Superconductor UPt3 Research Articles

Topological Structure of the Order Parameter of Unconventional Superconductors Based on d- and f- Elements

The superconducting order parameter (SOP) of a triplet superconductor UTe2 was constructed using the topological space group approach, in which, in contrast to phenomenological and topological approaches, the single pair function and phase winding in condensate are different quantities. The connection between them is investigated for the D2h point group and the m′m′m magnetic group. It is shown how a non-unitary pair function of UTe2 can be constructed using one-dimensional real irreducible representations and Ginzburg–Landau phase winding. It is also shown that the total phase winding is non-zero in magnetic symmetry only. Experimental data on the superconducting order parameter of topological superconductors UPt3, Sr2RuO4, LaPt3P, and UTe2 are considered and peculiarities of their nodal structures are connected with the theoretical results of the topological space group approach.

Effects of the Order Parameter Anisotropy on the Vortex Lattice in UPt3

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt3 for the applied magnetic field along the crystalline c-axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal plane that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt ±15° vortex lattice rotation was previously reported by Huxley et al., Nature 406, 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al., Nature Physics 16, 531-535 (2020), can be attributed directly to the symmetry breaking field.

Additional quantum numbers for two-electron states in solids. Application to topological superconductor UPt3

Topological superconductors, which are assumed to be a key ingredient for topological quantum computing, reveal unconventional structures of their superconducting order parameter (SOP), which is usually represented by model functions. However, the central problem of the theory of topological superconductivity is to describe the observed topological structures of SOP in terms of quantum mechanics and group theory. In present work making use of the Anderson ansatz for a Cooper pair and induced representation method a complete group theoretical classification of chiral states in D 6h symmetry (point symmetry group of topological superconductor UPt3) is performed. In this technique topological invariant phase winding is defined by the complex irreducible representation (IR) of symmetry group D 6h , whose structure strongly depends on additional quantum numbers, which are the labels of IRs of Cooper pair’s rotational symmetry group C 6h . The technique is extended on the description of time reversal symmetry of the state in terms of Shubikov groups, and B phase of UPt3 with horizontal nodal plane only was connected with corepresentation of magnetic group 6/mm′m′. The structure of A phase with vertical nodes 45° to a axis is a combinations of two complex conjugate E 2u states. Twofold spontaneous symmetry breaking in C phase is connected with the E 1u SOP.

Generalized spin fluctuation feedback in heavy fermion superconductors

This paper develops a phenomenological generalization of the spin fluctuation feedback effect, which allows for a unified explanation of the observed multiple superconducting phases in the correlated fermion superconductors UPt${}_{3}$, U${}_{1\ensuremath{-}x}$Th${}_{x}$Be${}_{13}$, and PrOs${}_{4}$Sb${}_{12}$.

Broken time-reversal symmetry in the topological superconductor UPt3

The topological superconductor UPt3, has three distinct vortex phases, a strong indication of its unconventional character. Using small-angle neutron scattering we have probed the vortex lattice in the UPt3 B phase with the magnetic field along the crystal c-axis. We find a difference in the vortex lattice configuration depending on the sign of the magnetic field relative to the field direction established upon entering the B phase at low temperature in a field sweep, showing that the vortices in this material posses an internal degree of freedom. This observation is facilitated by the discovery of a field driven non-monotonic vortex lattice rotation, driven by competing effects of the superconducting gap distortion and the vortex-core structure. From our bulk measurements we infer that the superconducting order parameter in the UPt3 B phase breaks time reversal symmetry and exhibits chiral symmetry with respect to the c-axis.

Evidence for Weak Spin–Orbit Interaction Experienced by Cooper Pairs in the Spin-Triplet Superconductor UPt3: 195Pt-NMR Study

195Pt-NMR measurements for H ∥ c in the vicinity of the upper critical field \(H_{\text{c2}}^{\| c}\) have been carried out on the heavy-fermion superconductor UPt3. The 195Pt NMR line does not cha...

Induced Representation Method in the Theory of Electron Structure and Superconductivity

It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered.

NMR studies on antiferromagnetic fluctuation in [formula omitted

We have carried out 195Pt-NMR measurements on a heavy Fermion superconductor UPt3 at H∼1.5−2.0T to investigate the in-plane anisotropy in the normal state. For an applied field parallel to [112¯0] direction, split 195NMR line are observed, which has not been reported previously. Such a line splitting is explained by anisotropic Knight shift tensors associated with the local symmetry of Pt-site in UPt3.

