Ratio Of Energy Gap Research Articles

On the Thermodynamic Properties of FexSe0.5Te0.5 Superconducting Single Crystals: An Experimental Study

The variation of the thermodynamic critical fields (Hc) with temperature has been obtained from the equilibrium magnetization of FexSe0.5Te0.5 superconducting single-crystal with (0.95 ≤ × ≤ 1.1). Based on the BCS theory, we used the Hc values to obtain the variations in the energy gap Δ(T), the cooper pair coupling, the energy gap ratio 2Δ(0)/kBTc, and the specific heat jump ΔCBCS/Tc with varying Fe content. We found that the Cooper pairs coupling strength decreases with increasing Fe content within the range (∼3.1 to 2.6) for 1.0 ≤ × ≤ 1.1, which is consistent with the BCS-weak coupling limit for all samples. Moreover, the value of the energy gap is nearly constant at about 3.5 meV for all samples, while the Hc(0)/Tc ratio reaches a maximum near x ∼ 1.05. The obtained values of the energy gap, the coupling strength, and the specific heat ratio are consistent with recently published results using various experimental techniques.

Normal and abnormal thermalization indicators in a one-dimensional low-density Jaynes-Cummings Hubbard model with and without dipole-dipole interaction.

In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.

Holographic p-wave superconductors with momentum relaxation

In the probe limit, we construct the p-wave conductor/superconductor phase transition with momentum relaxation originated from the axion fields by both numerical and analytical methods, and then study the effects of relaxation parameter (k/μ) on the superconductor model. Concretely, the increasing k/μ decreases monotonously the critical temperature and thus hinders the phase transition. The stable value of condensate (C00≡〈Jx〉1/(Δ+1)/μ|T≈0.15Tc) and the coefficient (C1) of condensate (〈Jx〉/μ1/(Δ+1)=C11−T/Tc|T≈Tc) always decrease with the larger k/μ. Near the critical point, the system suffers from a second order phase transition. Meanwhile, for fixed value of k/μ, the larger mass of vector field also suppresses the vector condensate to emerge. As for the above conclusions, the analytical results from the improved trial function agree with the numerical ones. The calculation of the ratio of energy gap to the critical temperature shows that the present superconductor indeed involves strong interaction, which increases with the increasing k/μ.

Gap Structure of 12442-Type KCa2(Fe1−x Co x )4As4F2 (x = 0, 0.1) Revealed by Temperature Dependence of Lower Critical FieldSupported by the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2015187), the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB30000000), and the National Natural Science Foundation of China (Grant Nos.

We report an in-depth investigation on the out-of-plane lower critical field H c1 of the KCa2(Fe1−x Co x )4As4F2 (12442-type, x = 0, 0.1). The multi-gap feature is revealed by the kink in the temperature-dependent H c1(T) curve for the two samples with different doping levels. Based on a simplified two-gap model, the magnitudes of the two gaps are determined to be Δ 1 = 1.2 meV and Δ 2 = 5.0 meV for the sample with x = 0, Δ 1 = 0.86 meV and Δ 2 = 2.8 meV for that with x = 0.1. With the cobalt doping, the ratio of energy gap to critical transition temperature (Δ/k B T c) remains almost unchanged for the smaller gap and is suppressed by 20% for the larger gap. For the undoped KCa2Fe4As4F2, the obtained gap sizes are generally consistent with the results of angle-resolved photoemission spectroscopy experiments.

Unconventional superconductivity in CuxBi2Se3 from magnetic susceptibility and electrical transport

Although the Cu doped Bi2Se3 topological insulator was discovered and intensively studied for almost a decade, its electrical and magnetic properties in normal state, and the mechanism of ‘high-Tc’ superconductivity regarding the relatively low-carrier density are still not addressed yet. In this work, we report a systematic investigation of magnetic susceptibility, critical fields, and electrical transport on the nominal Cu0.20Bi2Se3 single crystals with = 4.18 K, the highest so far. The composition analysis yields the Cu stoichiometry of x = 0.09(1). The magnetic susceptibility shows considerable anisotropy and an obvious kink at around 96 K was observed in the magnetic susceptibility for H∥c, which indicates a charge density anomaly. The electrical transport measurements indicate the two-dimensional (2D) Fermi liquid behavior at low temperatures with a high Kadowaki–Woods ratio, A/γ2 = 30.3a0. The lower critical field at 0 K limit was extracted to be 6.0 Oe for H∥ab. In the clean limit, the ratio of energy gap to Tc was determined to be Δ0/kBTc = 2.029 ± 0.124 exceeding the standard BCS value 1.764, suggesting Cu0.09Bi2Se3 is a strong-coupling superconductor. The in-plane penetration depth at 0 K was calculated to be 1541.57 nm, resulting in an unprecedented high ratio of Tc/λ−2(0) ≅ 9.86. Moreover, the ratio of Tc to Fermi temperature is estimated to be = 0.034. Both ratios fall into the region of unconventional superconductivity according to Uemura’s regime, supporting the unconventional superconducting mechanism in CuxBi2Se3. Finally, the enhanced Tc value higher than 4 K is proposed to arise from the increased density of states at Fermi energy and strong electron–phonon interaction induced by the charge density instability.

