⇦Chinese Physics Letters, 2020, Vol. 37, No. 9, Article code 097403Express Letter Pressure-Dependent Point-Contact Spectroscopy of Superconducting PbTaSe$_2$ Single Crystals Hai Zi (子海)1,2, Ling-Xiao Zhao (赵凌霄)2, Xing-Yuan Hou (侯兴元)2, Lei Shan (单磊)2, Zhian Ren (任治安)2, Gen-Fu Chen (陈根富)2, and Cong Ren (任聪)1,2* Affiliations 1School of Physics and Astronomy, Yunnan University, Kunming 650500, China 2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Science, Beijing 100190, China Received 20 July 2020; accepted 20 August 2020; published online 24 August 2020 Supported by the National Science Foundation of China (Grant Nos. 11574373 and 11774303), and the Joint Fund of Yunnan Provincial Science and Technology Department (Grant No. 2019FY003008).
*Corresponding author. Email: cong_ren@iphy.ac.cn Citation Text: Zi H, Zhao L X, Hou X Y, Dan L and Ren Z A et al. 2020 Chin. Phys. Lett. 37 097403    Abstract We develop an experimental tool to investigate the order parameter of superconductors by combining point-contact spectroscopy measurement with high-pressure technique. It is demonstrated for the first time that planar point-contact spectroscopy measurement on noncentrosymmetric superconducting PbTaSe$_2$ single crystals is systematically subjected to hydrostatic pressures up to 12.1 kbar. Under such a high pressure, the normal-state contact resistance is sensitive to the applied pressure, reflecting the underlying variation of contact transparency upon pressures. In a superconducting state, the pressure dependence of the energy gap $\varDelta_0$ and the critical temperature $T_{\rm c}$ for gap opening/closing are extracted based on a generalized Blond–Tinkham–Klapwijk model. The gap ratio $2\varDelta_0/k_{_{\rm B}}T_{\rm c}$ indicates a crossover from weak coupling to strong coupling in electron pairing strength upon pressure for PbTaSe$_2$. Our experimental results show the accessibility and validity of high-pressure point-contact spectroscopy, offering rich information about high-pressure superconductivity. DOI:10.1088/0256-307X/37/9/097403 PACS:74.45.+c, 74.62.Fj © 2020 Chinese Physics Society Article Text Pressure as a basic thermodynamics parameter and as a tuning parameter in perturbing symmetries of systems under study plays a unique and fundamental role in condensed matter physics. At high pressure, most ambient structures become unstable and transform into structures of higher density and frequently, of higher symmetries. As a consequence, application of pressure can change crystal structures and thus, leads to a modification of electronic structures without introducing any chemical impurities and minimizing the physical complexity. Many of these new high-pressure structures are metallic, and superconductivity has been observed in a number of high-pressure phases, often exhibiting higher coordination and completely different physical properties with respect to the “parent” phases. Highlighted examples of these intriguing high-pressure superconductivity include the high-temperature superconductivity of cuprates[1,2] and iron-based compounds,[3–5] two-dimensional superconductors,[6] or strongly correlated heavy fermion compounds,[7] in which high-pressure superconductivity emerges in the vicinity of a spin and/or charge ordered phase which can be suppressed upon pressures. This strongly pressure-dependent interrelation between the lattice, electronic, and magnetic degrees of freedom calls for new experimental technique combining with high pressure for a deeper understanding of these new superconducting states. However, due to the difficulties of high-pressure experiment, most of the high-pressure experiments involving superconducting properties are limited to electrical transport,[8,9] specific heat[10,11] and NMR[12] experiments. Recently we have developed and demonstrated the success and validity of pressure-dependent tunneling spectroscopy in probing superconducting density of state (DOS) and/or the associated low-energy excitation modes for conventional superconductor.[13] As is expected, the pressure-dependent tunneling spectroscopy has been proven to be a powerful tool in exploring the properties of the superconducting states within high energy resolution. However, progress in high-pressure electron tunneling has been hampered by the formidable difficulties in forming an effective and homogenous 1–2 nm oxide tunnel barrier onto crystals or films. Alternatively, point-contact Andreev reflection (PCAR) spectroscopy, to some extent equivalent to tunneling spectroscopy, has been adopted for probing the magnitude and the structure of superconducting gap and/or low-energy excitation modes of superconductors. In addition, the capability of this technique to probe the gap structure makes it an important tool in providing invaluable information for various mechanisms of unconventional superconductivity.[14,15] In this Letter, we report, for the first time, on an experiment of the pressure-dependent point-contact spectroscopy measurement on a superconductor/normal metal planar junctions. Under high pressures, both the normal and superconducting states of the point-contact spectra are investigated. The results shrew light on high-pressure superconductivity.
