Isotropic Gap Research Articles

Evidence for Multiple Underlying Fermi Surface and Isotropic Energy Gap in the Cuprate Parent Compound Ca2CuO2Cl2**Supported by the National Key Research and Development Program of China (2016YFA0300300), the National Natural Science Foundation of China (11334010 and 11534007), the National Basic Research Program of China (2015CB921000), and the Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB07020300).

The parent compounds of the high-temperature cuprate superconductors are Mott insulators. It has been generally agreed that understanding the physics of the doped Mott insulators is essential to understanding the mechanism of high temperature superconductivity. A natural starting point is to elucidate the basic electronic structure of the parent compound. Here we report comprehensive high resolution angle-resolved photoemission measurements on Ca2CuO2Cl2, a Mott insulator and a prototypical parent compound of the cuprates. Multiple underlying Fermi surface sheets are revealed for the first time. The high energy waterfall-like band dispersions exhibit different behaviors near the nodal and antinodal regions. Two distinct energy scales are identified: a d-wave-like low energy peak dispersion and a nearly isotropic lower Hubbard band gap. These observations provide new information of the electronic structure of the cuprate parent compound, which is important for understanding the anomalous physical properties and superconductivity mechanism of the high temperature cuprate superconductors.

Geometric phase for a two-level system in photonic band gab crystal

In this work, we investigate the geometric phase (GP) for a qubit system coupled to its own anisotropic and isotropic photonic band gap (PBG) crystal environment without Born or Markovian approximation. The qubit frequency affects the GP of the qubit directly through the effect of the PBG environment. The results show the deviation of the GP depends on the detuning parameter and this deviation will be large for relatively large detuning of atom frequency inside the gap with respect to the photonic band edge. Whereas for detunings outside the gap, the GP of the qubit changes abruptly to zero, exhibiting collapse phenomenon of the GP. Moreover, we find that the GP in the isotropic PBG photonic crystal is more robust than that in the anisotropic PBG under the same condition. Finally, we explore the relationship between the variation of the GP and population in terms of the physical parameters.

Neutrino Emission from Cooper Pairs at Finite Temperatures

A brief review is given of the current state of the problem of neutrino pair emission through neutral weak currents caused by the Cooper pairs breaking and formation (PBF) in superfluid baryon matter at thermal equilibrium. The cases of singlet-state pairing with isotropic superfluid gap and spin-triplet pairing with an anisotropic gap are analyzed with allowance for the anomalous weak interactions caused by superfluidity. It is shown that taking into account the anomalous weak interactions in both the vector and axial channels is very important for a correct description of neutrino energy losses through the PBF processes. The anomalous contributions lead to an almost complete suppression of the PBF neutrino emission in spin-singlet superfluids and strong reduction of the PBF neutrino losses in the spin-triplet superfluid neutron matter, which considerably slows down the cooling rate of neutron stars with superfluid cores.

Band structure and Fermi surfaces of the reentrant ferromagnetic superconductor Eu(Fe0.86Ir0.14)2As2

The electronic structure of the reentrant superconductor Eu(Fe$_{0.86}$Ir$_{0.14}$)$_{2}$As$_{2}$ (T$_c$ = 22 K) with coexisting ferromagnetic order (T$_M$ = 18 K) is investigated using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS). We study the in-plane and out-of-plane band dispersions and Fermi surface (FS) of Eu(Fe$_{0.86}$Ir$_{0.14}$)$_{2}$As$_{2}$. The near E$_F$ Fe 3d-derived band dispersions near the $\Gamma$ and X high-symmetry points show changes due to Ir substitution, but the FS topology is preserved. From momentum dependent measurements of the superconducting gap measured at T = 5 K, we estimate an essentially isotropic s-wave gap ($\Delta\sim5.25\pm 0.25$ meV), indicative of strong-coupling superconductivity with 2$\Delta$/k$_{B}$T$_{c}\simeq$ 5.8. The gap gets closed at temperatures T $\geq$ 10 K, and this is attributed to the resistive phase which sets in at T$_M$ = 18 K due to the Eu$^{2+}$-derived magnetic order. The modifications of the FS with Ir substitution clearly indicates an effective hole doping with respect to the parent compound.