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO$_4$, protected by a mirror symmetry and DSM in Na$_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral symmetry order parameter and instantaneous long-range Coulomb interaction with the standard renormalization group method. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction and the electron velocity always becomes faster than one of a chiral symmetry order parameter. Thus, the transition {\it must not} be relativistic, which implies a supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. {Asymptotically exact} universal ratios of physical quantities such as energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

Description of High-Temperature Superconducting State in BSLCO Compound

In the study, we have calculated the dependence of the average value of the energy gap amplitude (G) on the hole concentration (p) and temperature (T) for the Bi2Sr2−x La x CuO6+δ (BSLCO) superconductor. The ratio of the zero temperature energy gap to the critical temperature (R G ≡ G(0)/k B T C) and the ratio of the energy gap to the pseudogap temperature ( $R^{\star }_{\mathrm {G}}\equiv G\left (0\right )/k_{\mathrm {B}}T^{\star }$ ) have been estimated on this basis. It has been found that the value of the parameter R G changes for p ∈ in the range from 32.98 to 7.98. On the other hand, $R^{\star }_{\mathrm {G}}$ takes the values from 2.60 to 3.28. The obtained results indicate that in the studied superconductor, the correlation exists only between the value of the energy gap and the pseudogap temperature, which stands in the sharp contrast with the predictions of the classical Bardeen-Cooper-Schrieffer (BCS) theory. In addition, the dependence of the energy gap on the momentum for the hole concentration corresponding to the maximum value of the pseudogap temperature and the maximum value of the critical temperature has been determined. It has been found that the theoretical results reproduce well the experimental data obtained by using the angle-resolved photoemission spectroscopy (ARPES) method.

Superconductivity in partially filled skutterudite Pr0.5Pt4Ge12

We have investigated the partially filled Skutterudite Pr0.5Pt4Ge12 for its superconducting properties. Resistivity measurements of Pr0.5Pt4Ge12 down to 2K and in the presence of fields up to 2T are reported. The superconducting transition, Tc of ~7.66K observed from zero fields of Resistivity and Heat Capacity measurements. The interesting observation is that the superconductivity survives even at a 50% filling of Pr in the parent compound and its Tc is equal to that of fully doped PrPt4Ge12. We have estimated relevant parameters of interest like the electron phonon coupling constant, critical field, energy gap ratio, coherence length etc.

Phonon-induced superconductivity and physical properties in intercalated fullerides Rb3C60

The nature of electron pairing mechanism and physical properties leading to superconducting state and normal state resistivity in alkali metal (Rb) intercalated fullerenes are explored. Keeping in mind that free electrons in lowest molecular orbital are coupled with inter-molecular phonons, the coupling with inter-molecular phonon leads to transition temperature (Tc) of about 4.17 K. The electrons also couple with the intra-molecular phonons. Within the framework of strong coupling theory, Tc is estimated at 34 K. The carbon isotope effect exponent, the energy gap ratio, influence of pressure and volume on Tc, and thermodynamical parameters describing the superconducting state confer that Rb3C60 as s-wave superconductor. Estimated contribution to resistivity using scattering with inter- and intra-molecular phonon, when subtracted from single crystal data, infers quadratic temperature dependence over most of the temperature range and is attributed to electron–electron inelastic scattering. Both low frequency intermolecular and high frequency intra-molecular phonons have significant bearing in Rb3C60 superconductor.

Robustness and dissipation of mitogen-activated protein kinases signal transduction network: Underlying funneled landscape against stochastic fluctuations

We uncovered the underlying energy landscape of the mitogen-activated protein kinases signal transduction cellular network by exploring the statistical natures of the Brownian dynamical trajectories. We introduce a dimensionless quantity: The robustness ratio of energy gap versus local roughness to measure the global topography of the underlying landscape. A high robustness ratio implies funneled landscape. The landscape is quite robust against environmental fluctuations and variants of the intrinsic chemical reaction rates. As the environmental fluctuations or the variances of the inherent chemical reaction rates increase further more, the landscape becomes less robust and more flatter. We also show that more robust network has less dissipation costs. Our approach is quite general and can be applied to other cellular networks.

