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

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Lifshitz transition underlying the metamagnetic transition of UPt3

Comparing quantum oscillation measurements, dc magnetoresistance measurements, and Fermi surfaces obtained from LDA calculations, we argue that the metamagnetic transition of UPt₃, which occurs at an applied field μ _◦ H _M ∼ 20 T, coincides with a Lifshitz transition at which an open orbit on the band 2 hole-like Fermi surface becomes closed for one spin direction. At low field, proximity of the Fermi energy to this particular van Hove singularity may have implications for the superconducting pairing potential of UPt₃. In our picture the magnetization comes from non-linear spin-splitting of the heavy fermion bands. In support of this, we show that the non-linear field dependence of a particular quantum oscillation frequency can be fitted by assuming that the corresponding extremal Fermi surface area is proportional to the magnetization. In addition, below H _M , we find in our LDA calculations a new, non-central orbit on band 1, whose non-linear behaviour explains a field-dependent frequency recently observed in magnetoacoustic quantum oscillation measurements.

Superconducting proximity effect in flat band systems

We study theoretically proximity-induced superconductivity and its inverse effect in dice lattice flat band model by considering Josephson junction with an s-wave pairing in the superconducting leads. Using self-consistent tight-binding Bogoliubov-de Gennes method, we show that there is a critical value for chemical potential of the superconductors depending on paring interaction strength over which for undoped normal region the proximity effect is enhanced. Whereas if the supserconductor chemical potential is less than the critical one the proximity effect decreases regardless of normal region doping and in the meanwhile, the pairing amplitude of superconducting region increases significantly. Furthermore, we unveil that the supercurrent passing through the junction is large (vanishingly small) when the superconductor chemical potential is smaller (larger) than the critical value which increases as a function of normal region chemical potential.

Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}

Discoveries of marked similarities to high-T_{c} cuprate superconductors point to the realization of superconductivity in the doped J_{eff}=1/2 Mott insulator Sr_{2}IrO_{4}. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+. In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective J_{eff}=1/2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry

It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z_{2} invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z_{2}-protected Fermi surfaces to be ubiquitous.

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.

Three-dimensional Majorana fermions in chiral superconductors

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.