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Register a new userNanocalorimetric Evidence for Nematic Superconductivity in the Doped Topological Insulator Sr$_{0.1}$Bi$_{2}$Se$_{3}$
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Spontaneous rotational-symmetry breaking in the superconducting state of doped $mathrm{Bi}_2mathrm{Se}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal $mathrm{Sr}_{0.1}mathrm{Bi}_2mathrm{Se}_3$ provides unequivocal evidence of a two-fold rotational symmetry in the superconducting gap by a emph{bulk thermodynamic} probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the materials low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of $H_{c2}$ is attributed to a nematic phase of a two-component topological gap structure $vec{eta} = (eta_{1}, eta_{2})$ and caused by a symmetry-breaking energy term $delta (|eta_{1}|^{2} - |eta_{2}|^{2}) T_{c}$. A quantitative analysis of our data excludes more conventional sources of this two-fold anisotropy and provides the first estimate for the symmetry-breaking strength $delta approx 0.1$, a value that points to an onset transition of the second order parameter component below 2K.
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Superconductivity mediated by phonons is typically conventional, exhibiting a momentum-independent s-wave pairing function, due to the isotropic interactions between electrons and phonons along different crystalline directions. Here, by performing inelastic neutron scattering measurements on a superconducting single crystal of Sr0.1Bi2Se3, a prime candidate for realizing topological superconductivity by doping the topological insulator Bi2Se3, we find that there exist highly anisotropic phonons, with the linewidths of the acoustic phonons increasing substantially at long wavelengths, but only for those along the [001] direction. This observation indicates a large and singular electron-phonon coupling at small momenta, which we propose to give rise to the exotic p-wave nematic superconducting pairing in the MxBi2Se3 (M = Cu, Sr, Nb) superconductor family. Therefore, we show these superconductors to be example systems where electron-phonon interaction can induce more exotic superconducting pairing than the s-wave, consistent with the topological superconductivity.
Sr$_x$Bi$_2$Se$_3$ and the related compounds Cu$_x$Bi$_2$Se$_3$ and Nb$_x$Bi$_2$Se$_3$ have attracted considerable interest, as these materials may be realizations of unconventional topological superconductors. Superconductivity with T$_c$ ~ 3 K in Sr$_x$Bi$_2$Se$_3$ arises upon intercalation of Sr into the layered topological insulator Bi$_2$Se$_3$. Here we elucidate the anisotropy of the normal and superconducting state of Sr$_{0.1}$Bi$_2$Se$_3$ with angular dependent magnetotransport and thermodynamic measurements. High resolution x-ray diffraction studies underline the high crystalline quality of the samples. We demonstrate that the normal state electronic and magnetic properties of Sr$_{0.1}$Bi$_2$Se$_3$ are isotropic in the basal plane while we observe a large two-fold in-plane anisotropy of the upper critical field in the superconducting state. Our results support the recently proposed odd-parity nematic state characterized by a nodal gap of $E_u$ symmetry in Sr$_x$Bi$_2$Se$_3$.
We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of Cu$_{x}$Bi$_{2}$Se$_{3}$ which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound is assumed to have the broken spin-rotation symmetry, similar to that of the A-phase of $^{3}$He as suggested by recent nuclear-magnetic resonance experiments. For both spheroidal and corrugated cylindrical Fermi surfaces with the hexagonal warping terms, we show that the bulk SC gap is rather anisotropic; the minimum of the gap is negligibly small as comparing to the maximum of the gap. This would make the fully-gapped pairing effectively nodal. For a clean system, our results indicate the bulk of this compound to be a topological superconductor with the SABSs appearing inside the bulk SC gap. The zero-energy SABSs which are Majorana fermions, together with the TSSs not gapped by the pairing, produce a zero-energy peak in the surface density of states (SDOS). The SABSs are expected to be stable against short-range nonmagnetic impurities, and the local SDOS is calculated around a nonmagnetic impurity. The relevance of our results to experiments is discussed.
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$_3$.
An archetypical layered topological insulator Bi$_2$Se$_3$ becomes superconductive upon doping with Sr, Nb or Cu. Superconducting properties of these materials in the presence of in-plane magnetic field demonstrate spontaneous symmetry breaking: 180$^circ$-rotation symmetry of superconductivity versus 120$^circ$-rotation symmetry of the crystal. Such behavior brilliantly confirms nematic topological superconductivity. To what extent this nematicity is due to superconducting pairing in these materials, rather than due to crystal structure distortions? This question remained unanswered, because so far no visible deviations from the 3-fold crystal symmetry were resolved in these materials. To address this question we grow high quality single crystals of Sr$_x$Bi$_2$Se$_3$, perform detailed X-ray diffraction and magnetotransport studies and reveal that the observed superconducting nematicity direction correlates with the direction of small structural distortions in these samples( $sim 0.02$% elongation in one crystallographic direction). Additional anisotropy comes from orientation of the crystallite axes. 2-fold symmetry of magnetoresistance observed in the most uniform crystals well above critical temperature demonstrates that these structural distortions are nevertheless strong enough. Our data in combination with strong sample-to-sample variation of the superconductive anisotropy parameter are indicative for significance of the structural factor in the apparent nematic superconductivity in Sr$_x$Bi$_2$Se$_3$.
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