic structure and the magnetic critical scattering in the three-dimensional percolating Heisenberg antiferromagnet, RbMn 0.31 Mg 0.69 F 3 , whose magnetic concentration is just at the percolation concentration for a cubic lattice, c P = 0.312 . Magnetic scattering was observed around the superlattice point, ( 1 2 , 1 2 , 1 2 ) . We determined the Néel temperature of this system to be T N = 4.0 ± 0.5 K , and found that the critical scattering above T N is similar to that observed in the homogeneous system. At T = 1.6 K well below T N , the scattering function is described by a sum of the critical scattering and elastic scattering components, and we demonstrated that the q -variation of the intensity of the elastic scattering component can be described using the fractal dimension.

In situ TEM Study of Electron Beam Stimulated Organization of Three-dimensional Void Superlattice in CaF2

CaF2 is widely adopted as deep-UV window material and thin film optical coating. It has been known that ordered defect superlattices may form in electron irradiated CaF2.[1] However, the nature of the defects on the superlattice point (i.e., Ca colloids or voids) has not been certain and the self-organization mechanism has not been fully understood. In this study, single crystal CaF2 were irradiated under 200 keV electron beam at room temperature with in situ TEM observation of the dynamic process of defect ordering. The superlattice reached steady state after an electron dose of 1×1021e−/cm2 with void radius about 5 nm. Videos recorded during the in-situ observation reveal the dynamic self-organization process of the void superlattice. Coalescence was prevalent at the initial stages. Migration and preferential growth were dominant at the final stages of the superlattice formation. At a dose higher than 3×1021e−/cm2 the superlattice structure was destroyed. These critical doses of void superlattice formation and deformation seem to be independent of dose rate. The anisotropic diffusivity of the migrating “molecules” may explain the superlattice formation.

IN SITU Tem Study of Electron Beam Stimulated Organization of Three-Dimensional Void Superlattice in Caf2

ABSTRACTCaF2 is widely adopted as deep-UV window material and thin film optical coating. It has been known that ordered defect superlattices may form in electron irradiated CaF2.[1] However, the nature of the defects on the superlattice point (i.e., Ca colloids or voids) has not been certain and the self-organization mechanism has not been fully understood. In this study, single crystal CaF2 were irradiated under 200 keV electron beam at room temperature with in situ TEM observation of the dynamic process of defect ordering. The superlattice reached steady state after an electron dose of 1×1021e-/cm2 with void radius about 5 nm. Videos recorded during the in-situ observation reveal the dynamic self-organization process of the void superlattice. Coalescence was prevalent at the initial stages. Migration and preferential growth were dominant at the final stages of the superlattice formation. At a dose higher than 3×1021 e-/cm2 the superlattice structure was destroyed. These critical doses of void superlattice formation and deformation seem to be independent of dose rate. The anisotropic diffusivity of the migrating “molecules” may explain the superlattice formation.

Anomalous critical scattering from a three-dimensional percolating antiferromagnet RbMn 0.31 Mg 0.69 F 3

A neutron-diffraction experiment was performed to measure the critical scattering from a percolating antiferromagnet RbMn0.31Mg0.69F3, whose magnetic concentration is just at the percolation concentration for a cubic lattice, cp=0.312. The magnetic scattering was observed at around the superlattice point (1/2, 1/2, 1/2). We found that the scattering function exhibits a non-Lorentzian line shape, S(q)=(q2+κ2)-x (q and κ are the momentum transfer and the inverse correlation length, respectively), with the exponent x=0.6±0.1 at the low temperature of 1.6 K, and that the exponent is attributed to the fractal structure of the percolating network. Also, the system was found to exhibit a crossover to the homogeneous state at high temperature.

