Pairing of j=3/2 fermions in half-Heusler superconductors
P. M. R. Brydon, Limin Wang, M. Weinert, D. F. Agterberg
备注：
9 pages, 6 figures (including supplemental materials). References updated, including companion paper arXiv:1603.03375 . To appear in Physical Review Letters
We theoretically consider the superconductivity of the topological half-Heusler semimetals YPtBi and LuPtBi. We show that pairing occurs between j=3/2 fermion states, which leads to qualitative differences from the conventional theory of pairing between j=1/2 states. In particular, this permits Cooper pairs with quintet or septet total angular momentum, in addition to the usual singlet and triplet states. Purely on-site interactions can generate s-wave quintet time-reversal symmetry-breaking states with topologically nontrivial point or line nodes. These local s-wave quintet pairs reveal themselves as d-wave states in momentum space. Furthermore, due to the broken inversion symmetry in these materials, the s-wave singlet state can mix with a p-wave septet state, again with topologically-stable line nodes. Our analysis lays the foundation for understanding the unconventional superconductivity of the half-Heuslers.
In superconductors, electrons with spin ${s=1/2}$ form Cooper pairs whose spin structure is usually singlet (${S=0}$) or triplet (${S=1}$). When the electronic structure near the Fermi level is characterized by fermions with angular momentum ${j=3/2}$ due to strong spin-orbit interactions, novel pairing states such as even-parity quintet (${J=2}$) and odd-parity septet (${J=3}$) states become allowed. Prime candidates for such exotic states are half-Heusler superconductors, which exhibit unconventional superconducting properties, but their pairing nature remains unsettled. Here we show that th…
Signatures of nodal line/point superconductivity have been observed in half-Heusler compounds, such as LnPtBi (Ln = Y, Lu). Topologically non-trivial band structures, as well as topological surface states, has also been confirmed by angular-resolved photoemission spectroscopy in these compounds. In this work, we present a systematical classification of possible gap functions of bulk states and surface states in half-Heusler compounds and the corresponding topological properties based on the representations of crystalline symmetry group. Different from all the previous studies based on four ban…
We report the synthesis and physical properties of a full Heusler compound, MgPd$_2$Sb, which we found to show superconductivity below $T_c$ = 2.2 K. MgPd$_2$Sb was obtained by a two-step solid-state reaction method and its purity and cubic crystal structure (Fm-3m, a=6.4523(1) Å) were confirmed by powder x-ray diffraction. Normal and superconducting states were studied by electrical resistivity, magnetic susceptibility, and heat capacity measurements. The results show that MgPd$_2$Sb is a type-II, weak coupling superconductor ($λ_{e-p}$ = 0.53). The observed pressure dependence of $T_c$ ($ΔT_…
The half-Heusler compounds YPdBi and TbPdBi, while having similar band structure, exhibit different magnetic properties. YPdBi is a diamagnet, while TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with T${_c}\approx$1 K for YPdBi and T${_c}\approx$1.75 K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator (TDO) and a commercial dilution refrigerator, we measured temperature dependent magnetic penetrat…
We theoretically study the effects of spin-orbit interactions on symmetry of a Cooper pair in a spin-singlet d-wave superconductor in two-dimension. The pairing symmetry is analyzed in terms of the anomalous Green's function which is obtained by solving the Gor'kov equation analytically. A spin-orbit interaction induces a spin-triplet p-wave pairing correlation in a uniform superconductor. An odd-frequency spin-triplet s-wave pairing correlation appears at a surface of such superconductor as a result of breaking inversion symmetry locally. We also discuss a close relationship among the odd-fre…
The single impurity effect on the graphene-based superconductor is studied theoretically. Four different pairing symmetries are discussed. Sharp resonance peaks are found near the impurity site for the $d+id$-wave pairing symmetry and the $p+ip$-wave pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the $d+id$ pairing symmetry while they disappear for the $p+ip$ pairing symmetry. Such in-gap peaks are absent for the fully gapped extended $s$-wave pairing symmetry and the nodal $f$-wave pairing symmetry. The existence of…
We study subgap states induced by a single impurity in an s-wave superconductor with suppressed pairing. For concreteness, we consider a bulk superconductor containing a normal spherical region. We find that a point impurity in this system induces two Yu-Shiba-Rusinov states inside the minigap instead of one, which one would have in a homogeneous superconductor. Moreover, the subgap states appear even if the impurity is nonmagnetic. We prove that this result actually holds almost for any superconductor with a real and spatially inhomogeneous order parameter, if the quasiparticle spectrum is ga…
Probing Sign-Changing Order Parameters via Impurity States in unconventional superconductors: Implications for La$_3$Ni$_2$O$_7$ Superconductors with interlayer pairing
A prime category of superconducting materials in which to look for spin-triplet pairing and topological superconductivity are superconductors without inversion symmetry. It is predicted that the breaking of parity symmetry gives rise to an admixture of spin-singlet / spin-triplet pairing states; a triplet pairing component, being substantial, seems all but guaranteed. However, the experimental confirmation of pair mixing in any particular material remains elusive. In this work, we perform phase-sensitive experiment to examine the pairing state of noncentrosymmetric superconductor $α-$BiPd. The…
One of the outstanding problems in Iron pnictide research is the unambiguous detection of its pairing symmetry. The most probable candidates are the two-band s$++$ and sign reversed s$\pm$ wave pairing. In this work, the Andreev conductance and shot noise are used as a probe for the pairing symmetry of Iron pnictide superconductors. Clear differences emerge in both the zero bias differential conductance and the shot noise in the tunneling limit for the two cases enabling an effective distinction between the two.
