Isotropic Energy Gap Research Articles

Superconductivity by hidden spin fluctuations in electron-doped iron selenide

Berg, Metlitski and Sachdev, Science 338, 1606 (2012), have shown that the exchange of hidden spin fluctuations by conduction electrons with two orbitals can result in high-temperature superconductivity in copper-oxide materials. We introduce a similar model for high-temperature iron-selenide superconductors that are electron doped. Conduction electrons carry the minimal 3d xz and 3d yz iron-atom orbitals. Low-energy hidden spin fluctuations at the checkerboard wavevector Q_AF result from nested Fermi surfaces at the center and at the corner of the unfolded (one-iron) Brillouin zone. Magnetic frustration from super-exchange interactions via the selenium atoms stabilize hidden spin fluctuations at Q_AF versus true spin fluctuations. At half filling, Eliashberg theory based purely on the exchange of hidden spin fluctuations reveals a Lifshitz transition to electron/hole Fermi surface pockets at the corner of the folded (two-iron) Brillouin zone, but with vanishing spectral weights. The underlying hidden spin-density wave groundstate is therefore a Mott insulator. Upon electron doping, Eliashberg theory finds that the spectral weights of the hole Fermi surface pockets remain vanishingly small, while the spectral weights of the larger electron Fermi surface pockets become appreciable. This prediction is therefore consistent with the observation of electron Fermi surface pockets alone in electron-doped iron selenide by angle-resolved photoemission spectroscopy (ARPES). Eliashberg theory also finds an instability to S+- superconductivity at electron doping, with isotropic Cooper pairs that alternate in sign between the visible electron Fermi surface pockets and the faint hole Fermi surface pockets. Comparison with the isotropic energy gaps observed in electron-doped iron selenide by ARPES and by scanning tunneling microscopy (STM) is consistent with short-range hidden magnetic order.

Current-phase relation in a short clean josephson junction model: application to MgB2

Motivated by recent data on high-quality MgB2 thin films implying that the smaller energy gap has l = 6 (i-wave) symmetry, we consider a simple model for an all-MgB2 symmetric Josephson Junction (JJ). The model assumes an arbitrary-strength delta-function barrier and one-dimensional current conduction. It is shown that in this context a nodal energy gap with i-wave symmetry acts as an isotropic energy gap (s-wave) with an amplitude modified by the energy-gap misalignment-angle with respect to the crystal principal axes. The corresponding exact Green’s function in momentum space is derived employing a novel approach. The ensuing current-phase relations in the strong and weak barrier-strengths limits are calculated and found to confirm known results, e.g., the Ambegaokar-Baratoff current-phase relation. Inspired by an HTS experiment that established the d-wave energy-gap symmetry, we propose a JJ-related experiment with a MgB2 bicrystal to confirm our premise that the smaller energy has i-wave symmetry.

Electron magnetic resonance of iron-gallium borate single crystals

Electron magnetic resonance (EMR) studies of iron-gallium borate, FexGa1−xBO3, single crystals have been carried out in the frequency range ca. 8–38 GHz in magnetizing fields up to 10 kOe and the temperature range of 4–310 K. With decreasing x in the range of 0.34≤x≤1, the EMR spectra show a gradual passage from a low-frequency antiferromagnetic resonance (AFMR) mode at x = 1 toward a coexistence of AFMR and cluster magnetic resonance arising, respectively, from completely and partially magnetically ordered crystal regions. Temperature and concentration dependences of magnetic characteristics of iron-gallium borates, namely, the Néel temperature, the Dzyaloshinskii–Moriya field, and the isotropic energy gap, have been determined by means of AFMR. In contrast to unmixed FeBO3, FexGa1−xBO3 crystals with 0.34≤x≤0.85 show anomalous nonmonotonic temperature dependences of the Dzyaloshinskii–Moriya field with a maximum well below the Néel temperature suggesting the occurrence of another magnetic transition in this temperature range.

Type-I superconductivity in the noncentrosymmetric superconductor BeAu

The noncentrosymmetric superconductor AuBe have been investigated using the magnetization, resistivity, specific heat, and muon-spin relaxation/rotation measurements. AuBe crystallizes in the cubic FeSi-type B20 structure with superconducting transition temperature observed at $T_{c}$ = 3.2 $\pm$ 0.1 K. The low-temperature specific heat data, $C_{el}$(T), indicate a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap 2$\Delta(0)/k_{B}T_{c}$ = 3.76, which is close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $\mu$SR measurements, which is in contrast with the earlier reports of type-II superconductivity in AuBe. The Ginzburg-Landau parameter is $\kappa_{GL}$ = 0.4 $<$ 1/$\sqrt{2}$. The transverse-field $\mu$SR data transformed in the maximum entropy spectra depicting the internal magnetic field probability distribution, P(H), also confirms the absence of the mixed state in AuBe. The thermodynamic critical field, $H_{c}$, calculated to be around 259 Oe. The zero-field $\mu$SR results indicate that time-reversal symmetry is preserved and supports a spin-singlet pairing in the superconducting ground state.