LATTICE INSTABILITY OF 2H-TaSe2

The charge density wave (CDW) in the layered compound 2H-TaSe 2 at low temperatures has a commensurate phase, which causes super lattice points to appear in the Brillöuin zone of the undistorted phase. A Born-von Karman formalism has been employed for the calculation of phonon frequency distribution curves of 2H-TaSe 2 both in the normal and in the commensurate charge density wave (CCDW) phases. A folding technique has been adopted for the calculation in the CCDW phase. The phonon distribution for both the phases have been reported. With these distributions the thermal properties such as specific heat capacity, Debye Waller factor W(k) and thermal conductivity have been worked out, and compared with the available experimental results.

Specific Study on 1T-TaSe2 in the Context of Commensurate Charge Density Wave

The Charge Density Wave (CDW) in the layered compound 1T-TaSe2 at low temperatures has a commensurate phase which causes superlattice points to appear in the Brillouin zone of the undistorted phase. The phonon frequency distribution of this system for both the normal and the Commensurate Charge Density Wave (CCDW) phases have been worked out theoretically using the Born-von Karmann formalism. With these results the thermal properties such as specific heat capacity, Debye-Waller factor and thermal conductivity have been worked out and are compared with the available experimental results.

Soft Phonons and Anti-phase Domains in SrTiO3 : an Electron Diffuse Scattering Study

Abstract It is well known that cubic SrTiO3 possesses a typical perovskite structure whose reciprocal unit cell is shown in Fig. 1 where X, M, and R designate particular points at Brillouin zone boundaries with the Γ point being the zone origin. The instability of the phonon mode designated by the R point leads to the cubic-to-tetragonal phase transition of SrTiO3 at Tc=103 K. By using the same unit-cell as the cubic SrTiO3, reflections (h k 1) / 2 with h, k, and 1 all odd are superlattice reflections characteristic of tetragonal SrTiO3. Previous investigations of diffuse scattering were carried out by neutron and xray diffraction at Temperatures below 240 K. In the present work, observation of the diffuse scattering was extended to a broad Temperature range of 20 ∼ 700 K. Selected-area electron diffraction patterns (EDPs) reveal splitting and streaking of the superlattice reflections as shown in Fig. 2. We can see streaks along the [1 0 0]* direction, e.g., the streak connecting (5 3-5) / 2 and (7 3-5) / 2, the streak connecting (-3-5 7) / 2 and (-1-5 7) / 2. Splitting of the superreflections (7-1-1) / 2, (9-1-1) / 2, and (-7 1 1) / 2, along [0 1-1]* direction is evident. All the splitting and streaking behaviors shown in Fig. 2 and observed in other EDPs may be interpreted as being formed by the intersection of the Ewald sphere with reciprocal rods MRM shown in Fig. 1, which are along the <100>* direction passing through superlattice points.

Raman-active modes in wurtzite(GaN)m(AlN)nsuperlattices

We have established that the symmetry of wurtzite $(\mathrm{GaN}{)}_{m}(\mathrm{AlN}{)}_{n}$ superlattices grown along the symmetry axis depends on the numbers of monolayers $m$ and $n:$ the appropriate space groups are ${C}_{6v}^{4}$ and ${C}_{3v}^{1}$ for odd and even values of $m+n,$ respectively. The difference in the superlattice point symmetry drastically influences the first-order vibrational spectra: the number of Raman-active modes depends nonmonotonically on $m+n$ whereas the dependence for the IR-active modes is monotonic. A simple Raman test to distinguish the superlattices with even and odd $m+n$ values is proposed.

Spin Dynamics in an Ordered Stripe Phase

Inelastic neutron scattering has been used to measure the low-energy spin excitations in the ordered charge-stripe phase of ${{\mathrm{La}}_{2}\mathrm{NiO}}_{4+\ensuremath{\delta}}$ with $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.133$. Spin-wave-like excitations disperse away from the incommensurate magnetic superlattice points with a velocity $\ensuremath{\sim}60%$ of that in the $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ compound. Incommensurate inelastic peaks remain well resolved up to at least twice the magnetic ordering temperature. Paramagnetic scattering from a $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.105$ sample, which has a N\'eel-ordered ground state, shows anomalies suggestive of incipient stripe correlations. Similarities between these results and measurements on superconducting cuprates are discussed.

