Cusp-like Behavior Research Articles

Two-dimensional Superconductivity in Misfit Layered Compound (BiSe)1.10NbSe2

Novel two-dimensional superconductivity in a misfit layered compound (BiSe)1.10NbSe2 with a critical temperature T c of 2.7 K is reported. The temperature dependence of H c2 is linear close to T c for both H ∥ c-axis and H ∥ ab-plane, suggesting that the superconductivity is three-dimensional with some anisotropy. However, the angular dependence of H c2 clearly reveals a cusp-like behavior, which can be explained by Tinkham model, indicating that the system is two-dimensional. In order to clarify the relationship between stripe structures on the surface and the two-dimensional superconductivity, we also performed the same measurement on a uniform microbridge sample. We found similar two-dimensional behavior even in a microbridge without linear defects, indicating that the origin of two-dimensional superconductivity in (BiSe)1.10NbSe2 is not related to the stripe structure.

Characterizations of Anisotropic Superconductivity in (BiSe)1+δNbSe2

Anisotropy of superconductivity in misfit layered compounds (BiSe)1+δNbSe2 was studied. We synthesized single crystals of (BiSe)1+δNbSe2 using CsCl/KCl flux method. There existed two phases with different T c depending on the starting composition δ, although their structures were almost unaffected by changing δ. Anisotropy of the upper critical field was determined by magneto-resistance measurements with various out-of-plane and in-plane field angles. The out-of-plane anisotropy of H c2 showed a cusp-like behavior for fields close to ab-plane similar to that predicted by 2D Tinkham model. Furthermore, a clear two-fold symmetry was observed in the in-plane angular dependence of H c2.

On the Best Choice of Lasso Program Given Data Parameters

Compressed sensing (CS) is a paradigm in which a structured high-dimensional signal may be recovered from random, under-determined, and corrupted linear measurements. Lasso programs are effective for solving CS problems due to their proven ability to leverage underlying signal structure. Three popular Lasso programs are equivalent in a sense and sometimes used interchangeably. Tuned by a governing parameter, each admit an optimal parameter choice. For sparse or low-rank signal structures, this choice yields minimax order-optimal error. While CS is well-studied, existing theory for Lasso programs typically concerns this optimally tuned setting. However, the optimal parameter value for a Lasso program depends on properties of the data, and is typically unknown in practical settings. Performance in empirical problems thus hinges on a program’s parameter sensitivity: it is desirable that small variation about the optimal parameter choice begets small variation about the optimal risk. We examine the risk for these three programs and demonstrate that their parameter sensitivity can differ for the same data. We prove a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gauge-constrained</i> Lasso program admits asymptotic cusp-like behaviour of its risk in the limiting low-noise regime. We prove that a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">residual-constrained</i> Lasso program has asymptotically suboptimal risk for very sparse vectors. These results contrast observations about an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unconstrained</i> Lasso program, which is relatively less sensitive to its parameter choice. We support the asymptotic theory with numerical simulations, demonstrating that parameter sensitivity of Lasso programs is readily observed for even modest dimensional parameters. Importantly, these simulations demonstrate regimes in which a Lasso program exhibits sensitivity to its parameter choice, though the other two do not. We hope this work aids practitioners in selecting a Lasso program for their problem.

Extreme in-plane upper critical magnetic fields of heavily doped quasi-two-dimensional transition metal dichalcogenides

