By means of high-pressure resistivity measurements on single crystals, we investigate the charge transport properties of Cu$_x$PdTe$_2$, notable for the combination of topological type-II Dirac semimetallic properties with superconductivity up to $T_c = 2.5$ K. In both cases of pristine ($x = 0$) and intercalated ($x=0.05$) samples, we find an unconventional $T^4$ power law behavior of the low-temperature resistivity visible up to $\sim$40 K and remarkably stable under pressure up to 8.2 GPa. This observation is explained by the low carrier density $n$, which strongly reduces the $k$-region available for electron-phonon scattering, as previously reported in other low-$n$ two-dimensional systems, such as multilayer graphene and semiconductor heterostructures. Our data analysis complemented by specific heat measurements and supported by previous quantum oscillation studies and \textit{ab initio} calculations suggests a scenario of one-band charge transport. Within this scenario, our analysis yields a large value of transport electron-phonon coupling constant $λ_{tr} = 1.2$ at ambient pressure that appears to be strongly enhanced by pressure assuming a constant effective mass.
Superconducting PdTe Thin Film Via Topotactic Transformation, Toward Topological Superconductors
Rutgers University（罗格斯大学）；University of Science and Technology of China（中国科学技术大学）；Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences（中国科学院宁波材料技术与工程研究所）；Carnegie Mellon University（卡内基梅隆大学）
Two-dimensional transition metal dichalcogenide PdTe$_2$ recently attracts much attention due to its phase coexistence of type-II Dirac semimetal and type-I superconductivity. Here we report a 67 % enhancement of superconducting transition temperature in the 1T-PdSeTe in comparison to that of PdTe2 through partial substitution of Te atoms by Se. The superconductivity has been unambiguously confirmed by the magnetization, resistivity and specific heat measurements. 1T-PdSeTe shows type-II superconductivity with large anisotropy and non-bulk superconductivity nature with volume fraction ~ 20 % e…
The type II Dirac semimetal PdTe$_2$ is unique in the family of topological parent materials because it displays a superconducting ground state below 1.7 K. Despite wide speculations on the possibility of an unconventional topological superconducting phase, tunneling and heat capacity measurements revealed that the superconducting phase of PdTe$_2$ follows predictions of the microscopic theory of Bardeen, Cooper and Shriefer (BCS) for conventional superconductors. The superconducting phase in PdTe$_2$ is further interesting because it also displays properties that are characteristics of type-I…
The Dirac semimetal PdTe${}_2$ becomes superconducting at a temperature $T_{c}=1.6$~K. Thermodynamic and muon spin rotation experiments support type-I superconductivity, which is unusual for a binary compound. A key property of a type-I superconductor is the intermediate state which presents a coexistence of superconducting and normal domains (flux structures) at magnetic fields lower than the thermodynamic critical field $H_{c}$. By means of scanning SQUID microscopy (SSM) we observe flux structures in the superconducting state of PdTe${}_2$. The flux structures are strongly history dependent…
The transition metal dichalcogenide PdTe$_2$ was recently shown to be a unique system where a type II Dirac semimetallic phase and a superconducting phase co-exist. This observation has led to wide speculation on the possibility of the emergence of an unconventional topological superconducting phase in PdTe$_2$. Here, through direct measurement of the superconducting energy gap by scanning tunneling spectroscopy (STS), and temperature and magnetic field evolution of the same, we show that the superconducting phase in PdTe$_2$ is conventional in nature. The superconducting energy gap is measure…
We have fabricated superconductor-normal metal side-junctions with different barrier transparencies out of PdTe$_2$ crystalline flakes and measured the differential conductance spectra. Modeling our measurements using a modified Blonder Tinkham Klapwijk (BTK) formalism confirms that the superconductivity is mostly comprised of the conventional $s$-wave symmetry. We have found that for junctions with very low barrier transparencies, the junctions can enter a thermal regime, where the critical current becomes important. Adding this to the BTK-model allows us to accurately fit the experimental da…