Specific heat of FeSe: Two gaps with different anisotropy in superconducting state

We present detailed study of specific heat of FeSe single crystals with critical temperature Tc=8.45K at 0.4−200K in magnetic fields 0−9T. Analysis of the electronic specific heat at low temperatures shows the coexistence of isotropic s-wave gap and strongly anisotropic extended s-wave gap without nodes. It was found two possibilities of superconducting gap parameters which give equally description of experimental data: (i) two gaps with approximately equal amplitudes and weight contribution to specific heat: isotropic Δ1=1.7 meV (2Δ1/kBTc=4.7) and anisotropic gap with the amplitude Δ2max=1.8 meV (2Δ2max/kBTc=4.9 and anisotropy parameter m=0.85); (ii) two gaps with substantially different values: isotropic large gap Δ1=1.65 meV (2Δ1/kBTc=4.52) and anisotropic small gap Δ2max=0.75 meV (2Δ2max/kBTc=2) with anisotropy parameter m=0.71. These results are confirmed by the field behavior of the residual electronic specific heat γr.

Microstructure and mechanical properties of hyperuniform heterogeneous materials.

A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.

Highly anisotropic superconducting gaps and possible evidence of antiferromagnetic order in FeSe single crystals

Specific heat has been measured in FeSe single crystals down to 0.414 K under magnetic fields up to 16 T. A sharp specific heat anomaly at about 8.2 K is observed and is related to the superconducting transition. Another jump of specific heat is observed at about 1.08 K which may either reflect an antiferromagnetic transition of the system or a superconducting transition arising from Al impurity. We would argue that this anomaly in low temperature region may be the long sought antiferromagnetic transition in FeSe. Global fitting in wide temperature region shows that the models with a single contribution with isotropic s-wave, anisotropic s-wave, and d-wave gap all do not work well, nor the two isotropic s-wave gaps. We then fit the data by a model with two components in which one has the gap function of $\Delta_0(1+\alpha cos2\theta)$. To have a good global fitting and the entropy conservation for the low temperature transition, we reach a conclusion that the gap minimum should be smaller than 0.15 meV ($\alpha$ = 0.9 to 1), indicating that the superconducting gap(s) are highly anisotropic. Our results are very consistent with the gap structure derived recently from the scanning tunneling spectroscopy measurements and yield specific heat contributions of about 32\% weight from the hole pocket and 68\% from the electron pockets.

Band gap formation and Anderson localization in disordered photonic materials with structural correlations

Disordered dielectric materials with structural correlations show unconventional optical behavior: They can be transparent to long-wavelength radiation, while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency in these materials is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here, we investigate band gaps, and we report Anderson localization in 2D disordered dielectric structures using numerical simulations of the density of states and optical transport statistics. The disordered structures are designed with different levels of positional correlation encoded by the degree of stealthiness [Formula: see text] To establish a unified view, we propose a correlation-frequency ([Formula: see text]-[Formula: see text]) transport phase diagram. Our results show that, depending only on [Formula: see text], a dielectric material can transition from localization behavior to a band gap crossing an intermediate regime dominated by tunneling between weakly coupled states.

Quasiparticle Excitations in the Superconducting State of FeSe Probed by Thermal Hall Conductivity in the Vicinity of the BCS–BEC Crossover

There is growing evidence that the superconducting semimetal FeSe ($T_c\sim8$ K) is in the crossover regime between weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein-condensate (BEC) limits. We report on longitudinal and transverse thermal conductivities, $\kappa_{xx}$ and $\kappa_{xy}$, respectively, in magnetic fields up to 20 T. The field dependences of $\kappa_{xx}$ and $\kappa_{xy}$ imply that a highly anisotropic small superconducting gap forms at the electron Fermi-surface pocket whereas a more isotropic and larger gap forms at the hole pocket. Below $\sim1.0$ K, both $\kappa_{xx}$ and $\kappa_{xy}$ exhibit distinct anomalies (kinks) at the upper critical field $H_{c2}$ and at a field $H^*$ slightly below $H_{c2}$. The analysis of the thermal Hall angle ($\kappa_{xy}/\kappa_{xx}$) indicates a change of the quasiparticle scattering rate at $H^*$. These results provide strong support to the previous suggestion that above $H^*$ a distinct field-induced superconducting phase emerges with an unprecedented large spin imbalance.