We study the momentum-integrated quasiparticle interference (QPI) in the FeSe-based superconductors. This method was recently proposed theoretically and has been applied to determine the pairing symmetry in these materials experimentally. Our findings suggest that, if the incipient bands and the superconducting (SC) pairing on them are taken into consideration, then the experimentally measured bound states and momentum-integrated QPI can be well fitted, even if the SC order parameter does not change sign on the Fermi surfaces. Therefore, we offer an alternative explanation to the experimental …
Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the symmetry properties and nodal structure of superconductors, especially for the interband gap functions. Focusing on tetragonal superconductors, we show that the interband pairing in the conventional (s-wave) channel can have features which are traditionally associated with unconventional pairing, such as triplet components and odd parity, and can produce line nodes i…
Pairing Symmetry and Spin Excitations of Iron Selenide Superconductors
本文对新发现的铁硒化物超导体APDMATHABMM Fe $_{2-y}$ Se $_2$（A=Tl，K，Rb，Cs）提出了一个有效的单带模型.基于该最小模型和无规相位近似，从理论上揭示了$d_{x^2-y^2}$对对称性，并在费米面拓扑的框架下加以理解。一个共同的起源的超导性阐明这种化合物和其他高T $_c$材料。在超导态的$(π,π/2)$上观察到自旋激发，与中子散射实验符合得很好。自旋共振只出现在d波配对中，这为这类超导体的d波配对对称性提供了额外的指示。
Single nonmagnetic impurity resonance in FeSe-based 122-type superconductors as a probe for pairing symmetry
我们研究了一个单一的非磁性杂质在A $_{y}$ Fe $_{2-x}$ Se $_{2}$（A=K，Rb，或Cs）超导体中的影响，通过考虑各种配对状态的基础上的三轨道模型与光电子能谱实验一致。通过自洽求解Bogoliubov-de Gennes方程，计算了杂质位上及其附近的局域态密度。在无节点的$d_{x^2-y^2}$波配对态中，杂质诱导的带隙束缚态仅在吸引杂质散射势下存在，如掺杂Co或Ni的情况，其特征在于强的粒子-空穴不对称性.这一性质可用于探测FeSe基122型超导体的配对对称性。
For the newly discovered ironbased superconductors we propose a one band model for conduction band with first and secondnearestneighbor electron hoppings with two types of d wave and three types of s wave pairing symmetries for the superconductivity. We have calculated the Greens functions from which the temperature dependent superconducting (SC) gap and tunneling conductance are calculated and computed numerically. The evolution of the SC gap and the tunneling conductance spectra are investigated for different model parameters of the system.
Weak phonon-mediated pairing in BiS$_2$ superconductor from first principles
新型铋硫超导体中的超导性吸引了大量的实验和理论研究工作，但这些材料中超导性的性质尚未达成共识。利用超导体的密度泛函理论，研究了LaO $_{0.5}$ F $_{0.5}$ BiS $_2$的电子-声子配对机制.我们首先确认存在一个相称的电荷密度波的不稳定性，根据以前的研究。使用最近开发的集成方案的电子-声子耦合，我们发现，它的强度比以前计算的低得多，由于改进的状态密度计算。我们最后得出结论，传统的声子介导的配对不能解释在这种材料中观察到的高超导转变温度。
Recent experiments have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g. YPtBi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the (111) surface of half-Heusler superconductors. Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. In this work, we studied the effect of the surface order parameter and the surface impurity o…