The type-II Dirac semimetal PdTe2 was recently reported to be a type-I superconductor with a superconducting transition temperature Tc = 1.65 K. However, the recent results from tunneling and point contact spectroscopy suggested the unusual state of a mixture of type-I and type-II superconductivity. These contradictory results mean that there is no clear picture of the superconducting phase diagram and warrants a detailed investigation of the superconducting phase. We report here the muon spin rotation and relaxation ($μ$SR) measurements on the superconducting state of the topological Dirac se…
We use electrical transport, magnetoresistance, and heat capacity measurements on high quality single crystals of the recently discovered superconducting Type-II Dirac semi-metal PdTe$_2$, to probe the nature of it's superconducting phase. The magnitude of the electronic heat capacity anomaly at $T_c$, the low temperature exponential $T$ dependence of the heat capacity, and a conventional $H - T$ phase diagram establish that the superconductivity in PdTe$_2$ is conventional in nature despite the presence of a topologically non-trivial Fermi surface band which contributes to the electrical cond…
Though the superconducting phase of the type-II Dirac semimetal PdTe$_2$ was shown to be conventional in nature, the phase continued to be interesting in terms of its magnetic properties. While certain experiments indicated an unexpected type-I superconducting phase, other experiments revealed formation of vortices under the application of magnetic fields. Recently, scanning tunneling spectroscopy (STS) experiments revealed the existence of a mixed phase where type-I and type-II behaviours coexist. Here, based on our temperature and magnetic field dependent STS experiments on Cu-intercalated P…
Superconducting gap structure was probed in type-II Dirac semimetal PdTe$_2$ by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding $λ(T=0)=230$~nm as the only fit parameter at a fixed $Δ(0)/T_c\approx 1.76$, and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-indep…
Type I superconductivity has recently been reported for the Dirac semimetal PdTe$_2$ (Tc approximately 1.6K) with, remarkably, multiple critical fields and a complex phase diagram. Here, measurements of the specific heat utilizing a thermal relaxation technique are presented. Conventional weak-coupling BCS superconductivity is confirmed by examining the temperature dependence of the specific heat in zero field. By probing the latent heat accompanying the superconducting transition, thermodynamic evidence for type I superconductivity is attained. The presence of the intermediate state is observ…
We report our point-contact spectroscopy (PCS) study on the superconducting state of the type-II Dirac semimetal PdTe$_2$ with a superconducting transition temperature $T\rm_c \sim$ 1.65 K. Both mechanical- and soft- PCS differential conductance curves at 0.3 K show a consistent double-peak structure and they can be perfectly fitted by a single s-wave gap based on the Blonder-Tinkham-Klapwijk model. The gap follows a typical Bardeen-Cooper-Schrieffer temperature behavior, yielding $Δ_0 \sim$ 0.29 meV and 2$Δ_0$/$k\rm_{B}$$T\rm_{c}$ = 4.15 in the strong coupling regime. A sudden suppression of …
The transition metal dichalcogenide PdTe$_2$ has attractive features based on its classification as a type-II Dirac semimetal and the occurrence of type-I superconductivity, providing a platform for discussion of a topological superconductor. Our recent work revealed that type-I superconductivity persists up to pressures of $\sim2.5$ GPa and the superconducting transition temperature $T_{\rm c}$ reaches a maximum at around 1 GPa, which is inconsistent with the theoretical prediction. To understand its non-monotonic variation and investigate superconductivity at higher pressures, we performed s…
We report on the fabrication of Josephson junction devices with weak links utilizing the Weyl and higher-order topological semimetal $\text{WTe}_2$. We show that $\text{WTe}_2\text{/Pd}$ contact annealed at a low temperature of 80°C did not exhibit superconducting properties because neither $\text{WTe}_2$ nor Pd are superconductors in the ground state. Upon 180°C annealing, spontaneous formation of superconducting $\text{PdTe}$ due to Pd diffusion enabled us to obtain the interface between $\text{WTe}_2$ and superconductor suitable for the Josephson junction. This result is a facile technique …
Effect of pressure on the superconducting properties of Au substituted PdTe$_2$ with the CdI$_2$-type structure
Niigata University（新潟大学）；National Institute for Materials Science (NIMS)（国立材料研究所）；University of the Ryukyus（冲绳大学）；Tokyo Metropolitan University（东京都立大学）；University of Amsterdam（阿姆斯特丹大学）