Low-Temperature Dependence of the Shear Viscosity in Superconductor S r 2 R u O 4

Low-temperature dependence of the shear viscosity components in superconductor Sr2RuO4 is investigated within the framework of the Boltzmann equation. We will show that this dissipative viscosity has a power-law temperature dependence as T2 for the γ band of the Fermi surface with the isotropic gap. Lupien et al. experimentally found that the shear viscosity components of superconductor Sr2RuO4 change as T1.8 at low temperatures. This relative consistency between the temperature dependence for the isotropic gap and experimental results implies that the gap node of Sr2RuO4 may be a horizontal line node.

Drastic changes in electronic properties of Kondo semiconductor CeRu2Al10 induced by Rh doping: Anisotropic transport properties in the antiferromagnetic ordered state

Electrical resistivity ($\ensuremath{\rho}$), thermopower, and specific heat measurements have been performed on the novel Kondo semiconductor $\mathrm{Ce}{({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Rh}}_{x})}_{2}{\mathrm{Al}}_{10}$ ($x=0$, 0.02, 0.03, and 0.05), which has been attracting a great deal of interest due to an unusual antiferromagnetic (AFM) order below ${T}_{0}$, in order to clarify the Rh doping effect on the anisotropy of the electronic properties in the ordered state. In ${\mathrm{CeRu}}_{2}{\mathrm{Al}}_{10}, \ensuremath{\rho}$ shows an anisotropic increase below ${T}_{0}$ independently of the electric current direction. We propose the existence of two different mechanisms to explain the anisotropic increase of $\ensuremath{\rho}$. One is an isotropic charge gap which enhances $\ensuremath{\rho}$ below ${T}_{0}$ isotropically, although its origin is not known at present. The other is an anisotropic suppression of $\ensuremath{\rho}$ which originates from the anisotropic c-f hybridization and is largest along the orthorhombic $a$ axis. By the Rh doping, the anisotropic temperature dependence of $\ensuremath{\rho}$ below ${T}_{0}$ is drastically changed. For $I\ensuremath{\parallel}b$, the increase is almost completely suppressed and a metallic-like behavior is observed, whereas it is small and isotropic for $I\ensuremath{\parallel}a$ and $c$. From these results, we propose that as a result of the destruction of the spin-gap excitation by the Rh doping, a metallic-like electronic state is formed along the $b$ axis and the small isotropic charge gap is opened in the $ac$ plane. By taking into account the present results and the still high ${T}_{0}$ even in $x=0.05$, we conclude that the AFM order in the Rh-doped ${\mathrm{CeRu}}_{2}{\mathrm{Al}}_{10}$ should be viewed as unusual as the AFM order in ${\mathrm{CeRu}}_{2}{\mathrm{Al}}_{10}$ although the localized character of the Ce-$4f$ electron is apparently enhanced by the Rh doping. We have also examined the evolution of the AFM ordered state from $x=0$ to $x=0.05$, where the AFM ordered moment (${m}_{\mathrm{AF}}$) is aligned along the $c$ axis in $x=0$ and $a$ axis in $x=0.05$. From the results of those experiments in magnetic field, we have revealed that the spin reorientation from ${m}_{\mathrm{AF}}\ensuremath{\parallel}c$ to ${m}_{\mathrm{AF}}\ensuremath{\parallel}a$ takes place quite abruptly just at ${x}_{c}\ensuremath{\sim}0.03$, which could be related to the topology change of the Fermi surfaces.