cpl-37-9-097403-fig1.png
Fig. 1. (a) Optical microscope image of PbTaSe$_2$ crystal (upper), and schematic of soft point-contact junction between the PbTaSe$_2$ sample and silver particles (lower). (b)–(f) Raw data of conductance spectra at various temperatures for $c$-axis Ag/PbTaSe$_2$ soft point contact under the hydrostatic pressures as labeled. The contact resistance $R_{\rm c}$ is defined based on the value of the conductance ($R_{\rm c}=1/G_{\rm N}$) at high bias voltage in the normal state.
We choose PbTaSe$_2$ as the superconductor under investigation due to its availability of sizable single crystals with atomic flatness on the surface. PbTaSe$_2$ is a non-centrosymmetric material in the $P\bar{6}m2$ space group consisting of TaSe$_2$ layers well separated by Pb interlayers, and it was found to be superconducting with a transition temperature $T_{\rm c}=3.8$ K.[16,17] Recently, it has been demonstrated that $T_{\rm c}$ of PbTaSe$_2$ shows an intriguing hydrostatic pressure dependence.[18,19] High quality single crystals of PbTaSe$_2$ were grown by chemical vapor transport, and the single crystalline samples are usually triangle-shaped with typically $\sim $6 mm in size [Fig. 1(a) up]. “Soft” planar contacts to the flat and shiny surface cleaved along the $c$-axis of PbTaSe$_2$ crystals were made using a thick silver paste bonding with Pt wires (of 16 µm in diameter) in a glove box. The typical size of these planar contacts is about 50–80 µm under a microscope, while for the backside electrical wiring, we applied ultrapure indium or silver paste to cover the whole area of the bottom surfaces of the crystals to minimize the back-contact resistance. Figure 1(a) (lower) shows a sketch of the PbTaSe$_2$/Ag planar point-contact used in this work. It was reported that the contacts made in this way are actually formed with many nano-contacts due to the nanocrystalline nature of the silver paint, analogous to the tip point-contact technique. The contact resistance $R_{\rm c}$ between the silver particles and PbTaSe$_2$ sample was usually in the range of 0.8–5 $\Omega$, typical values of a genuine point-contact between normal metals and superconductors.[20,21] The contact as made ensures a much higher mechanical and thermal stability of the contact itself. More importantly, these planar contacts have the advantage of avoiding inhomogeneous pressure effects induced by the metal tip.[22] Samples were pressurized in a piston-cylinder clamp cell made of Be–Cu alloy 25 with the inner jacket made of alloy MP35N and Daphne 7373 as the pressure transmission medium. A calibrated cernox attached directly on the cell close to the junction was used for thermometry. For each measurement run the pressure inside the cell was determined by monitoring the magnitude change of critical transition temperature $\delta T_{\rm c}$ of the lead film stripe in four-probe measurement. Figures 1(b)–1(f) show the raw point-contact conductance spectra $G(V)$ of a Ag/PbTaSe$_2$ planar contact within varying temperatures under several hydrostatic pressures up to 12.1 kbar. As is shown, these pressure-dependent $G(V)$ curves exhibit systematic and consistent behaviors: (i) An underlying double-peak at gap edge in Andreev conductance is gradually smeared out with increasing $P$, implying a crossover from a low contact transparency at low $P$'s to a dominant Andreev reflection process (high contact transparency) at high $P$'s. (ii) A flat featureless $G(V)$ curve at $T$ close to $T_{\rm c}$ overlapping at high bias voltage is for the normal state, indicative of the similar origin of the underlying normal-state background for each $P$. These flat normal-state $G(V)$'s allow us to unambiguously define contact resistance $R_{\rm c}=1/G_{\rm N}$ and the background-normalized curve for each $P$. As shown in Fig. 2, the contact resistance $R_{\rm c}$ decreases with increasing $P$ in this limited pressure region. In principle, in ballistic regime, $R_{\rm c}=1/G_{\rm N}\propto 1/\tau_{_{\rm N}}$ with $\tau_{_{\rm N}}$ the contact transparency.[23] Accordingly, these lowered contact resistance reflects the variation of contact transparency upon pressure, completely consistent with the aforementioned Andreev conductance. It is interesting to note that in this ballistic regime $R_{\rm c}$ roughly follows a linearly decreasing function with $P$, as shown in the main panel of Fig. 2. For a comparison, the tunneling resistance of a tunnel junction is exponentially lowered with increasing $P$, reflecting the variation of band structure of the barrier material upon pressures.[13] However, it is noted that Mikrajuddin et al.[24] derived a pressure dependence of contact resistance as $R_{\rm c}\propto P^{-1/2}$, inconsistent with our observation in these junctions.