We report a doping study directed to intentionally induce disorder in PdTe$_2$ by the isoelectronic substitution of Pt. Two single-crystalline batches Pd$_{1-x}$Pt$_x$Te$_2$ have been prepared with nominal doping concentrations x = 0.05 and x = 0.10. Sample characterization by energy dispersive x-ray spectroscopy (EDX) revealed Pt did not dissolve homogeneously in the crystals. For the nominal value x = 0.10 small single crystals cut from the batch appeared to have x = 0.09, as well as the non stoichiometric composition Pd$_{0.97}$Pt$_{<0.004}$Te$_{2.03}$. Magnetic and heat capacity measuremen…
The Dirac semimetal PdTe$_2$ was recently reported to be a type-I superconductor ($T_c = $1.64 K, $μ_0 H_c (0) = 13.6$ mT) with unusual superconductivity of the surface sheath. We here report a high-pressure study, $p \leq 2.5$ GPa, of the superconducting phase diagram extracted from ac-susceptibility and transport measurements on single crystalline samples. $T_c (p)$ shows a pronounced non-monotonous variation with a maximum $T_c = $1.91 K around 0.91 GPa, followed by a gradual decrease to 1.27 K at 2.5 GPa. The critical field of bulk superconductivity in the limit $T \rightarrow 0$, $H_c(0,p…
Low temperature ($\sim$ 20~K) electron irradiation with 2.5 MeV relativistic electrons was used to study the effect of controlled non-magnetic disorder on the normal and superconducting properties of the type-II Dirac semimetal PdTe$_2$. We report measurements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using tunnel-diode resonator technique for various irradiation doses. The normal state electrical resistivity follows Matthiessen rule with an increase of the residual resistivity at a rate of $\sim$0.77$ μΩ$cm/$(\textrm{C}/\textrm{cm}^2)$. London pen…
Enhanced (001) anomalous scattering by YBa2Cu3O7-d 50 nm films on SrTiO3 substrates with and without a grain boundary versus temperature is interpreted using crystallographic weights to distinguish it from total electron yield and fluorescence spectra. The power of diffraction enhancement is to ascertain the film oxygen composition from the changes in the c-axis, c0 as the film surface is scanned across the grain boundary, and to determine that c0 is constant versus temperature across the superconducting phase transition.
The superconducting transition temperature $T_{c}$ of multilayers of electron-doped cuprates, composed of underdoped (or undoped) and overdoped La% $_{2-x}$Ce$_{x}$CuO$_{4}$ (LCCO) and Pr$_{2-x}$Ce$_{x}$CuO$_{4}$ (PCCO) thin films, is found to increase significantly with respect to the $T_{c}$ of the corresponding single-phase films. By investigating the critical current density of superlattices with different doping levels and layer thicknesses, we find that the $T_{c}$ enhancement is caused by a redistribution of charge over an anomalously large distance.
The study of subtle effects on transport in semiconductors requires high-quality epitaxial structures with low defect density. Using hybrid molecular beam epitaxy (MBE), SrTiO$_3$ films with low-temperature mobility exceeding 42,000 cm$^2$V$^{-1}$s$^{-1}$ at low carrier density of 3 x 10$^{17}$ cm$^{-3}$ were achieved. A sudden and sharp decrease in residual resistivity accompanied by an enhancement in the superconducting transition temperature were observed across the second Lifshitz transition (LT) where the third band becomes occupied, revealing dominant intra-band scattering. These films f…
We have introduced an improved X-ray phase-retrieval method with unprecedented speed of convergence and precision, and used it to determine with sub-Ångstrom resolution the complete atomic structure of an ultrathin superconducting bilayer film, composed of La$_{1.55}$Sr$_{0.45}$CuO$_{4}$ and La$_{2}$CuO$_{4}$ neither of which is superconducting by itself. The results show that phase-retrieval diffraction techniques enable accurate measurement of structural modifications in near-surface layers, which may be critically important for elucidation of surface-sensitive experiments. Specifically we f…
We present measurements of $ab$-plane resistivity $ρ_{ab}(T)$ and superfluid density [$\propto λ^{-2}$, $λ$ = magnetic penetration depth] in $La_{2-x}Sr_{x}CuO_{4}$ films. As Sr concentration $x$ exceeds about 0.22, the superconducting transition sharpens dramatically, becoming as narrow as 200 mK near the super-to-normal metal quantum critical point. At the same time, $ρ_{ab}(T)$, $λ^{-2}(T)$, and transition temperature $T_c$ decrease, and upward curvature develops in $λ^{-2}(T)$. Given the sharp transitions, we interpret these results in the context of a homogeneous d-wave superconducting st…