EXCITONS IN SINGLE-WALL CARBON NANOTUBES

Excitonic states in single-wall carbon nanotubes have been studied within the tight-binding approximation. An analytical expression for the dielectric function of the nanotube has been obtained in the random phase approximation. It was demonstrated that calculations with the static dielectric function yield an overestimated exciton binding energy exceeding the nanotube energy gap. Self-consistent calculation of the exciton binding energy with the frequency-dependent dielectric function has been performed. The binding energy to energy gap ratio has been shown to have no dependence on the nanotube radius and to be a universal constant ~0.87 for given resonance integral γ0=2.7 eV .

Superconductivity and normal state in-plane resistivity of electron-dopedcuprates Nd-Ce-CuO: screened optical-phonon approach

We have evolved an effective two-dimensional dynamic interaction, whichembodies the screening of electrons by optical phonons and by plasmons to confer theattributes of the pairing mechanism leading to superconductivity in layeredelectron-doped cuprates. The electron-doped Nd-Ce-CuO cuprate behaves as anionic solid containing isolated CuO2 layers of electrons as carriers, and amodel dielectric function is set up that fulfils the appropriate sum rules onthe electronic and ionic polarizabilities. Following strong coupling theory, thesuperconducting transition temperature of optimally-doped Nd-Ce-CuO isestimated as 28 K and the energy gap ratio is larger than theBardeen-Cooper-Schrieffer value. The isotope effect exponent, coherence lengthand magnetic penetration depth are also estimated. Ziman's formula ofresistivity is employed for analysis and a comparison is made with thetemperature-dependent resistivity of a single crystal. The estimated phononcontribution together with the residual resistivity is lower than the reporteddata. The subtracted data infers a clear quadratic temperature dependence fromTc to near to room temperature. The implications of the model and itsanalysis are discussed.

Pairing mechanism and superconducting state parameters of cubic perovskite Ba 0.6K 0.4BiO 3

We develop an effective three-dimensional dynamic interaction, which incorporates screening of charge carriers by optical phonons and by plasmons, to discuss the nature of the pairing mechanism leading to superconductivity in cubic perovskite Ba 0.6K 0.4BiO 3. The potassium-doped barium–bismuth oxide system (Ba–K–BiO) is treated as an ionic solid containing carriers and a model dielectric function is set up which fulfils the appropriate sum rules on the ionic and electronic polarizabilities. The values of the coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the strong coupling regime. Following strong-coupling theory, the superconducting transition temperature of optimally doped Ba–K–BiO is estimated as 30 K. The energy gap ratio is slightly enhanced and the isotope exponent is severely reduced relative to the Bardeen–Cooper–Schrieffer values. The present analysis points to the importance of both plasmons and optical phonons in determining the effective electron–electron interaction leading to superconductivity in doped cubic perovskites.

Pairing Mechanism and Superconductivity of Rb3C60 Fullerides

The nature of electron pairing mechanism and the superconducting transition temperature (T c ) of alkali metal (Rb) doped fullerenes is studied within the framework of strong coupling theory. Chemical substitution of alkali metal in the parent compound introduces free electrons in the lowest unoccupied molecular orbital and for Rb3C60, the band is filled up to the Fermi level. The intercage interactions between the adjacent C60 cages and expansion of lattice due to the intercalation of Rb atoms are investigated using nearest-neighbor interactions. The free electrons in lowest molecular orbital are coupled with intermolecular phonons. The renormalized Coulomb repulsive parameter μ* and the attractive coupling strength λ are obtained for the intermolecular phonon frequency ωer. T c is then estimated as 8.6 K, which is lower as compared with the published data of 30 K. The electrons also couple with the intramolecular phonons and introducing them in ad hoc way, T c enhances to 34 K. Analytical results on T c allow one to visualise the relative interplay between the strength of inter- and intramolecular phonons. To illustrate the usefulness of the above approach the carbon isotope effect exponent and the energy gap ratio are estimated which are consistent with the experimental data. The present analysis reveals that both low frequency intermolecular and high frequency intramolecular phonons participate in the pairing mechanism, T c mainly arises from high frequency intramolecular phonons.