Rh2Mo3N: Noncentrosymmetrics-wave superconductor

$\mathrm{R}{\mathrm{h}}_{2}\mathrm{M}{\mathrm{o}}_{3}\mathrm{N}$, with a noncentrosymmetric $\ensuremath{\beta}$-manganese structure, has been found to be superconducting with critical temperature ${T}_{c}\ensuremath{\approx}4.3\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Magnetic field dependence of resistivity, magnetization, and specific heat measurements show that its upper critical field of ${\ensuremath{\mu}}_{0}{H}_{c2}^{*}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}7.41\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ comes close to, but does not exceed, the Pauli paramagnetic limit and that the $2\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}{T}_{c}$ value of about 3.62 is in accordance with a conventional $s$-wave superconductor. Andreev reflection spectroscopy measurements using both normal metal and half-metal show conclusively $s$-wave pairing with an isotropic gap.

Optimal width of quasicrystalline slabs of dielectric cylinders to microwave radiation transmission contrast

Light confinement induced by resonant states in aperiodic photonic structures is interesting for many applications. A particular case of these resonances can be found in 2D quasicrystalline arrangements of dielectric cylinders. These systems present a rather isotropic band gap as well as isolated in-gap photonic states (as a result of spatially localized resonances). These states are built by high symmetry polygonal clusters that can be regarded as photonic molecules. In this paper, we study the transmission properties of a slab of glass cylinders arranged in approximants of the decagonal quasicrystalline structure. In particular, we investigate the influence of the slab width in the transmission contrast between the states and the gap. The study is both experimental and numerical in the microwave regime. We find that the best transmission contrast is found for a width of around three times the radiation wavelength. The transmission in the band gap region is mediated by the resonances of the photonic molecules. If the samples are thin enough, they become transparent except around a resonance of the photonic molecule which reflects the incoming light.

Impact of pressure anisotropy on magnetic configuration and stability

A number of tools have recently been developed to study equilibrium and stability in tokamaks with pressure anisotropy. Here we apply these tools to a Mega Ampere Spherical Tokamak (MAST) discharge to calculate equilibrium, Alfvén continua and eigenmodes, through to linear growth and nonlinear saturation of a toroidal Alfvén eigenmode (TAE); this is the first study of wave growth and saturation for anisotropic equilibria. Comparisons with the standard tools which assume an isotropic pressure reveal various differences in equilibrium and modes: the safety factor profile in the isotropic reconstruction is reversed shear while the anisotropic reconstruction gives normal shear; the isotropic TAE gap is much narrower than the anisotropic gap; and the TAE radial mode structure is wider in the anisotropic case. These lead to a modification in the resonant regions of fast-ion phase space, and produce a 35% larger linear growth rate and an 18% smaller saturation amplitude for the TAE in the anisotropic analysis compared to the isotropic analysis.

Thermal properties and electronic structure of superconducting germanide skutterudites and : a multi-band perspective

We present the temperature (T) and magnetic field (H) dependence of heat capacity (C) of the superconducting skutterudite compounds and along with their electronic band structure. We show that the zero-field C(T) in the superconducting state of both the samples cannot be explained using an isotropic single gap or an anisotropic single gap perspective. We find that it can only be explained in terms of two superconducting gaps. The Sommerfeld coefficient of electronic heat capacity in the mixed superconducting state of these compounds obtained from the C(T) closely follows the measured C(H) at 2 K. Observation of two distinct linear regions in with a change of slope in between for both the samples supports the fact that the two gap superconductivity is intrinsic to this family of skutterudites. A large observed in the limit of zero magnetic field for both the samples indicates the possibility of anisotropy in the superconducting gaps of these compounds. Apart from supporting the evidence for the above experimental observations, the band structure calculations also show that the anisotropy of the gaps in is different from that of .