Interest in superconducting proximity effect has been revived by the exploitation of Andreev states and by the possible emergence of Majorana bound states at the interface. Spectroscopy of these states has been so far restricted to just a handful of superconductor-metal systems in the diffusion regime, whereas reports in otherwise clean superconductor-superconductor heterojunctions are scarce. Here, we realize molecular beam epitaxy growth of atomically sharp planar heterojunctions between Pb and a topological superconductor candidate RhPb2 that allows us to spectroscopically image the proximi…
We have studied an anomalous microwave (mw) response of superconducting YBa_{2}Cu_{3}O_{7-delta} (YBCO) microstrip resonators in the presence of a weak dc magnetic field, H_{dc}. The surface resistance (R_{s}) and reactance (X_{s}) show a correlated non-monotonic behaviour as a function of H_{dc}. R_{s} and X_{s} were found to initially decrease with elevated H_{dc} and then increase after H_{dc} reaches a crossover field, H_{c}, which is independent of the amplitude and frequency of the input mw signal within the measurements. The frequency dependence of R_{s} is almost linear at fixed H_{dc}…
A high-entropy-alloy-type (HEA-type) superconductor is new category of highly disordered superconductors. Therefore, finding brand-new superconducting characteristics in the HEA-type superconductors would open new avenue to investigate the relationship between structural disorder and superconductivity. Here, we report on the remarkable broadening of specific heat jump near a superconducting transition tempreature (Tc) in transition-metal zirconides (TrZr2) with different mixing entropy (ΔSmix) at the Tr site. With increasing ΔSmix, the superconducting transition seen in specific heat became br…
The anomalous decrease in microwave surface resistance, R_{s}, of superconducting YBa_{2}Cu_{3}O_{7-d} (YBCO) thin films in the presence of a low dc magnetic field is studied using a microstrip resonator technique. We have done a dc field hysteresis measurement of R_{s} to study the effects of vortex penetration on the anomalous effect. It is shown that the anomaly happens at a field level far below the low critical field, H_{c1,strip}, of the superconducting microstrip and vortex (Abrikosov) penetration would eliminate the anomalous effect observed at low field. This implies that the anomalou…
We have discovered an oscillatory magnetoresistance phenomenon in a wide range of superconducting systems, with a periodicity that is essentially independent of temperature, transport current, magnetic field, and even material parameters. The nearly universal period points to a possible fundamental mechanism deeper than superconductivity itself, and may result from intrinsic pair-breaking mechanisms at sub-atomic length scales.
We report the superconducting transition temperature of 6Li between 16-26 GPa, the lightest system to exhibit superconductivity to date. The superconducting phase diagram of 6Li is compared to that of 7Li through simultaneous measurement in a diamond anvil cell (DAC) 1, 2. Below 21.5 GPa, Li exhibits a direct, but unusually large isotope effect, while between 21.5-26 GPa, lithium shows an inverse superconducting isotope effect. The unusual dependence of the superconducting phase diagram of lithium on its atomic mass provides evidence that quantum solid effects dominate the low temperature prop…
Raman studies on Ca4Al2O5.7Fe2As2 superconductor in the temperature range of 5 K to 300 K, covering the superconducting transition temperature Tc ~ 28.3 K, reveal that the Raman mode at ~ 230 cm-1 shows a sharp jump in frequency by ~ 2 % and linewidth increases by ~ 175 % at To ~ 60 K. Below To, anomalous softening of the mode frequency and a large decrease by ~ 10 cm-1 in the linewidth is observed. These precursor effects at T0 (~ 2Tc) are attributed to significant superconducting fluctuations, possibly enhanced due to reduced dimensionality arising from weaked coupling between the well separ…
In a standard Josephson junction the current is zero when the phase difference between the superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin-orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect -- the hallmark effect of superconducting spintronics --and can be characterized by the corresponding anomalous phase shift ($ϕ_0$). We report the observation of a tunable anomalous Jose…
The field distribution inside the superconducting radiofrequency (SRF) film with different mean free path is studied using niobium (Nb) as an example. The surface resistance of clean Nb film with different substrate and different film thickness is calculated. We also show the study of a special structured multilayer superconducting film called Superconductor-Insulator-Superconductor (SIS) structure.