Unconventional superconducting gap structure protected by space group symmetry

Recent superconducting gap classifications based on space group symmetry have revealed nontrivial gap structures that were not shown by point group symmetry. First, we review a comprehensive classification of symmetry-protected line nodes within the range of centrosymmetric space groups. Next, we show an additional constraint; line nodes peculiar to nonsymmorphic systems appear only for primitive or orthorhombic base-centered Bravais lattice. Then, we list useful classification tables of 59 primitive or orthorhombic base-centered space groups for the superconducting gap structures. Furthermore, our gap classification reveals the $j_z$-dependent point nodes (gap opening) appearing on a 3- or 6-fold axis, which means that the presence (absence) of point nodes depends on the Bloch-state angular momentum $j_z$. We suggest that this unusual gap structure is realized in a heavy-fermion superconductor UPt$_3$, using a group-theoretical analysis and a numerical calculation. The calculation demonstrates that a Bloch phase contributes to $j_z$ as effective orbital angular momentum by site permutation. We also discuss superconducting gap structures in MoS$_2$, SrPtAs, UBe$_{13}$, and PrOs$_4$Sb$_{12}$.

Möbius topological superconductivity in UPt3

Intensive studies for more than three decades have elucidated multiple superconducting phases and odd-parity Cooper pairs in a heavy fermion superconductor UPt$_3$. We identify a time-reversal invariant superconducting phase of UPt$_3$ as a recently proposed topological nonsymmorphic superconductivity. Combining the band structure of UPt$_3$, order parameter of $E_{\rm 2u}$ representation allowed by $P6_3/mmc$ space group symmetry, and topological classification by $K$-theory, we demonstrate the nontrivial $Z_2$-invariant of three-dimensional DIII class enriched by glide symmetry. Correspondingly, double Majorana cone surface states appear at the surface Brillouin zone boundary. Furthermore, we show a variety of surface states and clarify the topological protection by crystal symmetry. Majorana arcs corresponding to tunable Weyl points appear in the time-reversal symmetry broken B-phase. Majorana cone protected by mirror Chern number and Majorana flat band by glide-winding number are also revealed.

Surface State Tunneling Signatures in the Two-Component Superconductor UPt_{3}.

Quasiparticle interference (QPI) imaging of Bogoliubov excitations in quasi-two-dimensional unconventional superconductors has become a powerful technique for measuring the superconducting gap and its symmetry. Here, we present the extension of this method to three-dimensional superconductors and analyze the expected QPI spectrum for the two-component heavy-fermion superconductor UPt_{3} whose gap structure is still controversial. Starting from a 3D electronic structure and the three proposed chiral gap models E_{1g,u} or E_{2u}, we perform a slab calculation that simultaneously gives extended bulk states and topologically protected in-gap dispersionless surface states. We show that the number of Weyl arcs and their hybridization with the line node provides a fingerprint that may finally determine the true nodal structure of the UPt_{3} superconductor.

Temperature and angular dependence of the upper critical field in K2Cr3As3

We report measurements of the upper critical field $H_{\mathrm{c2}}$ as functions of temperature $T$, polar angle $\theta$ (of the field direction with respect to the crystallographic $c$ axis), and azimuthal angle $\phi$ (of the field direction relative to the $a$ axis within the $ab$ plane) for the Cr-based superconductor K$_{2}$Cr$_{3}$As$_{3}$ with a quasi-one-dimensional and non-centrosymmetric crystal structure. We confirm that the anisotropy in $H_{\mathrm{c2}}(T)$ becomes inverse with decreasing temperature. At low temperatures, $H_{\mathrm{c2}}(\theta)$ data are featured by two maxima at $\theta$ = 0 ($\mathbf{H}\parallel c$) and $\pi/2$ ($\mathbf{H}\bot c$), which can be quantitatively understood only if uniaxial effective-mass anisotropy and absence of Pauli paramagnetic effect for $\mathbf{H}\bot c$ are taken simultaneously into consideration. The in-plane $H_{\mathrm{c2}}(\phi)$ profile shows a unique threefold modulation especially at low temperatures. Overall, the characteristic of the $H_{\mathrm{c2}}(\theta, \phi, T)$ data mostly resemble those of the heavy-fermion superconductor UPt$_3$, and we argue in favor of a dominant spin-triplet superconductivity with odd parity in K$_{2}$Cr$_{3}$As$_{3}$.

Exotic Multigap Structure in UPt_{3} Unveiled by a First-Principles Analysis.

A heavy-fermion superconductor UPt_{3} is a unique spin-triplet superconductor with multiple superconducting phases. Here, we provide the first report on a first-principles analysis of the microscopic superconducting gap structure. We find that the promising gap structure is an unprecedented E_{2u} state, which is completely different from the previous phenomenological E_{2u} models. Our obtained E_{2u} state has in-plane twofold vertical line nodes on small Fermi surfaces and point nodes with linear dispersion on a large Fermi surface. These peculiar features cannot be explained in the conventional spin 1/2 representation, but is described by the group-theoretical representation of the Cooper pairs in the total angular momentum j=5/2 space. Our findings shed new light on the long-standing problems in the superconductivity of UPt_{3}.