Fully gapped superconductivity in the topological superconductorβ−PdBi2

The recent discovery of the topologically protected surface states in the beta-phase of PdBi2 has reignited the research interest in this class of superconductors. Here, we show results of our muon spin relaxation and rotation (muSR) measurements carried out to investigate the superconducting and magnetic properties and the topological effect in the superconducting ground state of beta-PdBi2. Zero-field muSR data reveal that no sizeable spontaneous magnetization arises with the onset of superconductivity implying that the time reversal symmetry is preserved in the superconducting state of beta-PdBi2. Further, a strong diamagnetic shift of the applied field has been observed in the transverse-field (TF) muSR experiments, indicating that any triplet-pairing channel, if present, does not dominate the superconducting condensate. Using TF-muSR, we estimate that the magnetic penetration depth is 263(10) nm at zero temperature. Temperature dependence of the magnetic penetration depth provides evidence for the existence of a nodeless single s-wave type isotropic energy gap of 0.78(1) meV at zero temperature. Our results further suggest that the topologically protected surface states have no effect on the bulk of the superconductor.

The energy gap of the compound FeSe0.5Te0.5 determined by specific heat and Point Contact Spectroscopy

Abstract The superconductor FeSe 0.5 Te 0.5 was studied with Point Contact spectroscopy and specific heat in polycrystalline samples. The transition temperature determined by magnetic measurement was T C =14.5 K. The size of the energy gap measured by junctions is Δ = 1.9 meV, whereas the gap determined by the specific heat measurements was Δ = 2.3 meV. The gap evolution with temperature follows BCS, the ratio 2 Δ / K B T C has values between 2.88 ≤ 2 Δ / K B T C ≤ 3.04 . The compound was grown by solid state synthesis in quartz ampoules under vacuum at 950 °C. Crystal structure was characterized by X-ray diffraction. The superconducting properties were characterized by magnetization, resistivity and specific heat. This superconductor shows an isotropic energy gap as observed with the fitting of the specific heat at low temperature.

Evidence of double-gap superconductivity in noncentrosymmetricNb0.18Re0.82single crystals

We combine point contact spectroscopy with specific heat measurements to probe the superconducting state in noncentrosymmetric ${\mathrm{Nb}}_{0.18}{\mathrm{Re}}_{0.82}$ single crystals. The conductance spectra clearly exhibit a two-peak structure that is well reproduced within a two-band model with isotropic gaps in the spectrum. Such an observation is confirmed by distinct features of the specific heat both at low temperatures and in the range approaching the transition to the normal state. The analyses provide convincing evidence that the two-gap superconducting pairing is a robust feature of ${\mathrm{Nb}}_{0.18}{\mathrm{Re}}_{0.82}$.

Dirac surface states and nature of superconductivity in Noncentrosymmetric BiPd.

In non-magnetic bulk materials, inversion symmetry protects the spin degeneracy. If the bulk crystal structure lacks a centre of inversion, however, spin–orbit interactions lift the spin degeneracy, leading to a Rashba metal whose Fermi surfaces exhibit an intricate spin texture. In superconducting Rashba metals a pairing wavefunction constructed from these complex spin structures will generally contain both singlet and triplet character. Here we examine the possible triplet components of the order parameter in noncentrosymmetric BiPd, combining for the first time in a noncentrosymmetric superconductor macroscopic characterization, atomic-scale ultra-low-temperature scanning tunnelling spectroscopy, and relativistic first-principles calculations. While the superconducting state of BiPd appears topologically trivial, consistent with Bardeen–Cooper–Schrieffer theory with an order parameter governed by a single isotropic s-wave gap, we show that the material exhibits Dirac-cone surface states with a helical spin polarization.

High-Qoptical cavities in hyperuniform disordered materials

We introduce the first designs for high-Q photonic cavities in slab architectures in hyperuniform disordered solids displaying isotropic band gaps. Despite their disordered character, hyperuniform disordered structures have the ability to tightly confine the TE-polarised radiation in slab configurations that are readily fabricable. The architectures are based on carefully designed local modifications of otherwise unperturbed hyperuniform dielectric structures. We identify a wide range of confined cavity modes, which can be classified according to their approximate symmetry (monopole, dipole, quadrupole, etc.) of the confined electromagnetic wave pattern. We demonstrate that quality factors ($Q$) $Q>10^{9}$ can be achieved for purely 2D structures, and that for three--dimensional finite-height photonic slabs, quality factors $Q>20,000$ can be maintained.