We have employed magneto-optical imaging to visualize the occurrence of flux avalanches in a superconducting film of a-MoGe. The specimen was decorated with square antidots arranged in a square lattice. We observed avalanches with the anomalous habit of forming trees where the trunk is perpendicular to the main axis of the square lattice, whereas the branches form angles of 45 degrees. The overall features of the avalanches, and in particular the 45 degree direction of the branches, were confirmed by numerical simulations.
There have been continuous efforts in searching for unconventional superconductivity over the past five decades. Compared to the well-established d-wave superconductivity in cuprates, the existence of superconductivity with other high-angular-momentum pairing symmetries is less conclusive. Bi/Ni epitaxial bilayer is a potential unconventional superconductor with broken time reversal symmetry (TRS), for that it demonstrates superconductivity and ferromagnetism simultaneously at low temperatures. We employ a specially designed superconducting quantum interference device (SQUID) to detect, on the…
AC susceptibility measurements have been carried out on superconducting LaO1-xFxFeAs for x=0.07 and 0.14 under He-gas pressures to about 0.8 GPa. Not only do the measured values of dTc/dP differ substantially from those obtained in previous studies using other pressure media, but the Tc(P) dependences observed depend on the detailed pressure/temperature history of the sample. A sizeable sensitivity of Tc(P) to shear stresses provides a possible explanation.
$^{75}$As NMR investigation of a single crystal of superconducting LiFeAs is presented. The Knight shift and the \textit{in situ} ac susceptibility measurements as a function of temperature and external field are indicative of two superconducting (SC) transition temperatures, each of which is associated with its own upper critical field. Strikingly, the Knight shift maintains its normal state value over a temperature range in the SC state before it drops abruptly being consistent with spin-singlet pairing. Together with our previous NMR study, the anomalous SC state featured by the constant Kn…
The thermal expansion coefficient $α$ of MgB$_2$ is revealed to change from positive to negative on cooling through the superconducting transition temperature $T_c$. The Grüneisen function also becomes negative at $T_c$ followed by a dramatic increase to large positive values at low temperature. The results suggest anomalous coupling between superconducting electrons and low-energy phonons.
Anomalous resistive peaks below the superconducting transition temperature in heavily boron doped nanocrystalline diamond films could have potential application in switching devices, however the exact origin is still under study. We establish a temperature dependence of this resistive phase similar to what has been reported for in Josephson junction arrays and other granular superconductors where the charge duel of the Berezinskii-Kosterlitz-Thouless (BKT) transition has been observed. Non-linear magnetoresistance with a temperature dependent peak feature below the critical field are also pres…
A superconductor with broken time reversal and inversion symmetry may exhibit nonreciprocal charge transport, including a nonreciprocal critical current, also known as superconducting diode effect. We report an intrinsic superconducting diode effect in a polar strontium titanate film. Differential resistance measurements reveal a superconducting state whose depairing current is polarity dependent. There is, however, no measurable deviation from Ohmic behavior, implying that this state does not arise from a bulk magnetochiral anisotropy. In the entire measurement range, the only deviation from …
Using micro fabrication techniques, we extracted individual channels of 3-Kelvin (3-K) phase superconductivity in Sr2RuO4-Ru eutectic systems and confirmed odd-parity superconductivity in the 3-K phase, similar to pure Sr2RuO4. Unusual hysteresis in the differential resistance-current and voltage-current characteristics observed below 2 K indicates the internal degrees of freedom of the superconducting state. A possible origin of the hysteresis is current-induced chiral-domain-wall motion due to the chiral p-wave state.