Nonsymmorphic Weyl superconductivity inUPt3based onE2urepresentation

We show that a heavy fermion superconductor UPt_3 is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the E_2u representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc node protected by the nonsymmorphic crystal symmetry on the Brillouin zone face.

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid $^3$He, which serves as a rich repository of novel topological quantum phenomena originating from the intertwining of symmetries and topologies. In particular, it is emphasized that the quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase, the A-phase as a Weyl superfluid, the nodal planar and polar phases, and the crystalline ordered stripe phase. All these phases generate noteworthy topological phenomena, including topological phase transitions concomitant with spontaneous symmetry breaking, Majorana fermions, Weyl superfluidity, emergent supersymmetry, spontaneous edge mass and spin currents, topological Fermi arcs, and exotic quasiparticles bound to topological defects. In relation to the mass current carried by gapless edge states, we also briefly review a longstanding issue on the intrinsic angular momentum paradox in $^3$He-A. Moreover, we share the current status of our knowledge on the topological aspects of unconventional superconductors, such as the heavy-fermion superconductor UPt$_3$ and superconducting doped topological insulators, in connection with the superfluid $^3$He.

Search for Superconducting Energy Gap in UPt3 by Point-Contact Spectroscopy

We have investigated the differential resistance of the point contacts between heavy-fermion superconductor UPt3 and a normal metal Pt, which were fabricated using a commercial piezo-electric actuator, and retried the observation of the energy gap of UPt3. A V-shaped dip is observed in both normal and superconducting states and disappeared around TK ~ 20 K, suggesting that it is related to the Kondo effect. Below the superconducting transition temperature, a shallow double-minimum structure, which indicates the energy gap, has been observed for the contacts on the faces perpendicular to the a-, b- and c-axes of UPt3.

Fermi surface, magnetic, and superconducting properties in actinide compounds

Abstract The de Haas–van Alphen effect, which is a powerful method to explore Fermi surface properties, has been observed in cerium, uranium, and nowadays even in neptunium and plutonium compounds. Here, we present the results of several studies concerning the Fermi surface properties of the heavy fermion superconductors UPt3 and NpPd5Al2, and of the ferromagnetic pressure-induced superconductor UGe2, together with those of some related compounds for which fascinating anisotropic superconductivity, magnetism, and heavy fermion behavior has been observed.

UPt3 as a Topological Crystalline Superconductor

We investigate the topological aspect of the spin-triplet $f$-wave superconductor UPt$_3$ through microscopic calculations of edge- and vortex-bound states based on the quasiclassical Eilenberger and Bogoliubov-de Gennes theories. It is shown that a gapless and linear dispersion exists at the edge of the $ab$-plane. This forms a Majorana valley, protected by the mirror chiral symmetry. We also demonstrate that, with increasing magnetic field, vortex-bound quasiparticles undergo a topological phase transition from topologically trivial states in the double-core vortex to zero-energy states in the normal-core vortex. As long as the $d$-vector is locked into the $ab$-plane, the mirror symmetry holds the Majorana property of the zero-energy states, and thus UPt$_3$ preserves topological crystalline superconductivity that is robust against the crystal field and spin-orbit interaction.

Anomalous Field-Angle Dependence of the Specific Heat of Heavy-Fermion Superconductor UPt3

We have investigated the field-angle variation of the specific heat C(H, phi, theta) of the heavy-fermion superconductor UPt3 at low temperatures T down to 50 mK, where phi and theta denote the azimuthal and polar angles of the magnetic field H, respectively. For T = 88 mK, C(H, theta=90) increases proportionally to H^{1/2} up to nearly the upper critical field Hc2, indicating the presence of line nodes. By contrast, C(H, theta=0) deviates upward from the H^{1/2} dependence for (H/Hc2)^{1/2} > 0.5. This behavior can be related to the suppression of Hc2 along the c direction, whose origin has not been resolved yet. Our data show that the unusual Hc2 limit becomes marked only when theta is smaller than 30. In order to explore the possible vertical line nodes in the gap structure, we measured the phi dependence of C in wide T and H ranges. However, we did not observe any in-plane angular oscillation of C within the accuracy of dC/C~0.5%. This result implies that field-induced excitations of the heavy quasiparticles occur isotropically with respect to phi, which is apparently contrary to the recent finding of a twofold thermal-conductivity oscillation.

Searching for the in-plane anisotropy of the specific heat of UPt3 in rotating fields

In order to identify the gap structure of a spin-triplet superconductor UPt3, we performed field-angle-resolved specific heat (Cϕ) measurements in a magnetic field rotated around the [0001] axis. Although various theories predict fourfold symmetry of the gap in the superconducting C phase, we observed no angular variation in Cϕ in a temperature range down to 88 mK (~ 0.17Tc). This absence of the variation in Cϕ implies that the field-angle-dependent quasiparticle excitations, reflecting the gap anisotropy, are averaged out in the bulk of UPt3.