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Register a new userMagnetic and thermodynamic properties of Cu$_x$TiSe$_2$ single crystals
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We present a detailed study of the phase diagram of copper intercalated TiSe$_2$ single crystals, combining local Hall-probe magnetometry, tunnel diode oscillator technique (TDO), specific-heat, and angle-resolved photoemission spectroscopy measurements. A series of the Cu$_x$TiSe$_2$ samples from three different sources with various copper content $x$ and superconducting critical temperatures $T_c$ have been investigated. We first show that the vortex penetration mechanism is dominated by geometrical barriers enabling a precise determination of the lower critical field, $H_{c1}$. We then show that the temperature dependence of the superfluid density deduced from magnetic measurements (both $H_{c1}$ and TDO techniques) clearly suggests the existence of a small energy gap in the system, with a coupling strength $2Delta_s sim [2.4-2.8]k_BT_c$, regardless of the copper content, in puzzling contradiction with specific heat measurements which can be well described by one single large gap $2Delta_l sim [3.7-3.9]k_BT_c$. Finally, our measurements reveal a non-trivial doping dependence of the condensation energy, which remains to be understood.
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Single crystals of Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$, $x<0.37$, have been grown and characterized by structural, magnetic and transport measurements. These measurements show that the structural/magnetic phase transition found in pure BaFe$_2$As$_2$ at 134 K is suppressed monotonically by Ru doping, but, unlike doping with TM=Co, Ni, Cu, Rh or Pd, the coupled transition seen in the parent compound does not detectably split into two separate ones. Superconductivity is stabilized at low temperatures for $x>0.2$ and continues through the highest doping levels we report. The superconducting region is dome like, with maximum T$_c$ ($sim16.5$ K) found around $xsim 0.29$. A phase diagram of temperature versus doping, based on electrical transport and magnetization measurements, has been constructed and compared to those of the Ba(Fe$_{1-x}$TM$_x$)$_2$As$_2$ (TM=Co, Ni, Rh, Pd) series as well as to the temperature-pressure phase diagram for pure BaFe$_2$As$_2$. Suppression of the structural/magnetic phase transition as well as the appearance of superconductivity is much more gradual in Ru doping, as compared to Co, Ni, Rh and Pd doping, and appears to have more in common with BaFe$_2$As$_2$ tuned with pressure; by plotting $T_S/T_m$ and $T_c$ as a function of changes in unit cell dimensions, we find that changed in the $c/a$ ratio, rather than changes in $c$, $a$ or V, unify the $T(p)$ and $T(x)$ phase diagrams for BaFe$_2$As$_2$ and Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ respectively.
A series of high quality NaFe$_{1-x}$Cu$_x$As single crystals has been grown by a self-flux technique, which were systematically characterized via structural, transport, thermodynamic, and high pressure measurements. Both the structural and magnetic transitions are suppressed by Cu doping, and bulk superconductivity is induced by Cu doping. Superconducting transition temperature ($T_c$) is initially enhanced from 9.6 to 11.5 K by Cu doping, and then suppressed with further doping. A phase diagram similar to NaFe$_{1-x}$Co$_x$As is obtained except that insulating instead of metallic behavior is observed in extremely overdoped samples. $T_c$s of underdoped, optimally doped, and overdoped samples are all notably enhanced by applying pressure. Although a universal maximum transition temperature ($T_c^{max}$) of about 31 K under external pressure is observed in underdoped and optimally doped NaFe$_{1-x}$Co$_x$As, $T_c^{max}$ of NaFe$_{1-x}$Cu$_x$As is monotonously suppressed by Cu doping, suggesting that impurity potential of Cu is stronger than Co in NaFeAs. The comparison between Cu and Co doping effect in NaFeAs indicates that Cu serves as an effective electron dopant with strong impurity potential, but part of the doped electrons are localized and do not fill the energy bands as predicted by the rigid-band model.
Single crystalline samples of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with $x < 0.12$ have been grown and characterized via microscopic, thermodynamic and transport measurements. With increasing Co substitution, the thermodynamic and transport signatures of the structural (high temperature tetragonal to low temperature orthorhombic) and magnetic (high temperature non magnetic to low temperature antiferromagnetic) transitions are suppressed at a rate of roughly 15 K per percent Co. In addition, for $x ge 0.038$ superconductivity is stabilized, rising to a maximum $T_c$ of approximately 23 K for $x approx 0.07$ and decreasing for higher $x$ values. The $T - x$ phase diagram for Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ indicates that either superconductivity can exist in both low temperature crystallographic phases or that there is a structural phase separation. Anisotropic, superconducting, upper critical field data ($H_{c2}(T)$) show a significant and clear change in anisotropy between samples that have higher temperature structural phase transitions and those that do not. These data show that the superconductivity is sensitive to the suppression of the higher temperature phase transition.
Superconductivity of YBa$_2$Cu$_3$O$_{7-delta}$ single crystals was investigated in small magnetic fields. In magnetic measurements the superconducting transition for $textbf{H} | c$ appears 0.4 K higher than for $textbf{H} bot c$. In this temperature range superconductivity is two-dimensional and the total thickness of superconducting layers is about 0.83 of the sample thickness, which is a consequence of the occurrence of the quasi-insulating plane in the unit cell of the crystal structure. Resistivity in the textit{ab}-plane and along the textit{c}-axis was measured simultaneously. In these measurements two-dimensional superconductivity was observed in a temperature range of 0.6-0.8 K with the clear signs of the Berezinskii-Kosterlitz-Touless (BKT) transition which occurs approximately 0.15 K below $T_c$, the mean-field transition temperature.
Unconventional superconductivity is characterized by the spontaneous symmetry breaking of the macroscopic superconducting wavefunction in addition to the gauge symmetry breaking, such as rotational-symmetry breaking with respect to the underlying crystal-lattice symmetry. Particularly, superconductivity with spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus in bulk properties, not yet reported previously, is intriguing and can be termed nematic superconductivity in analogy to nematic liquid-crystal phases. Here, based on specific-heat measurements of the single-crystalline Cu$_x$Bi$_2$Se$_3$ under accurate magnetic-field-direction control, we report thermodynamic evidence for nematic superconductivity, namely, clear two-fold-symmetric behavior in a trigonal lattice. The results indicate realization of an odd-parity nematic state, feasible only by macroscopic quantum condensates and distinct from nematic states in liquid crystals. The results also confirm topologically non-trivial superconductivity in Cu$_x$Bi$_2$Se$_3$.
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