We report investigations of molybdenum nitride (MoN) thin films with different thickness and disorder and with superconducting transition temperature 9.89 K $\ge{T_c}\ge$ 2.78 K. Using terahertz frequency-domain spectroscopy we explore the normal and superconducting charge carrier dynamics for frequencies covering the range from 3 to 38 cm$^{-1}$ (0.1 to 1.1 THz). The superconducting energy scales, i.e. the critical temperature $T_c$, the pairing energy $Δ$, and the superfluid stiffness $J$, and the superfluid density $n_s$ can be well described within the Bardeen-Cooper-Schrieffer theory for …
Recent scanning tunnelling microscopy experiments in NbN thin disordered superconducting films found an emergent inhomogeneity at the scale of tens of nanometers. This inhomogeneity is mirrored by an apparent dimensional crossover in the paraconductivity measured in transport above the superconducting critical temperature $T_c$. This behavior was interpreted in terms of an anomalous diffusion of fluctuating Cooper pairs, that display a {\em quasi-confinement} (i.e., a slowing down of their diffusive dynamics) on length scales shorter than the inhomogeneity identified by tunnelling experiments.…
We have calculated the temperature dependence of the conductance variation ($δS(T)$) of mesoscopic superconductor normal metal(S/N) structures, in the diffusive regime, analysing both weak and strong proximity effects. We show that in the case of a weak proximity effect there are two peaks in the dependence of $δS(T)$ on temperature. One of them (known from previous studies) corresponds to a temperature $T_1$ of order of the Thouless energy ($ε_{Th}$), and another, newly predicted maximum, occurs at a temperature $T_2$ where the energy gap in the superconductor $Δ(T_2)$ is of order $ε_{Th}$. I…
We report an investigation of current transport in Nb/Au/CaSrCuO/YBaCuO heterostructures including an antiferromagnetic interlayer (CaSrCuO). Epitaxial thin films of YBaCuO and CaSrCuO were grown by laser ablation on NdGaO substrates; the thicknesses of CaSrCuO films were 20 and 50 nm, and x=0.15 or 0.5. Our experimental results show that the superconducting current transport is increased in the Nb/Au/CaSrCuO/YBaCuO heterostructures in comparison with the ones observed in previously studied Nb/Au/YBaCuO heterostructures. It was found that the critical current of the structure is very sensitive…
In two-dimensional electron systems with broken inversion and time-reversal symmetries, a Josephson junction reveals an anomalous response: the supercurrent is nonzero even at zero phase difference between two superconductors. We consider details of this peculiar phenomenon in the planar double-barrier configurations of hybrid circuits, where the noncentrosymmetric normal region is described in terms of the paradigmatic Rashba model of spin-orbit coupling. We analyze this anomalous Josephson effect by means of both the Ginzburg-Landau formalism and the microscopic Green's functions approach in…
It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from [Zhang {\it et al.}, Nature 556, 74 (2018)]. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric…
We study the transport properties of a diffusive Josephson junction between two spin-split superconductors made of superconductor-ferromagnetic insulator bilayers (FIS) on top of a 3D topological insulator (TI). We derive the corresponding Usadel equation describing the quasiclassical Green's functions in these systems and first solve the equation analytically in the weak-proximity case. We demonstrate the appearance of an anomalous phase in the absence of an external magnetic field. We also explore non-reciprocal electronic transport. Specifically, we calculate the junction's diode efficiency…
We present fermi liquid expressions for the low temperature behavior of the superfluid stiffness, explain why they differ from those suggested recently by Lee and Wen, and discuss their applicability to data on high-$T_c$ superconductors. We find that a consistent description requires a strong, doping dependent anisotropy, which affects states near the zone corners much more strongly than those near the zone diagonals.
Superconductivity in LaRu$_3$Si$_2$ with the honeycomb structure of Ru atoms has been investigated. It is found that the normal state specific heat C/T exhibits a deviation from the Debye model down to the lowest temperature. A relation $C/T = γ_n+βT^2-ATlnT$ which concerns the electron correlations can fit the data very well. The suppression to the superconductivity by the magnetic field is not the mean-field like, which is associated well with the observation of strong superconducting fluctuations. The field dependence of the induced quasiparticle density of states measured by the low temper…
The doping dependence of the superconducting condensate density, n_{s}^{o}, has been studied by muon-spin-rotation for Y_{0.8}Ca_{0.2}Ba_{2}(Cu_{1-z}Zn_{z})_{3}O_{7-δ} and Tl_{0.5-y}Pb_{0.5+y}Sr_{2}Ca_{1-x}Y_{x}Cu_{2}O_{7}. We find that n_{s}^{o} exhibits a pronounced peak at a unique doping state in the slightly overdoped regime. Its position coincides with the critical doping state where the normal state pseudogap first appears depleting the electronic density of states. A surprising correlation between n_{s}^{o} and the condensation energy U_{o} is observed which suggests unconventional beh…