Extreme in-plane upper critical magnetic fields $B_{c2//ab}$ strongly violating the Pauli paramagnetic limit have been observed in the misfit layer $(LaSe)_{1.14}(NbSe_2)$ and $(LaSe)_{1.14}(NbSe_2)_2$ single crystals with $T_c$ = 1.23 K and 5.7 K, respectively. The crystals show a two-dimensional to three-dimensional transition at temperatures slightly below $T_c$ with an upturn in the temperature dependence of $B_{c2//ab}$, a temperature dependent huge superconducting anisotropy and a cusplike behavior of the angular dependence of $B_{c2}$. Both misfits are characterized by a strong charge transfer from LaSe to $NbSe_2$. As shown in our previous work, $(LaSe)_{1.14}(NbSe_2)$ is electronically equivalent to the highly doped $NbSe_2$ monolayers. Then, the strong upper critical field can be attributed to the Ising coupling recently discovered in atomically thin transition metal dichalcogenides with strong spin-orbit coupling and a lack of inversion symmetry. A very similar behavior is found in $(LaSe)_{1.14}(NbSe_2)_2$, where the charge transfer is nominally twice as big, which could eventually lead to complete filling of the $NbSe_2$ conduction band and opening superconductivity in LaSe. Whatever the particular superconducting mechanism would be, a common denominator in both misfits is that they behave as a stack of almost decoupled superconducting atomic layers, proving that Ising superconductivity can also exist in bulk materials.

Weak antilocalization and Shubnikov–de Haas oscillations in single crystal CaCuSb

Quantum oscillations in both linear and Hall resistivities and weak antilocalization (WAL) are barely observed in bulk single crystals. Here we report the transport properties of a CaCuSb single crystal that crystallizes in the hexagonal crystal structure. The magnetotransport studies reveal WAL and $\mathrm{Shubnikov}\ensuremath{-}\mathrm{de}$ Haas (SdH) quantum oscillations with a unique frequency at 314 T. A cusplike behavior in the low-field regime of magnetotransport for $J\ensuremath{\parallel}(ab)$-plane and $B\ensuremath{\parallel}[0001]$ confirms the WAL in CaCuSb. Angular-dependent normalized magnetoconductance and SdH oscillations studies reveal that the observed phenomena originate from the $2\mathrm{D}$ transport channels. The high magnetic-field (up to 45 T) experiments demonstrate plateaulike features in the Hall measurements. The first-principles calculations unfold that CaCuSb is a nontopological semimetal with dominant hole carriers at the Fermi level. Our study reveals that CaCuSb is a promising candidate to explore the quasi-2D quantum transport phenomenon in the transition metal pnictide materials.

Effect of Magnetic (Nd) Doping on Electrical and Magnetic Properties of Topological Sb2Te3 Single Crystal

Here, we report the growth and characterization of single crystals of NdxSb2-xTe3 (x = 0 and 0.1), by solid-state reaction route via self-flux method. The phase and layered growth are confirmed through X-ray diffraction and scanning electron microscopy respectively. A slight contraction in lattice parameters is seen after Nd doping. Also a minute shift in vibrational modes of recorded Raman spectra has been observed by doping of Nd in Sb2Te3. The magneto-resistance values under magnetic field of 5 Tesla for Sb2Te3 are 75% at 2.5 K and 60% at 20 K, but only 40% at 5 K for Nd0.1Sb1.9Te3. DC magnetic measurements exhibit expected diamagnetic and paramagnetic behaviors for pure and Nd doped crystals respectively. A cusp-like behavior is observed in magneto-conductivity of both pure and Nd doped crystals at low magnetic fields (< 1 Tesla) which is analyzed using Hikami-Larkin-Nagaoka (HLN) model. For Sb2Te3, the fitted parameters α are −1.02 and −0.58 and the phase coherence lengths Lφ are 50.8(6)nm and 34.9(8)nm at temperatures 2.5 and 20 K respectively. For Nd0.1Sb1.9Te3, α is −0.29 and Lφ is 27.2(1)nm at 5 K. The α values clearly show the presence of weak anti-localization effect in both pure and Nd doped samples. Also with Nd doping, the contribution of bulk states increases in addition to conducting surface states in overall conduction mechanism.