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect.

We present a new measurement method which can be used to image the gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8% anisotropy, as expected for a superconductor with a nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa2Cu3O7-δ thin film shows a clear 4-fold symmetric image with ∼12.5% anisotropy, indicating the well-known 4-fold symmetric dx2-y2 gap nodal structure in the ab-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which are simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.

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.

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.

Majorana excitations, spin and mass currents on the surface of topological superfluid3He-B

The B-phase of superfluid ${}^{3}$He is a 3D time-reversal-invariant topological superfluid with an isotropic energy gap, $\ensuremath{\Delta}$, separating the ground state and bulk continuum states. We report calculations of surface spectrum and spin and mass current densities originating from the Andreev surface states for confined ${}^{3}$He-B. The surface states are Majorana Fermions with their spins polarized transverse to their direction of propagation along the surface, ${\mathbf{p}}_{\ensuremath{\parallel}}$. The negative-energy states give rise to a ground-state helical spin current confined on the surface. The spectral functions reveal the subtle role of the spin-polarized surface states in relation to the ground-state spin current. By contrast, these states do not contribute to the $T=0$ mass current. Superfluid flow through a channel of confined ${}^{3}$He-B is characterized by the flow field, ${\mathbf{p}}_{s}=\frac{\ensuremath{\hbar}}{2}\ensuremath{\nabla}\ensuremath{\varphi}$. The flow field breaks $\mathrm{SO}{(2)}_{{\mathrm{L}}_{\mathrm{z}}+{\mathrm{S}}_{\mathrm{z}}}$ rotational symmetry and time reversal ($T$). However, the Bogoliubov-Nambu Hamiltonian remains invariant under the combined symmetry, ${U}_{\mathrm{z}}(\ensuremath{\pi})\ifmmode\times\else\texttimes\fi{}T$, where ${U}_{\mathrm{z}}(\ensuremath{\pi})$ is a $\ensuremath{\pi}$ rotation about the surface normal. As a result the B phase in the presence of a superflow remains a topological phase with a gapless spectrum of Majorana modes on the surface. Thermal excitation of the Doppler-shifted Majorana branches leads to a power-law suppression of the superfluid mass current for $0&lt;T\ensuremath{\lesssim}0.5{T}_{c}$, providing a direct signature of the Majorana branches of surface excitations in the fully gapped 3D topological superfluid, ${}^{3}$He-B. Results are reported for the superfluid fraction (mass current) and helical spin current for confined ${}^{3}$He-B, including the temperature dependencies, as well as dependencies on confinement, pressure and interactions between quasiparticles.

Superconductivity in the Einstein solid V Al10.1

We used magnetic susceptibility, resistivity and heat capacity measurements to characterize the superconducting state in the Einstein solid V Al10.1. We find that V Al10.1 is a weak-coupling, type-II superconductor with Tc = 1.53 K and an upper critical field of Hc2(0) = 800 Oe. The heat capacity data in the range 0.07 K < T < 1.53 K are consistent with an isotropic energy gap of Δ0 = 0.23 meV.

Evidence for conventional superconducting behavior in noncentrosymmetric Mo3Al2C

We report on measurements of the magnetic penetration depth of polycrystalline samples of nonmagnetic Mo${}_{3}$Al${}_{2}$C (${T}_{c}=9$ K) without inversion symmetry. Two previous specific-heat measurements in this compound found different anomalous peaks in the low-temperature limit. One of these peaks was attributed to the superconducting transition at 3 K of the impurity phase Mo${}_{2}$C. We argue here that the second anomalous peak may be caused by the superconducting transition of SiC:Al at 1.45 K, another impurity phase possibly present in Mo${}_{3}$Al${}_{2}$C samples. The temperature-independent behavior of the penetration depth observed below 0.5 K is taken as firm evidence for the presence of a nodeless superconducting gap in Mo${}_{3}$Al${}_{2}$C. Numerical calculations using the BCS expression for the penetration depth give qualitative support for an isotropic energy gap in Mo${}_{3}$Al${}_{2}$C. The present results suggest that Mo${}_{3}$Al${}_{2}$C is a conventional $s$-wave superconductor, although two-gap or anisotropic-gap superconductivity cannot be ruled out.

