Superconducting states of reduced symmetry: General order parameters and physical implications

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

Quasi-Two-Dimensional Fermi Surfaces and Unitary Spin-Triplet Pairing in the Heavy Fermion Superconductor UTe_{2}

We report first-principles and strongly correlated calculations of the newly discovered heavy fermion superconductor UTe_{2}. Our analyses reveal three key aspects of its magnetic, electronic, and superconducting properties that include (i) a two-leg ladder-type structure with strong magnetic frustrations, which might explain the absence of long-range orders and the observed magnetic and transport anisotropy, (ii) quasi-two-dimensional Fermi surfaces composed of two separate electron and hole cylinders with similar nesting properties as in UGe_{2}, which may potentially promote magnetic fluctuations and help to enhance the spin-triplet pairing, and (iii) a unitary spin-triplet pairing state of strong spin-orbit coupling at zero field, with point nodes presumably on the heavier hole Fermi surface along the k_{x} direction, in contrast to the previous belief of nonunitary pairing. Our proposed scenario is in excellent agreement with latest thermal conductivity measurement and provides a basis for understanding the peculiar magnetic and superconducting properties of UTe_{2}.

TaRh2B2 and NbRh2B2: Superconductors with a chiral noncentrosymmetric crystal structure

It is a fundamental truth in solid compounds that the physical properties follow the symmetry of the crystal structure. Nowhere is the effect of symmetry more pronounced than in the electronic and magnetic properties of materials-even the projection of the bulk crystal symmetry onto different crystal faces is known to have a substantial impact on the surface electronic states. The effect of bulk crystal symmetry on the properties of superconductors is widely appreciated, although its study presents substantial challenges. The effect of a lack of a center of symmetry in a crystal structure, for example, has long been understood to necessitate that the wave function of the collective electron state that gives rise to superconductivity has to be more complex than usual. However, few nonhypothetical materials, if any, have actually been proven to display exotic superconducting properties as a result. We introduce two new superconductors that in addition to having noncentrosymmetric crystal structures also have chiral crystal structures. Because the wave function of electrons in solids is particularly sensitive to the host material's symmetry, crystal structure chirality is expected to have a substantial effect on their superconducting wave functions. Our two experimentally obtained chiral noncentrosymmetric superconducting materials have transition temperatures to superconductivity that are easily experimentally accessible, and our basic property characterization suggests that their superconducting properties may be unusual. We propose that their study may allow for a more in-depth understanding of how chirality influences the properties of superconductors and devices that incorporate them.

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.