Probing band-center anomaly with the Kernel polynomial method

We investigate the anomalous behavior of localization length of a non-interacting one-dimensional Anderson model at zero temperature. We report numerical calculations of the Thouless expression of localization length, based on the Kernel polynomial method (KPM), which has an computational complexity, where N is the system size. The KPM results show excellent agreement with perturbative results in a large system size limit, confirming the validity of the Thouless formula. In the perturbative regime, we show that the KPM approximation of the Thouless expression produces the correct localization length at the band center in the thermodynamic limit. The Thouless expression relates localization length in terms of density of states in a one-dimensional disordered system. By calculating the KPM estimates of the density of states, we find a cusp-like behavior around the band center in the perturbative regime. This cusp-like singularity can not be obtained by approximate analytical calculations within the second-order approximations, reflects the band-center anomaly.

Magnetotransport properties of noncentrosymmetric CaAgBi single crystal

We report on the single crystal growth and transport properties of a topological semimetal CaAgBi which crystallizes in the hexagonal ABC-type structure with the non-centrosymmetric space group P63mc (No. 186). The transverse magnetoresistance measurements with current in the basal plane of the hexagonal crystal structure reveal a value of about 30% for I∥[10̄0] direction and about 50% for I∥[1̅10] direction at 10 K in an applied magnetic field of 14 T. The magnetoresistance shows a cusp-like behavior in the low magnetic field region, suggesting the presence of weak antilocalization effect for temperatures less than 100 K. The Hall measurements reveal that predominant charge carriers are p-type, exhibiting a linear behavior at high fields. The magnetoconductance of CaAgBi is analyzed based on the modified Hikami–Larkin–Nagaoka model. Our first-principle calculations within a density-functional theory framework reveal that the Fermi surface of CaAgBi consists of both the electron and hole pockets and the size of the hole pocket is much larger than electron pockets suggesting the dominant p-type carriers in accordance with our experimental results.

Angle dependence of Hc2 with a crossover between the orbital and paramagnetic limits

This paper establishes the angle dependence of the upper critical field H${}_{c2}$ of a two-dimensional Ising superconductor NbSe${}_{2}$. The experimental results demonstrate the cusp-like behavior around the parallel magnetic fields even at the lowest temperature where H${}_{c2}$ should be determined by the pure paramagnetic effect. Those results are well described by the formula that includes contributions both from the orbital and paramagnetic effects.

Production of plasmons in two layers of graphene with different doping densities traversed by swift electrons

We apply a fully relativistic formulation to calculate the average number of plasmons excited by an energetic electron traversing two parallel graphene layers separated by a given distance d. We use a Drude model in the non-dissipative limit to describe the conductivity of each layer in the THz frequency range, and address the general case in which the layers have different doping densities of charge carriers by defining an asymmetry parameter. With this, we obtain the probability density of exciting the hybridized Dirac Plasmon-Polariton modes that result from the coupling of the layers, and hence the number of plasmons excited by the passing electron along its trajectory. We analyze the effect of different parameters, such as the interlayer distance, the incident particle velocity, and the asymmetry in doping densities. In particular, we find a cusp-like behaviour for nearly equal conductivities, that indicates a high sensitivity of the system to slight variations in doping densities.