Two-dimensional measurements of soft phonons and phase transitions in SrTiO 3

The flat-cone instrument at the BER-II reactor in Berlin is well suited for systematic measurements of elastic and inelastic scattering events in large and continuous areas of Q-space. With this instrument the soft phonon branch, connected with the structural phase transition in SrTiO 3, has been studied in the ( hll) plane. In integral measurements the phonon branch shows up as two triangular intensity distributions around the superlattice points. The two-dimensional intensity distributions for a constant energy transfer reveal the anisotropy of the branch. The data collection time is considerably faster than with a conventional triple-axis instrument.

Crossover of the dynamical regime of the spt in A-TCNB under hydrostatic pressure

Abstract Anthracene-TCNB is a weak charge-transfer molecular crystal which presents a second order phase transition. At atmospheric pressure, a soft mode has been observed by inelastic neutron scattering in the high temperature phase. Under hydrostatic pressure, the transition remains continuous whereas a drastic change occurs in the dynamical regime. At 3 kbar, at the superlattice point, the soft mode-type scattering is indeed replaced by a quasielastic response. This feature indicates a continuous crossover from a displacive regime to an order-disorder regime for a modest pressure of 1.5 kbar.

Order-disorder phase transition in potassium thiocyanate.

The order-disorder phase transition in KSCN near 142 \ifmmode^\circ\else\textdegree\fi{}C, which is connected with the head-tail orientation of the linear SCN molecules, is investigated by diffuse-neutron-scattering techniques. The results show a transition from a long-range-ordered structure to a short-range-ordered state which persists up to temperatures near the melting point. Above ${\mathit{T}}_{\mathit{c}}$ near the (100) superlattice point, a Lorentzian intensity distribution is observed whose temperature dependence shows a mean-field behavior. The short-range-ordered state is described by an ensemble of ordered microdomains.

Effect of spin-density waves on the lattice dynamics of lead.

The phonon spectrum of Pb, first determined by Brockhouse et al. in 1962, exhibits large depressions in both longitudinal and transverse modes at the zone-boundary points {100}. The origin of this behavior has remained unclear. We show that a possible explanation involves the existence of a cubic family of small-amplitude spin-density waves (SDW's), having wave vectors {Q} at each of the twelve {211}, or alternatively {210}, superlattice points. Each SDW causes a peak in the conduction-electron charge response function \ensuremath{\chi}(q) near the points q=\ifmmode\pm\else\textpm\fi{}Q. SDW's have built-in charge modulations, equal in magnitude but opposite in sign, for both spin states. Only a small shift in the spatial phase \ensuremath{\delta}\ensuremath{\varphi}=\ensuremath{\epsilon}${\ensuremath{\sigma}}_{z}$, depending on the spin ${\ensuremath{\sigma}}_{z}$, creates an additional charge response for q near \ifmmode\pm\else\textpm\fi{}Q. When this spin-split-phase contribution to \ensuremath{\chi}(q) is incorporated into the theory for the phonon spectrum, the anomalous behavior at {100} can be understood.

Inelastic neutron scattering of the low-dimensional conductors (TaSe 4) 2I and Mo 8O 23

Inelastic neutron scattering was carried out on the low-dimensional conductors (TaSe 4) 2I and Mo 8O 23. For (TaSe 4) 2I, a ‘spoon-like’ anomaly of the dispersion curve of the TA phonon branch was observed around the superlattice point. This result is in direct support of the TA mode condensation at the CDW transition, which was predicted based on X-ray studies and the Raman scattering study. Mo 8O 23 has a structural transition due to the incommensurate CDW formation at T c1⋍315K and a lock-in transition at T c2⋍285K. The present inelastic neutron scattering discloses the existence of a temperature dependent soft mode at the incommensurate superlattice point above T c1. A central peak is observed in the dynamical structure factor and grows as the temperature approaches T c1.