cpl-37-9-097403-fig2.png
Fig. 2. The normalized junction resistance $R_{\rm c}/R_{\rm c}$($P=0.6$ kbar) as a function of hydrostatic pressure $P$'s. The red solid line is the linearity fit in this limited region. Inset: the same $R_{\rm c}$ vs $P$ data in log-log plot to show the deviation from the power-law relationship. The dashed line is a guide to the eyes.
To explicitly describe the variety of spectral behaviors observed and quantitatively resolve the pressure-dependent gap value, we invoke a generalized two-dimensional (2D) Blonder–Tinkham–Klapwijk (BTK) formula[25] developed by Tanaka and Kashiwaya with three parameters:[26] a dimensionless parameter $Z$ which represents the junction transparency, an imaginary quasiparticle energy modification which reflects the spectral broadening, and the superconducting gap size $\varDelta$. Examples of normalized $G(V)$ curves and their 2D BTK-model fits[27] at $T\simeq 0.36$ K are shown in the main panels of Figs. 3(a)–3(c) for junctions under different $P$'s, respectively. As the first check, in Fig. 3(a) we fit the normalized $G(V)$ curve using an isotropic s-wave gap at $P\simeq 0.6$ kbar, yielding a gap value of ${\varDelta}=0.55$ meV. This isotropic s-wave gap and its value are highly consistent with the results of $\mu$SR experiment,[28] scanning tunneling microscopy[29] and penetration depth measurements[30] with a $T_{\rm c}\simeq 3.8$ K at ambient pressure. As $P$ increases, the single s-wave gap BTK model still excellently fits the Andreev conductance curves with a set of fitting parameters $Z$, $\varGamma$ and $\varDelta$, as shown in the main panels of Figs. 3(b) and 3(c) under $P=5.2,\, 12.1$ kbar, respectively. It can be seen that the $Z$ value decreases with increasing $P$, resulting in an increasing $\tau_{_{\rm N}}$ with $P$. This is self-consistent with the observation that the contact resistance $R_{\rm c}$ decreases with increasing $P$. With these fitting parameters, we check the validity of these fits by extending the fit to the overall temperature spectral to extract $\varDelta(T)$ functions under each $P$. As shown in the inset of Figs. 3(a)–3(c), the fitted $Z$ and $\varGamma$ do not vary with $T$ except at temperature close to $T_{\rm c}$ (not shown here).
cpl-37-9-097403-fig3.png
Fig. 3. Normalized conductance $G(V)/G_{\rm N}$ curves at the limited $T\simeq 0.37$ K under different $P$'s (symbols). The red solid lines are the relevant fits with the 2D BTK model for the fitting parameters as labeled, see the text. Insets: the $T$-dependent $G(V)/G_{\rm N}$ curves and their fits at the corresponding $P$.
In Fig. 4 we summarize the extracted gap value as a function of $T$ for different $P$'s. As shown in Fig. 4(a) the obtained $\varDelta$–$T$ relationship can be approximated by an empirical BCS gap formula: $\varDelta(T)=\varDelta(0)\tanh(\alpha\sqrt{T_{\rm c}/T-1})$ with $T_{\rm c}$ the critical temperature at which ${\varDelta}=0$. The obtained $T_{\rm c}$ presents a genuine critical temperature of superconducting order parameter, and usually $T_{\rm c}$ is equal or very close to the $T_{\rm c}$ of the superconductor in the BCS theory, as the case of $P=0.6$ kbar with $T_{\rm c}=3.80\pm 0.02$ K. As $P$ increases, both ${\varDelta}_0$ and $T_{\rm c}$ decrease, as shown in Fig. 4(b).
cpl-37-9-097403-fig4.png
Fig. 4. (a) Temperature dependence of the superconducting gaps $\varDelta$ for each $P$. The colored solid lines are the fits within the framework of BCS theory. (b) The resulted superconducting gap ${\varDelta}_0$ and the critical temperature $T_{\rm c}$ for gap opening/closing as a function of $P$, respectively. (c) The corresponding gap ratio $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ as a function of $P$. The dashed lines are guides to the eyes.