New families of vortex patch equilibria for the two-dimensional Euler equations

Various modified forms of contour dynamics are used to compute multipolar vortex equilibria, i.e., configurations of constant vorticity patches which are invariant in a steady rotating frame. There are two distinct solution families for “N + 1” point vortex-vortex patch equilibria in which a finite-area central patch is surrounded by N identical point vortices: one with the central patch having opposite-signed vorticity and the other having same-signed vorticity to the satellite vortices. Each solution family exhibits limiting states beyond which no equilibria can be found. At the limiting state, the central patch of a same-signed equilibrium acquires N corners on its boundary. The limiting states of the opposite-signed equilibria have cusp-like behaviour on the boundary of the central patch. Linear stability analysis reveals that the central patch is most linearly unstable as it approaches the limiting states. For equilibria comprising a central patch surrounded by N identical finite-area satellite patches, again two distinct families of solutions exist: one with the central patch and satellite patches having the same-signed vorticity and the other in which they are opposite-signed. In each family, there are two limiting behaviours in which either the central patch or the satellite patches develop corners or cusps. Streamline plots and time-dependent simulations indicate that opposite-signed multipolar equilibria are robust structures and same-signed equilibria are generally less stable. Streamlines also reveal stable and unstable (saddle point) stagnation points, indicating the existence of new equilibria in which additional patches of vorticity are “grown” at the stagnation points. Examples of such equilibria are computed, and a general numerical routine is briefly described for finding even more complex finite-area equilibria. Finally, new nested polygonal vortex equilibria consisting of two sets of polygonally arranged vortex patches (named “N + N” equilibria here) are computed for two distinct cases: one with the corners of the polygons aligned with each other and the other when they are staggered. Various limiting states are computed for these equilibria. Time-dependent simulations reveal that the aligned equilibria are susceptible to instability, while the staggered equilibria survive a relatively long time. In some parameter regimes, following instability, these structures evolve into known structures such as “N + 1” multipolar vortex equilibria and N-polygon co-rotating equilibria.

Nonlinear electron transport in GaAs/InGaAs asymmetric double-quantum-well pseudomorphic high-electron-mobility transistor structure

We analyze the structural-asymmetry-induced nonlinear enhancement of the electron mobility μ in a GaAs/InxGa1−xAs double-quantum-well pseudomorphic high-electron-mobility transistor (p-HEMT). We consider the well widths wi and ws and the doping concentrations ndi and nds in the barriers along the substrate (inverted doping) and surface (surface doping), respectively. We show that for a suitable choice of ws and nds, the variation of wi leads to interesting changes in the occupation of subbands, i.e., first, single-subband, then double-subband, and again, single-subband occupancy. By increasing ndi, the range of double-subband occupancy is enhanced. However, the lowering of μ due to the inter-subband effects is minimized. In the case of a single-channel HEMT, i.e., say, for ndi = 0, only a single subband is occupied. The mobility exhibits a cusplike behavior with a minimum at a certain value of wi. If one takes a higher value of nds, the occupation of subbands shows a different trend, i.e., from single- to double-subband occupancy as a function of wi for different ndi values with nonmonotonic variations of μ. Our results of the nonlinear enhancement of mobility can be utilized for the analysis of the coupled GaAs/InxGa1−xAs double-quantum-well p-HEMT structure.

Change of magnetic behaviour of nitrogenated carbon nanotubes on chlorination/oxidation

The magnetic effects of chlorine and oxygen functionalised NCNTs have been studied. The diamagnetic behaviour of non-functionalised NCNTs changes to paramagnetic behaviour on Cl-functionalisation; on O-functionalisation NCNTs become ferromagnetic. A prominent cusp-like behaviour is observed at around ≈45 K in MFC and MZFC measurements, further confirming the ferromagnetic behaviour of O-functionalised NCNTs; but Cl-functionalised NCNTs do not shows any cusp-like behaviour indicating formation of paramagnetic behaviour. The change of magnetic behaviour occurs owing to formation of different bonding with carbon/nitrogen and/or Fe-catalyst atoms that is verified with theoretical calculation. The initial computational results show that the differential bonding patterns of the Cl-functionalised and the O-functionalised NCNTs are the main cause for the different magnetic behaviour in these systems.

Ionization of Atoms by Slow Heavy Particles, Including Dark Matter.

Atoms and molecules can become ionized during the scattering of a slow, heavy particle off a bound electron. Such an interaction involving leptophilic weakly interacting massive particles (WIMPs) is a promising possible explanation for the anomalous 9σ annual modulation in the DAMA dark matter direct detection experiment [R. Bernabei et al., Eur. Phys. J. C 73, 2648 (2013)]. We demonstrate the applicability of the Born approximation for such an interaction by showing its equivalence to the semiclassical adiabatic treatment of atomic ionization by slow-moving WIMPs. Conventional wisdom has it that the ionization probability for such a process should be exponentially small. We show, however, that due to nonanalytic, cusplike behavior of Coulomb functions close to the nucleus this suppression is removed, leading to an effective atomic structure enhancement. We also show that electron relativistic effects actually give the dominant contribution to such a process, enhancing the differential cross section by up to 1000 times.

