We present a variational analysis for a half-quantum vortex (HQV) in the equal-spin-pairing superfluid state which, under suitable conditions, is believed to be realized in Sr2RuO4 and 3He-A. Our approach is based on a description of the HQV in terms of a BCS-like wave function with a spin-dependent boost. We predict a novel feature: the HQV, if stable, should be accompanied by a non-zero spin polarization. Such a spin polarization would exist in addition to the one induced by the Zeeman coupling to the external field and hence may serve as an indicator in experimental search for HQV.
Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vort…
We theoretically investigate qualitative features of the field-temperature ($H$-$T$) phase diagram of superconductors with strong attractive interaction lying in the BCS-BEC crossover regime. Starting with a simple attractive Hubbard model, we estimate three kinds of characteristic fields, i.e., the pair-formation field $H^*$, the vortex-liquid-formation field $H_\mathrm{c2}$, and the vortex-lattice-formation field $H_\mathrm{melt}$. The region between $H_\mathrm{c2}$ and $H_\mathrm{melt}$, as well as that between $H_\mathrm{c2}$ and $H^*$, is found to be enlarged as the interaction is stronge…
We utilize a combination of vector magnetic field and scanning tunneling microscopy to elucidate the 3D field-based electronic phase diagram of a correlated iron-based superconductor, LiFeAs. We observe, under a zero-field-cooled method, an ordered hexagonal vortex lattice ground-state in contrast to the disordered lattice observed under a field-cooled method. It transforms into a four-fold-symmetric state by increasing c-axis field and distorts elliptically upon tilting the field in-plane. The vortex lattice transformations correlate with the field dependent superconducting gap that character…
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…
NMR experiments on superfluid 3He in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why the HQV in the polar phase in nematic aerogels became unstable in a transverse magnetic field upon a field-cooling is explained.
We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moiré supercells. With increasing the pairing potential, the system evolves from the mixed nontopological $d+id$ and $p+ip$ phase to the $s+p+d$ phase via the first-order phase transition. In the time-reversal symmetry breaking $d+id$ and $p+ip$ phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moiré unit cell. Nevertheless, the superconducting gap …
Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates
我们发现了超流$^3$ He A相在旋转条件下受限于窄间隙平行平板中的半量子涡旋的精确稳定区域。标准的Ginzburg-Landau自由能，这是很好地建立，解决了定位的温度$T$和转速（$/Omega$）跨越的稳定区域。该$/Omega$ - $T$稳定性区域足够宽以在可用的实验装置中通过实验对其进行检查。给出了以$_1$核为特征的HQV的详细序参量结构，以便于解释其相对于其他涡旋或织构稳定性的物理原因。
The helical electron states on the surface of topological insulators or elemental Bismuth become unstable toward superconducting pairing formation when coupled to the charge or magnetic fluctuations. The latter gives rise to pairing instability in chiral channels $d_{xy}\pm i d_{x^2-y^2}$, as has been observed recently in epitaxial Bi/Ni bilayer system at relatively high temperature, while the former favors a pairing with zero total angular momentum. Motivated by this observation we study the vortex bound states in these superconducting states. We consider a minimal model describing the superc…
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…
Casimir Force between Vortex Matter in Anisotropic and Layered Superconductors
本文提出了一种新的方法来计算各向异性和层状超导体中范德华型的吸引性长程涡旋-涡旋相互作用。将涡旋线的统计力学映射到二维带电玻色子的虚时量子力学上，我们可以定义一个二维Casimir问题：被宽度为R的间隙隔开的两个（稀）涡旋物质半空间映射到通过大质量规范场相互作用的两个带电玻色子介电半平面上。我们确定了两个半平面之间的吸引力Casimir力，并表明它与Blatter和Geshkenbein先前发现的涡旋之间的范德华力的成对求和一致[Phys. Rev. Lett. 77、4958（1996）]
Vortex core states in a minimal two-band model for iron-based superconductors
对对称性是铁基超导体研究中的主要问题之一。我们采用一个最小的双带紧束缚模型，考虑了不同的配对作用通道，导出了一组双带Bogoliubov-de Gennes（BdG）方程。BdG方程在实空间中实现，然后通过精确对角化自洽求解。在均匀情况下，我们发现$d_{x^2-y^2}$波配对态最有利于最近邻配对相互作用，而$s_{x^2y^2}$波配对态最有利于次最近邻配对相互作用.这与Seo { \em et al.}报道的结果一致。[Phys. Rev. Lett. { \bf 101}，206404（2008）]。然后，我们继续研究的局部电子结构周围的磁涡旋核心的$d_{x^2-y^2}$波和$s_{x^2y^2}$波配对对称的混合状态。从局域态密度（LDOS）谱及其空间变化发现，对于$d_{x^2-y^2}$波对对称，费米能附近的共振芯态是束缚态，而对于$s_{x^2y^2}$波对对称，随着电子填充因子的变化，共振芯态可以从局域态演化到扩展态.此外，通过包括有效的交换相互作用，出现的反铁磁自旋密度波（SDW）序可以抑制共振芯态，这为理解Yin { \em et al.}最近的扫描隧道显微镜实验（STM）所揭示的共振峰的缺失提供了一种可能的途径。[Phys. Rev. Lett. { \bf 102}，097002（2009）]。
Vortices in topological superconductors host Majorana zero modes (MZMs), which are proposed to be building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform for realizing MZM has been discovered in iron-based superconductors, without involving hybrid semiconductor-superconductor structures. Here we report on a detailed scanning tunneling spectroscopy study of a FeTe0.55Se0.45 single crystal, revealing two distinct classes of vortices present in this system which differ by a half-integer level shift in the energy spectra of the vortex bound states.…
Motivated by the superconductivity of $M_x$Bi$_2$Se$_3$, we study topological excitations in a nematic superconductor using Ginzburg-Landau theory. An isolated excitation at low field is shown to be either a distorted phase vortex or a tightly-bounded pair of half quantum vortices. Close to upper critical field $H_{c2}$, the vortex lattice is shown to be always hexagonal in the extreme type-II limit. Due to the different symmetries of the vortex lattice states, at least two phase transitions must take place when the external field is lowered from $H_{c2}$.
Spin Diffusion Coefficient of A Phase of Liquid 3He at Low Temperatures and Stability of Half Quantum Vortex
本文利用Kubo公式方法，从准粒子寿命的角度研究了低温下液态~ 3 He A相中自旋扩散系数张量。通常，该系数是各向异性态的四阶张量，并且可以被定义为自旋电流和磁化强度的法向分量的函数。利用玻尔兹曼方程得到了准粒子寿命。我们发现在低温下自旋扩散系数的分量与T^（-2）成正比。因此，自旋流的简正分量具有很强的扩散性，在3 He-A态的等自旋配对中，这些分量对半量子涡旋稳定性的贡献可以忽略不计.因此，为了得到稳定的HQV，只要考虑弱相互作用和朗道费米液体的影响就足够了。
Recent experiments on superfluid $^3$He in globally anisotropic aerogels have shown realization of the polar superfluid phase and of the half-quantum vortices (HQVs) in this phase upon rotation. To clarify why the HQVs, which had not been detected clearly in the A phase of the bulk liquid, have been realized in the polar phase, we theoretically examine the relative stability of a HQV-pair against a single phase vortex in both the bulk A-phase and the polar phase in an aerogel. By taking care of important roles of a higher order gradient term, which assists the stability of HQVs but has never b…
Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently using the Bogoliubov-de Gennes equation with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momentums (OAM) for the TN SC…