Finally, we analyze the physical meanings of the obtained pressure-dependent energy gap ${\varDelta}_0$ and $T_{\rm c}$ from this high-pressure experiment. The gap ratio $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ is the measure of coupling strength of the superconducting state. For a BCS superconductor in the weak coupling limit, the gap ratio $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ is a universal constant 3.52. In Fig. 4(c) we plot the obtained $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ as a function of $P$. At $P=0.6$ kbar, $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}\simeq 3.50$, exactly the value of BCS superconductors in weak coupling. However, as $P$ increases, the gap ratio greatly increases, and reaches a value of 6.25 at $P=12.1$ kbar. The values of $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ clearly suggest that PbTaSe$_2$ undergoes a crossover from a weak coupling to a strong coupling regime in electron pairing strength upon pressures, opposite to the case of conventional BCS superconductors.[13] These experimental results provide important information for better understanding of noncentrosymmetric superconductors. In summary, we have demonstrated, for the first time, the success of the point-contact spectroscopy measurements on PbTaSe$_2$/Ag soft junctions under hydrostatic pressures up to 12.1 kbar. These pressure-dependent soft point-contact spectra offer wealthy information about both the normal and the superconducting states. In the normal state the junction resistance is sensitive to pressure, leading to a pressure-dependent junction transparency. In the superconducting state, the pressure dependence of the energy gap ${\varDelta}_0$, the critical temperature $T_{\rm c}$ and the gap ratio $2{\varDelta}_0/k_{_{\rm B}}T_{\rm c}$ suggest a crossover from a weak coupling to a strong coupling in electron pairing strength upon pressure. These experimental results provide wealthy information on high-pressure superconductivity. Acknowledgement. The author (Cong Ren) expresses thankfulness to Xin Lu, Yi-feng Yang, Qiang-Hua Wang, Hai-Hu Wen, Tao Xiang and Xing-Jiang Zhou for intensive discussions. References Solids, liquids, and gases under high pressureRe-emerging superconductivity at 48 kelvin in iron chalcogenidesSuperconductivity up to 29 K in SrFe 2 As 2 and BaFe 2 As 2 at high pressuresHigh pressure studies on Fe-pnictide superconductorsSuperconducting Single-Layer T-Graphene and Novel Synthesis RoutesSuperconductivity in Topological Semimetal θ -TaN at High Pressure *Quantum criticality in heavy-fermion metalsStudy of Fermi-Surface Topology Changes in Rhenium and Dilute Re Solid Solutions from T c Measurements at High PressureReemergence of high-Tc superconductivity in the (Li1-xFex)OHFe1-ySe under high pressureHigh- T c superconductivity up to 55 K under high pressure in a heavily electron doped L i 0 . 36 ( N H 3 ) y F e 2 S e 2 single crystalCalorimetric Study of CeRu2Ge2 Under Continuously Swept Hydrostatic Pressure up to 8 GPaThe effect of pressure on the positive muon spin precession in iron and nickelHigh pressure research using muons at the Paul Scherrer InstituteTunneling spectroscopy of Al/AlO x /Pb subjected to hydrostatic pressureAndreev–Saint-James reflections: A probe of cuprate superconductorsNoncentrosymmetric superconductor with a bulk three-dimensional Dirac cone gapped by strong spin-orbit couplingAnisotropic superconducting property studies of single crystal PbTaSe 2Highly responsive ground state of PbTaSe 2 : Structural phase transition and evolution of superconductivity under pressureTopological phase transition under pressure in the topological nodal-line superconductor PbTaSe 2 Metallic to tunneling transition in Cu-Nb point contactsSuperconducting gaps in FeSe studied by soft point-contact Andreev reflection spectroscopyAndreev bound state and multiple energy gaps in the noncentrosymmetric superconductor BiPdAndreev Reflection in Ferromagnet-Superconductor JunctionsSize-dependent electrical constriction resistance for contacts of arbitrary size: from Sharvin to Holm limitsTransition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversionTheory of Tunneling Spectroscopy of d -Wave SuperconductorsTheory for tunneling spectroscopy of anisotropic superconductorsProbing multiband superconductivity by point-contact spectroscopy μ SR study of the noncentrosymmetric superconductor PbTaSe 2 Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe 2Nodeless superconductivity in noncentrosymmetric PbTaSe 2 single crystals
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