Signature of a polyamorphic transition in the THz spectrum of vitreous GeO2.

The THz spectrum of density fluctuations, S(Q, ω), of vitreous GeO2 at ambient temperature was measured by inelastic x-ray scattering from ambient pressure up to pressures well beyond that of the known α-quartz to rutile polyamorphic (PA) transition. We observe significant differences in the spectral shape measured below and above the PA transition, in particular, in the 30–80 meV range. Guided by first-principle lattice dynamics calculations, we interpret the changes in the phonon dispersion as the evolution from a quartz-like to a rutile-like coordination. Notably, such a crossover is accompanied by a cusp-like behavior in the pressure dependence of the elastic response of the system. Overall, the presented results highlight the complex fingerprint of PA phenomena on the high-frequency phonon dispersion.

An alternative explanation of the change in T-dependence of the effective Debye-Waller factor at T(c) or T(B).

The cusp-like temperature dependence of the Debye-Waller factor or non-ergodicity parameter f(Q)(T) at some temperature T(c) above T(g) found by experiments in several fragile glassformers has been considered as critical evidence for validity of the ideal Mode Coupling Theory (MCT). A comprehensive review of experimental data of f(Q)(T) and beyond brings out various problems of the MCT predictions. For example, the molten salt, 0.4Ca(NO3)2-0.6KNO3 (CKN), was the first glassformer measured by neutron scattering to verify the cusp-like behavior of f(Q)(T) at T(c) predicted by ideal MCT. While the fits of the other scaling laws of MCT to viscosity, light scattering, and dielectric relaxation data all give T(c) in the range from 368 to 375 K, there is no evidence of cusp-like behavior of f(Q)(T) at T(c) from more accurate neutron scattering data obtained later on by Mezei and Russina [J. Phys.: Condens. Matter 11, A341 (1999)] at temperatures below 400 K. In several molecular glass-formers, experiments have found at temperatures below T(c) that [1-f(Q)(T)] is manifested as nearly constant loss (NCL) in the frequency dependent susceptibility. The NCL persists down to below T(g) and is not predicted by the ideal MCT. No clear evidence of the change of T-dependence of f(Q)(T) at any T(c) was found in intermediate and strong glassformers, although ideal MCT does not distinguish fragile and strong glassformers in predicting the critical behavior of f(Q)(T) a priori. Experiments found f(Q)(T) changes T-dependence not only at T(c) but also at the glass transition temperature T(g). The changes of T-dependence of f(Q)(T) at T(c) and T(g) are accompanied by corresponding changes of dynamic variables and thermodynamic quantities at T(B) ≈ T(c) and at T(g). The dynamic variables include the relaxation time τ(α)(T), the non-exponentiality parameter n(T), and the generalized fragility m(T) of the structural α-relaxation. The thermodynamic quantities are the free volume deduced from positron annihilation spectroscopy, and the configurational entropy obtained from adiabatic calorimetry measurements. These changes of dynamic variables and thermodynamic quantities in temperature dependence at T(B) ≈ T(c) occur concurrently with the change of f(Q)(T) and suggest the effects are related, and have to be explained altogether. Since this task cannot be carried out by the ideal MCT, we have provided a different interpretation of f(Q)(T) and an alternative explanation of the change in its T-dependence of f(Q)(T) at T(B) ≈ T(c) as well as the other dynamic variables. We show f(Q)(T) originates from the dissipation of the molecules while caged by the anharmonic intermolecular potential, and manifested as the NCL at lower temperatures. The cusp-like change of T-dependence of f(Q)(T) at T(c) originates from the corresponding change of free volume and configurational entropy at T(B) ≈ T(c), which also explains the simultaneous changes of the T-dependencies of the other dynamic variables. The alternative explanation is able to resolve the conundrum in CKN because T(B) is ≥400 K, and hence the change of T-dependence of f(Q)(T) at T(c) ≈ T(B) was not observed in data taken at temperatures lower than 400 K by Mezei and Russina. The alternative explanation also can rationalize the difference between fragile and non-fragile glassformers in the strength of the observed changes of f(Q)(T) at T(c) and T(g) as well as the other dynamic quantities at T(B) ≈ T(c) and T(g).

