Heavy Fermion Superconductor UPt3 Research Articles

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...

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.

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.

Magnetization in the superconducting state of UPt3from polarized neutron diffraction

The heavy fermion superconductor UPt$_3$ is thought to have odd-parity, a state for which the temperature dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different experiments, the NMR Knight shift and measurements of the anisotropy of the upper critical field, we have measured the bulk susceptibility in a high quality single crystal using polarized-neutron diffraction. A temperature independent susceptibility was observed for $H||a$ through the transitions between the normal state and the superconducting A-, B- and C-phases, consistent with odd-parity, spin-triplet superconductivity.

A Spin Triplet Superconductor UPt3

Motivated by a recent angle-resolved thermal conductivity experiment that shows a twofold gap symmetry in the high-field and low-temperature C phase in the heavy-fermion superconductor UPt$_3$, we group-theoretically identify the pairing functions as $E_{1u}$ with the $f$-wave character for all the three phases. The pairing functions are consistent with the observation as well as with a variety of existing measurements. By using a microscopic quasi-classical Eilenberger equation with the identified triplet pairing function under applied fields, we performed detailed studies of the vortex structures for three phases, including the vortex lattice symmetry, the local density of states, and the internal field distribution. These quantities are directly measurable experimentally by SANS, STM/STS, and NMR, respectively. It is found that, in the B phase of low $H$ and low $T$, the double-core vortex is stabilized over a singular vortex. In the C phase, thermal conductivity data are analyzed to confirm the gap structure proposed. We also give detailed comparisons of various proposed pair functions, concluding that the present scenario of $E_{1u}$ with the $f$-wave, which is an analogue to the triplet planar state, is better than the $E_{2u}$ or $E_{1g}$ scenario. Finally, we discuss the surface topological aspects of Majorana modes associated with the $E_{1u}^f$ state of planar like features.

Twofold Spontaneous Symmetry Breaking in the Heavy-Fermion SuperconductorUPt3

The field-orientation dependent thermal conductivity of the heavy-fermion superconductor UPt3 was measured down to very low temperatures and under magnetic fields throughout the distinct superconducting phases: B and C phases. In the C phase, a striking twofold oscillation of the thermal conductivity within the basal plane is resolved reflecting the superconducting gap structure with a line of node along the a axis. Moreover, we find an abrupt vanishing of the oscillation across a transition to the B phase, as a clear indication of a change of gap symmetries. We also identify extra two line nodes below and above the equator in both B and C phases. From these results together with the symmetry consideration, the gap function of UPt3 is determined as a E(1u) representation characterized by a combination of two line nodes at the tropics and point nodes at the poles.

Magnetic Field and Pressure Phase Diagrams of Uranium Heavy-Fermion Compound U2Zn17

We have performed magnetization measurements at high magnetic fields of up to 53 T on single crystals of a uranium heavy-fermion compound U$_2$Zn$_{17}$ grown by the Bridgman method. In the antiferromagnetic state below the N\'{e}el temperature $T_{\rm N}$ = 9.7 K, a metamagnetic transition is found at $H_c$ $\simeq$ 32 T for the field along the [11$\bar{2}$0] direction ($a$-axis). The magnetic phase diagram for the field along the [11$\bar{2}$0] direction is given. The magnetization curve shows a nonlinear increase at $H_m$ $\simeq$ 35 T in the paramagnetic state above $T_{\rm N}$ up to a characteristic temperature $T_{{\chi}{\rm max}}$ where the magnetic susceptibility or electrical resistivity shows a maximum value. This metamagnetic behavior of the magnetization at $H_m$ is discussed in comparison with the metamagnetic magnetism of the heavy-fermion superconductors UPt$_3$, URu$_2$Si$_2$, and UPd$_2$Al$_3$. We have also carried out high-pressure resistivity measurement on U$_2$Zn$_{17}$ using a diamond anvil cell up to 8.7 GPa. Noble gas argon was used as a pressure-transmitting medium to ensure a good hydrostatic environment. The N\'{e}el temperature $T_{\rm N}$ is almost pressure-independent up to 4.7 GPa and starts to increase in the higher-pressure region. The pressure dependences of the coefficient of the $T^2$ term in the electrical resistivity $A$, the antiferromagnetic gap $\Delta$, and the characteristic temperature $T_{{\rho}{\rm max}}$ are discussed. It is found that the effect of pressure on the electronic states in U$_2$Zn$_{17}$ is weak compared with those in the other heavy fermion compounds.

The Fermi surface and f-valence electron count of UPt3

Combining old and new de Haas-van Alphen (dHvA) and magnetoresistance data, we arrive at a detailed picture of the Fermi surface of the heavy fermion superconductor UPt3. Our work was partially motivated by a new proposal that two 5f valence electrons per formula unit in UPt3 are localized by correlation effects—agreement with previous dHvA measurements of the Fermi surface was invoked in its support. Comprehensive comparison with our new observations shows that this ‘partially localized’ model fails to predict the existence of a major sheet of the Fermi surface, and is therefore less compatible with experiment than the originally proposed ‘fully itinerant’ model of the electronic structure of UPt3. In support of this conclusion, we offer a more complete analysis of the fully itinerant band structure calculation, where we find a number of previously unrecognized extremal orbits on the Fermi surface.

Odd-parity superconductivity in UPt 3 and UNi 2Al 3–NMR studies

We will report the present status of experimental results on heavy-fermion superconductors UPt 3 and UNi 2Al 3. The NMR studies of UPt 3 revealed that no reduction in the 195Pt Knight shift below T c was observed for high-field C-phase. At low fields, the respective Knight shifts for the magnetic field parallel to b- and c-axis decrease at H<5 kOe and H<2.3 kOe below T c, whereas the shift for c-axis does not change across T c down to the lowest field of H∼1.764 kOe. This unconventional behavior in Knight shift which depends on magnetic-field strength and crystal orientation cannot be explained in terms of any even-parity Cooper pairing state, but provides evidence for the odd-parity one being realized in UPt 3. In UNi 2Al 3, 27Al Knight shift dose not change across T c, giving evidence for the odd-parity one as well. This is in marked contrast to the even-parity d-wave superconductivity in UPd 2Al 3. In order to gain further insight into the odd-parity Cooper pairing state, we remark on the quasi-particle spin susceptibility in the heavy-fermion state.

Weak Antiferromagnetic Order and Superconductivity in UPt3 Studied by Neutron Scattering

AbstractFor Abstract see ChemInform Abstract in Full Text.

Uniaxial pressure dependence of the antiferromagnetic order in UPt 3

The weak antiferromagnetic order of the heavy-fermion superconductor UPt3 has been investigated by elastic neutron-scattering measurements under applied uniaxial pressure up to 6 kbar along the a and c axes of the hexagonal crystal structure. For p||c the small antiferromagnetically ordered moment of 0.02 μB/U-atom shows a non-linear decrease for increasing pressures and is still not completely suppressed at the maximum applied pressure of 6 kbar. For p||a a significant increase in the magnetic Bragg peak intensity is observed, which suggests an incomplete domain repopulation and confirms the presence of a single-k structure.