Long-period thermal oscillations in superfluid millisecond pulsars

In previous papers, we have shown that, as the rotation of a neutron star slows down, it will be internally heated as a consequence of the progressively changing mix of particles (rotochemical heating). In previously studied cases (non-superfluid neutron stars or superfluid stars with only modified Urca reactions), this leads to a quasi-steady state in which the star radiates thermal photons for a long time, possibly accounting for the ultraviolet radiation observed from the millisecond pulsar J0437-4715. For the first time, we explore the phenomenology of rotochemical heating with direct Urca reactions and uniform and isotropic superfluid energy gaps of different sizes. We first do exploratory work by integrating the thermal and chemical evolution equations numerically for different energy gaps, which uncovers a rich phenomenology of stable and unstable solutions. To understand these, we perform a stability analysis around the quasi-steady state, identifying the characteristic times of growing, decaying, and oscillating solutions. For small gaps, the phenomenology is similar to the previously studied cases, in the sense that the solutions quickly converge to a quasi-steady state. For large gaps ($\gtrsim 0.05$ MeV), these solutions become unstable, leading to a limit-cycle behavior of periodicity $\sim 10^{6-7} yr, in which the star is hot ($T_s\gtrsim 10^5$ K) for a small fraction of the cycle ($\sim 5- 20 %$), and cold for a longer time.

Specific heat andμSR study on the noncentrosymmetric superconductor LaRhSi3

We have investigated the superconducting properties of the noncentrosymmetric superconductor LaRhSi${}_{3}$ by performing magnetization, specific heat, electrical resistivity, and muon spin relaxation ($\ensuremath{\mu}$SR) measurements. LaRhSi${}_{3}$ crystallizes with the BaNiSn${}_{3}$-type tetragonal structure (space group $I4 \mathit{mm}$), as confirmed through our neutron diffraction study. Magnetic susceptibility, electrical resistivity and specific heat data reveal a sharp and well-defined superconducting transition at ${T}_{c}=2.16\ifmmode\pm\else\textpm\fi{}0.08$ K. The low-temperature specific heat data reveal that LaRhSi${}_{3}$ is a weakly coupled bulk BCS superconductor and has an $s$-wave singlet ground state with an isotropic energy gap of $~$0.3 meV, $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}=3.24$. The specific heat data measured in an applied magnetic field strongly indicate a type I behavior. Type I superconductivity in this compound is also inferred from the Ginzburg-Landau parameter, $\ensuremath{\kappa}=0.25$. Various superconducting parameters, including the electron-phonon coupling strength, penetration depth, and coherence length, characterize LaRhSi${}_{3}$ as a moderate dirty-limit superconductor. A detailed study of the magnetic field-temperature ($H\ensuremath{-}T$) phase diagram is presented and from a consideration of the free energy, the thermodynamic critical field, ${H}_{c0}$, is estimated to be $17.1\ifmmode\pm\else\textpm\fi{}0.1$ mT, which is in very good agreement with that estimated from the transverse field $\ensuremath{\mu}$SR measurement that gives ${H}_{c0}=17.2\ifmmode\pm\else\textpm\fi{}0.1$ mT. The transverse field $\ensuremath{\mu}$SR results are consistent with conventional type I superconductivity in this compound. Further, the zero field $\ensuremath{\mu}$SR results indicate that time-reversal symmetry is preserved when entering the superconducting state, also supporting a singlet pairing superconducting ground state in LaRhSi${}_{3}$.

Superconductivity without Nesting in LiFeAs

We have studied the electronic structure of the nonmagnetic LiFeAs (T(c)∼18 K) superconductor using angle-resolved photoemission spectroscopy. We find a notable absence of the Fermi surface nesting, strong renormalization of the conduction bands by a factor of 3, high density of states at the Fermi level caused by a van Hove singularity, and no evidence for either a static or a fluctuating order except superconductivity with in-plane isotropic energy gaps. Our observations suggest that these electronic properties capture the majority of ingredients necessary for the superconductivity in iron pnictides.

Weak Superconducting Pairing and a Single Isotropic Energy Gap in Stoichiometric LiFeAs

We report superconducting (SC) properties of stoichiometric LiFeAs (T(c)=17 K) studied by small-angle neutron scattering (SANS) and angle-resolved photoemission (ARPES). Although the vortex lattice exhibits no long-range order, well-defined SANS rocking curves indicate better ordering than in chemically doped 122 compounds. The London penetration depth lambda(ab)(0)=210+/-20 nm, determined from the magnetic field dependence of the form factor, is compared to that calculated from the ARPES band structure with no adjustable parameters. The temperature dependence of lambda(ab) is best described by a single isotropic SC gap Delta(0)=3.0+/-0.2 meV, which agrees with the ARPES value of Delta(0)(ARPES)=3.1+/-0.3 meV and corresponds to the ratio 2Delta/k(B)T(c)=4.1+/-0.3, approaching the weak-coupling limit predicted by the BCS theory. This classifies LiFeAs as a weakly coupled single-gap superconductor.

