In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study.

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015 K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7 K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3) nm agrees with λ_{ab}≃130 nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Nonunitary superconductivity in complex quantum materials.

We revisit the concept of nonunitary superconductivity and generalize it to address complex quantum materials. Starting with a brief review of the notion of nonunitary superconductivity, we discuss its spectral signatures in simple models with only the spin as an internal degree of freedom. In complex materials with multiple internal degrees of freedom, there are many more possibilities for the development of nonunitary order parameters. We provide examples focusing on d-electron systems with two orbitals, applicable to a variety of materials. We discuss the consequences for the superconducting spectra, highlighting that gap openings of band crossings at finite energies can be attributed to a nonunitary order parameter if this is associated with a finite superconducting fitness matrix. We speculate that nonunitary superconductivity in complex quantum materials is in fact very common and can be associated with multiple cases of recently reported time-reversal symmetry breaking superconductors.

Emulating Heavy Fermions in Twisted Trilayer Graphene.

Twisted van der Waals materials have been shown to host a variety of tunable electronic structures. Here we put forward twisted trilayer graphene (TTG) as a platform to emulate heavy fermion physics. We demonstrate that TTG hosts extended and localized modes with an electronic structure that can be controlled by interlayer bias. In the presence of interactions, the existence of localized modes leads to the development of local moments, which are Kondo coupled to coexisting extended states. By electrically controlling the effective exchange between local moments, the system can be driven from a magnetic into a heavy fermion regime, passing through a quantum critical point, allowing one to electrically explore a generalized Doniach phase diagram. Our results put forward twisted graphene multilayers as a platform for the realization of strongly correlated heavy fermion physics in a purely carbon-based platform.

Generalized Anderson's theorem for superconductors derived from topological insulators.

A well-known result in unconventional superconductivity is the fragility of nodal superconductors against nonmagnetic impurities. Despite this common wisdom, Bi2Se3-based topological superconductors have recently displayed unusual robustness against disorder. Here, we provide a theoretical framework that naturally explains what protects Cooper pairs from strong scattering in complex superconductors. Our analysis is based on the concept of superconducting fitness and generalizes the famous Anderson's theorem into superconductors having multiple internal degrees of freedom with simple assumptions such as the Born approximation. For concreteness, we report on the extreme example of the Cu x (PbSe)5(BiSe3)6 superconductor. Thermal conductivity measurements down to 50 mK not only give unambiguous evidence for the existence of nodes but also reveal that the energy scale corresponding to the scattering rate is orders of magnitude larger than the superconducting energy gap. This provides the most spectacular case of the generalized Anderson's theorem protecting a nodal superconductor.

Electrically Tunable Gauge Fields in Tiny-Angle Twisted Bilayer Graphene.

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, α≪1°, the application of a perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field leads to the development of highly localized modes associated with flat bands close to charge neutrality, which form an emergent kagome lattice in real space. Our findings indicate that for tiny angles biased twisted bilayer graphene is a promising platform that can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.

Theory of the electron spin resonance in the heavy fermion metal ß-YbAlB4.

The heavy fermion metal ß-YbAlB4 exhibits a bulk room temperature conduction electron spin resonance (ESR) signal which evolves into an Ising-anisotropic f-electron signal exhibiting hyperfine features at low temperatures. We develop a theory for this phenomenon based on the development of resonant scattering off a periodic array of Kondo centers. We show that the hyperfine structure arises from the scattering off the Yb atoms with nonzero nuclear spin, while the constancy of the ESR intensity is a consequence of the presence of crystal electric field excitations of the order of the hybridization strength.

ß-YbAlB4: a critical nodal metal.

We propose a model for the intrinsic quantum criticality of ß-YbAlB(4), in which a vortex in momentum space gives rise to a new type of Fermi surface singularity. The unquenched angular momentum of the |J=7/2,m(J)=±5/2> Yb 4f states generates a momentum-space line defect in the hybridization between 4f and conduction electrons, leading to a quasi-two-dimensional Fermi surface with a k(⊥)(4) dispersion and a singular density of states proportional to E(-1/2). We discuss the implications of this line node in momentum space for our current understanding of quantum criticality and its interplay with topology.

Quantum criticality in inter-band superconductors.

In fermionic systems with different types of quasi-particles, attractive interactions can give rise to exotic superconducting states, such as pair density wave (PDW) superconductivity and breached pairing. In recent years the search for these new types of ground states in cold atoms and in metallic systems has been intense. In the case of metals the different quasi-particles may be the up and down spin bands in an external magnetic field or bands arising from distinct atomic orbitals that coexist at a common Fermi surface. These systems present a complex phase diagram as a function of the difference between the Fermi wavevectors of the different bands. This can be controlled by external means, varying the density in the two-component cold atom system or, in a metal, by applying an external magnetic field or pressure. Here we study the zero temperature instability of the normal system as the Fermi wavevector mismatch of the quasi-particles (bands) is reduced and find a second order quantum phase transition to a PDW superconducting state. From the nature of the quantum critical fluctuations close to the superconducting quantum critical point (SQCP), we obtain its dynamic critical exponent. It turns out to be z = 2 and this allows us to fully characterize the SQCP for dimensions d ≥ 2.