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Register a new userEvidence from $^{77}$Se Knight shifts for triplet superconductivity in (TMTSF)$_2$PF$_6$
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The layered quasi-one-dimensional molecular superconductor (TMTSF)$_2$PF$_6$ is a very exotic material with a superconducting order parameter whose ground state symmetry has remained ill-defined. Here we present a pulsed NMR Knight shift (K) study of $^{77}$Se measured simultaneously with transport in pressurized (TMTSF)$_2$PF$_6$. The Knight shift is linearly dependent on the electron spin susceptibility $chi_s$, and is therefore a direct measure of the spin polarization in the superconducting state. For a singlet superconductor, the spin contribution to the Knight shift, K$_s$, falls rapidly on cooling through the transition. The present experiments indicate no observable change in K between the metallic and superconducting states, and thus strongly support the hypothesis of triplet p-wave superconductivity in (TMTSF)$_2$PF$_6$.
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Nuclear magnetic resonance (NMR) measurements on the $^{195}$Pt nucleus in an aligned powder of the moderately heavy-fermion material U2PtC2 are consistent with spin-triplet pairing in its superconducting state. Across the superconducting transition temperature and to much lower temperatures, the NMR Knight shift is temperature independent for field both parallel and perpendicular to the tetragonal c-axis, expected for triplet equal-spin pairing superconductivity. The NMR spin-lattice relaxation rate 1/T$_1$, in the normal state, exhibits characteristics of ferromagnetic fluctuations, compatible with an enhanced Wilson ratio. In the superconducting state, 1/T$_1$ follows a power law with temperature without a coherence peak giving additional support that U$_2$PtC$_2$ is an unconventional superconductor. Bulk measurements of the AC-susceptibility and resistivity indicate that the upper critical field exceeds the Pauli limiting field for spin-singlet pairing and is near the orbital limiting field, an additional indication for spin-triplet pairing.
We have studied the temperature dependence of the integer quantum Hall transitions in the molecular crystal (TMTSF)$_2$PF$_6$. We find that the transition width between the quantum Hall plateaus does not exhibit the universal power-law scaling behavior of the integer quantum Hall effect observed in semiconducting devices. Instead, the slope of the $rho_{xy}$ risers, $drho_{xy}/dB$, and the (inverse) width of the $rho_{xx}$ peaks, $(Delta B)^{-1}$, show a BCS-like energy gap temperature dependence. We discuss these results in terms of the field-induced spin-density wave gap and order parameter of the system.
Superconductivity has its universal origin in the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc[1]. While electron Cooper pairs in most superconductors form anti-parallel spin-singlets with total spin S=0 [2,3], they can also form parallel spin-triplet Cooper pairs with S=1 and an odd parity wavefunction[4-6], analogous to the equal spin pairing state in the superfluid 3He[7]. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for fault tolerant quantum computation[8-11]. However, spin-triplet pairing is rare and has not been unambiguously identified in any solid state systems. Since spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations[4-6], uranium based heavy-fermion materials near a FM instability are considered ideal candidates for realizing spin-triplet superconductivity[12-14]. Indeed, UTe2, which has a Tc=1.6K [15,16], has been identified as a strong candidate for chiral spin-triplet topological superconductor near a FM instability[15-22], although the system also exhibits antiferromagnetic (AF) spin fluctuations[23,24]. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled with a sharp magnetic excitation at the Brillouin zone (BZ) boundary near AF order, analogous to the resonance seen in high-Tc copper oxide[25-27], iron-based[28,29], and heavy-fermion superconductors[30-32]. We find that the resonance in UTe2 occurs below Tc at an energy Er=7.9kBTc (kB is Boltzmanns constant) and at the expense of low-energy spin fluctuations. Since the resonance has only been found in spin-singlet superconductors near an AF instability[25-32], its discovery in UTe2 suggests that AF spin fluctuations can also induce spin-triplet pairing for superconductivity[33].
We present a detailed low-temperature investigation of the statics and dynamics of the anions and methyl groups in the organic conductors (TMTSF)$_2$PF$_6$ and (TMTSF)$_2$AsF$_6$ (TMTSF : tetramethyl-tetraselenafulvalene). The 4 K neutron scattering structure refinement of the fully deuterated (TMTSF)$_2$PF$_6$-D12 salt allows locating precisely the methyl groups at 4 K. This structure is compared to the one of the fully hydrogenated (TMTSF)$_2$PF$_6$-H12 salt previously determined at the same temperature. Surprisingly it is found that deuteration corresponds to the application of a negative pressure of 5 x 10$^2$ MPa to the H12 salt. Accurate measurements of the Bragg intensity show anomalous thermal variations at low temperature both in the deuterated PF$_6$ and AsF$_6$ salts. Two different thermal behaviors have been distinguished. Low-Bragg-angle measurements reflect the presence of low-frequency modes at characteristic energies {theta}$_E$ = 8.3 K and {theta}$_E$ = 6.7 K for the PF$_6$-D12 and AsF$_6$-D12 salts, respectively. These modes correspond to the low-temperature methyl group motion. Large-Bragg-angle measurements evidence an unexpected structural change around 55 K which probably corresponds to the linkage of the anions to the methyl groups via the formation of F...D-CD2 bonds observed in the 4 K structural refinement. Finally we show that the thermal expansion coefficient of (TMTSF)$_2$PF$_6$ is dominated by the librational motion of the PF$_6$ units. We quantitatively analyze the low-temperature variation of the lattice expansion via the contribution of Einstein oscillators, which allows us to determine for the first time the characteristic frequency of the PF6 librations: {theta}$_E$ = 50 K and {theta}$_E$ = 76 K for the PF$_6$-D12 and PF$_6$-H12 salts, respectively.
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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