Comment on “Muon-spin-rotation study of the superconducting properties of Mo_{3}Sb_{7}”

In a recent article, Tran et al. [Phys. Rev. B 78, 172505 (2008)] reported results from muon-spin-rotation (μSR) measurements of an Mo3Sb7 superconductor. Based on the analysis of the temperature and the magnetic field dependences of the Gaussian relaxation rate, σsc, it was suggested that Mo3Sb7 is a superconductor with two isotropic s-wavelike energy gaps. This relates to results found previously in the specific-heat measurements by several of the same authors in Acta Mater. 56, 5694 (2008). The purpose of this Comment is to point out that from the analysis made by Tran et al., the presence of two superconducting energy gaps in Mo3Sb7 cannot be justified. The analysis of μSR data does not account for the reduction in σsc with increasing temperature. The specific-heat data can be satisfactorily described within the framework of the one-gap model by assuming the presence of a small residual specific-heat component. The experimental data of Tran et al., as well as our earlier published μSR results [Phys. Rev. B 78, 014502 (2008)], all seem to be consistent with the presence of single isotropic superconducting energy gap in Mo3Sb7. © 2010 The American Physical Society

Magnetic Penetration Depth and Gap Symmetry of the Noncentrosymmetric Superconductors CePt3Si and LaPt3Si

We report on measurements of the temperature dependence of the magnetic penetration depth of a very high quality single crystal of nonmagnetic superconductor LaPt3Si without inversion symmetry. The results are compared with those previously reported for the isostructural antiferromagnetic superconductor CePt3Si. At low temperatures, the penetration depth follows a BCS exponential behavior that implies an isotropic energy gap in LaPt3Si, in contrast to a linear response that indicates line nodes in CePt3Si. These line nodes have been argued to be protected by symmetry or accidentally generated by parity mixing. The present results provide support for the viewpoint that parity mixing alone does not seem to lead to unconventionality in CePt3Si and that it requires the antiferromagnetic order to be included.

Muon-spin rotation measurements of the penetration depth of theMo3Sb7superconductor

Measurements of the magnetic field penetration depth \lambda in superconductor Mo_3Sb_7 (T_c~2.1 K) were carried out by means of muon-spin-rotation. The absolute values of \lambda, the Ginzburg-Landau parameter \kappa, the first H_{c1} and the second H_{c2} critical fields at T=0 are \lambda(0)=720(100)nm, \kappa(0)=55(9), \mu_0H_{c1}(0)=1.8(3)mT, and \mu_0H_{c2}(0)=1.9(2)T. The zero temperature value of the superconducting energy gap \Delta(0) was found to be 0.35(1)meV corresponding to the ratio 2\Delta(0)/k_BT_c=3.83(10). At low temperatures \lambda^{-2}(T) saturates and becomes constant below T~0.3T_c, in agreement with what is expected for s-wave BCS superconductors. Our results suggest that Mo_3Sb_7 is a BCS superconductor with the isotropic energy gap

Muon-spin rotation measurements of the penetration depth of the Mo3Sb7 superconductor

Measurements of the magnetic-field penetration depth lambda in superconductor Mo3Sb7 (Tc~=2.1 K) were carried out by means of muon-spin rotation. The absolute values of lambda, the Ginzburg-Landau parameter kappa, and the first Hc1 and the second Hc2 critical fields at T=0 are lambda(0)=720(100) nm, kappa(0)=55(10), µ0Hc1(0)=1.8(3) mT, and µ0Hc2(0)=1.9(2) T. The zero-temperature value of the superconducting energy gap Delta(0) was found to be 0.35(1) meV, corresponding to the ratio 2Delta(0)/kBTc=3.83(10). At low temperatures lambda−2(T) saturates and becomes constant below T~=0.3Tc, in agreement with what is expected for s-wave BCS superconductors. Our results suggest that Mo3Sb7 is a superconductor with the single isotropic energy gap.

Collective Excitations in Electron-Hole Bilayers

We report a combined analytic and molecular dynamics analysis of the collective mode spectrum of a bipolar (electron-hole) bilayer in the strong coupling classical limit. A robust, isotropic energy gap is identified in the out-of-phase spectra, generated by the combined effect of correlations and of the excitation of the bound dipoles. In the in-phase spectra we identify longitudinal and transverse acoustic modes wholly maintained by correlations. Strong nonlinear generation of higher harmonics of the fundamental dipole oscillation frequency and the transfer of harmonics between different modes is observed.