Antiferro- and ferromagnetic ordering in a PrGe single crystal

An equiatomic PrGe single crystal was grown by the Czochralski pulling method. The grown single crystal was found to have CrB-type orthorhombic crystal structure with the space group Cmcm (no. 63). Transport and magnetization data reveal large anisotropy in the electrical resistivity, magnetic susceptibility and magnetization. PrGe was found to exhibit two consecutive magnetic orderings at 44 K and 41.5 K, respectively. The magnetic susceptibility measurement along the three principal directions in low applied fields revealed a cusp-like behaviour at 44 K while at 41.5 K a ferromagnetic-like increase was observed. The hysteretic behaviour in the magnetization measurement at 1.8 K confirmed the ferromagnetic nature of PrGe at low temperatures. The heat capacity data clearly revealed the bulk nature of two magnetic transitions by the presence of two sharp peaks attaining values exceeding 40 J K−1 mol−1 at the respective temperatures. The absence of a Schottky contribution in the magnetic part of the heat capacity indicates a quasi-ninefold degenerate J = 4 magnetic ground state in this system. The low temperature data of electrical resistivity and the magnetic part of the heat capacity show the existence of a gap in the spin-wave spectrum.

Berry Phases and Entanglement of a Two Spin-1/2 Model with Dzyaloshinski-Moriya Interaction in Magnetic Fields

We show that the entanglement (as quantified by the concurrence) and Berry phases of the adiabatic quantum states vanish for a two spin-1/2 system with Dzyaloshinski-Moriya (DM) interaction, while one of the spins is driven by a time-varing rotating magnetic field and the other one is coupled with a strong static magnetic field. The system is described by the Heisenberg XX model and the static field is in the direction of the rotation axis. We also investigate that how the concurrence and Berry phases depend on the DM interaction, coupling coefficient and the static magnetic field. In addition, we show that reversing the sign of the static magnetic field can cause exchange of the Berry phases and entanglement between the adiabatic states. Finally it is shown that each energy level approach causes jumps or cusp-like behaviour in the Berry phases and the concurrences.

Spectrum of facet crystallization waves at smooth 4He crystal surfaces

Wavelike crystallization and melting processes or crystallization waves are widely known to exist at 4He crystal surfaces in the rough state. Much less is known about crystallization waves for 4He crystal surfaces in the smooth, well-faceted state below the roughening transition temperature. Here we analyze the spectrum of facet crystallization waves and its dependence on wavelength, perturbation amplitude, and the number of possible facet steps distributed over a wavelength. All the distinctive features of facet crystallization waves compared to conventional waves at a rough surface result from a nonanalytic cusplike behavior in the angular dependence of the surface tension of smooth crystal facets.

Observation of Threshold Effects in Positron Scattering from the Noble Gases

Channel coupling is a phenomenon that has been investigated for many scattering processes, and is responsible for the formation of cusps or steps in the cross sections for open scattering channels at, or near, the onset of a new scattering channel. It has long been speculated that the opening of the positronium formation channel may lead to the formation of such cusp features in the elastic positron scattering cross section. In this work, elastic scattering of positrons has been measured in the region of the positronium formation threshold for the noble gases He-Xe. Cusplike behavior is observed and, while the features which are observed appear broad, they represent a magnitude of between 4 and 15% of the total elastic cross section. No evidence is found of any other features in this region, at least within the uncertainty of the present data, discounting the possibility of scattering resonances.