Plasmon–Phonon Pairing Mechanism and Superconducting State Parameters in Layered Mercury Cuprates

An effective two-dimensional dynamic interaction is developed which incorporates screening of holes by plasmons and by optical phonons to discuss the nature of the pairing mechanism leading to superconductivity in layered mercury cuprates. The system is treated as an ionic solid containing layers of charge carriers and a model dielectric function is set up which fulfils the appropriate sum rules on the electronic and ionic polarizabilities. The static limit of the model dielectric function is used to calculate the effective hole-hole coupling strength. The values of the electron-phonon coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the strong coupling regime with effective screening of the charge carriers. The superconducting transition temperature of optimally doped HgBa2CuO4+δ is estimated as 120 K from Kresin's strong coupling theory and the energy gap ratio is substantially larger than the BCS value. The value of the isotope exponent is severely reduced below the BCS value. The implications of the model and its analysis are discussed.

Screened Optical-Phonon Pairing Mechanism in Electron Doped Cuprates

An effective two-dimensional dynamic interaction is developed which incorporates screening of electrons by plasmons and by optical phonons to discuss the nature of the pairing mechanism leading to superconductivity in layered electron doped cuprates. The system is treated as an ionic solid containing layers of electrons as carriers and a model dielectric function is set up which fulfils the appropriate sum rules on the electronic and ionic polarizabilities. Estimate of the Coulomb pseudo-potential (μ*=0.24), describing the screening effects on superconductivity is due to reduced electron density and large value of the optical dielectric constant as well the effective mass of electrons. The electron–phonon coupling constant (λ) is evaluated as 1.5 which infers strong strength of coupling. Following strong coupling theory, the superconducting transition temperature of optimally doped Nd–Ce–CuO is estimated as 30 K and the energy gap ratio is larger than the BCS value. The isotope exponent, coherence length and magnetic penetration depth are also estimated. The implications of the model and its analysis are discussed.

Superconductivity in alkali metal doped fullerenes (K 3C 60): a phonon mechanism

The nature of pairing mechanism and the superconducting state parameters of alkali metal doped fullerenes was investigated using the strong coupling theory. Doping of alkali metal ( K) in the parent compound introduces free electrons in the unfilled band of C 60. It was shown that these electrons distort the K 3C 60 lattice and yield low energy intermolecular vibrations. The developed approach properly incorporates the experimental observations on bulk modulus as well the lattice parameters. The Coulomb repulsive parameter, μ*, and the effective coupling strength, λ eff, are obtained for the intermolecular phonon frequency ω er. We then evaluated the transition temperature, T c, for the phonon frequency ω er (= 51.42 cm −1) as 6.0 K, which is lower when compared with the published data. By introducing the intramolecular phonons, ω ra, in an ad hoc way, the T c enhances from 6 to 21.1 K. The analytical results on T c allow one to visualise the relative interplay between the strength of inter- and intramolecular phonons. The approach was further applied to estimate the carbon isotope exponent and the energy gap ratio and were found to be consistent with the published data. We found that both the low frequency intermolecular and high frequency intramolecular phonons participate in the phonon mediated electron pairing, T c mainly arises from high frequency intramolecular phonons. In this article, the implications of the aforementioned analysis are discussed.

Temperature dependence of the penetration depth in Nd1.85Ce0.15CuO4- delta superconducting thin films.

Measurements of the in-plane magnetic-field penetration depth for the n-doped high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ are reported. The measurements were performed at 4 GHz by a microstrip resonator technique on thin films obtained by laser ablation. The temperature dependence of the penetration depth is carefully analyzed and the energy gap-ratio is estimated. The results confirm that ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ behaves as a BCS-like superconductor.

Band edge offset in strained InxGa1-xAs/GaAs quantum wells measured by high-excitation photoluminescence

A new method is presented for direct and reliable determination of the band edge offset in quantum well (QW) semiconductor heterostructures. It is based on luminescence measurements at various filling levels of the valence and conduction band quantum wells. Magnetoluminescence measurements were made to independently determine the effective masses. The conduction band offset to energy gap ratio for strained InxGa1-xAs QWS in an unstrained GaAs matrix was determined to be 0.79+or-0.05 for x=0.18 and 0.28.

A p-d Hybridization Pairing Model in the Cuprates

A new mechanism for the pairing in cuprate superconductors is proposed and studied by using the mean-field approximations. A hybridization singlet pair is formed by media of strong hybridization between a d hole on Cu site and a p doped hole with opposite spin on the nearest-neighbor O site in the CuO2 plane. The transition temperature can be found to reach a peak around δ ~ 0.1-0.3 and the ratio of energy gap to Tc has a maximum 4.0. This is in good agreement with experiments. The specific heat jump as a function of doping fraction δ, the upper critical field and the coherence length, are obtained.