# Publications

_{2}. We report measurements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using tunnel-diode resonator technique for various irradiation doses. The normal state electrical resistivity follows Matthiessen rule with an increase of the residual resistivity at a rate of ~0.77 \(\mu \Omega cm/(C/cm^2)\) London penetration depth and thermal conductivity results show that the superconducting state remains fully gapped. The superconducting transition temperature is suppressed at a non-zero rate that is about sixteen times slower than described by the Abrikosov-Gor'kov dependence, applicable to magnetic impurity scattering in isotropic, single-band s-wave superconductors. To gain information about the gap structure and symmetry of the pairing state, we perform a detailed analysis of these experimental results based on insight from a generalized Anderson theorem for multi-band superconductors. This imposes quantitative constraints on the gap anisotropies for each of the possible pairing candidate states. We conclude that the most likely pairing candidate is an unconventional \(A_{1g}^{+-}\)state. While we cannot exclude the conventional \(A_{1g}^{++}\) and the triplet \(A_{1u}\), we demonstrate that these states require additional assumptions about the orbital structure of the disorder potential to be consistent with our experimental results, e.g., a ratio of inter- to intra-band scattering for the singlet state significantly larger than one. Due to the generality of our theoretical framework, we think that it will also be useful for irradiation studies in other spin-orbit-coupled multi-orbital systems.

*A*, of the point group C3 of the system, while the subleading pairing phases belong to the

*E*channel. The resulting order parameter has no nodal points for electron-phonon pairing but exhibits 6 sign changes on the Fermi surface if the Coulomb interaction dominates. We also discuss the disorder sensitivity of the candidate pairing states.

_{c}cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, we systematically investigate different weakly-doped Mott insulators on the square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absence of a pseudogap depends sensitively on non-interacting band parameters and identify the crucial role played by the van Hove singularities of the system. Motivated by a SU(2) gauge theory for the pseudogap state, we propose and verify numerically a simple equation that governs the evolution of characteristic features in the electronic scattering rate.

_{+}x SU(2)

_{-}symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. We find that an approximate SU(2)

_{+}x SU(2)

_{-}symmetry can generically account for the linear increase of the critical temperature with small magnetic fields, and we map out the possible forms of the phase diagram as a function of temperature and magnetic field. We examine which of the pairing states can arise in mean-field theory and the type of pairing favored in the presence of strong ferromagnetic fluctuations, which are expected to be present in twisted double-bilayer graphene. Finally, we also detail the differences in the classification when the additional microscopic or emergent symmetries relevant for twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are taken into account. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and could allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.

_{h}Higgs fields transforming under the adjoint representation of SU(2), with N

_{h}=1 for the electron-doped cuprates, and N

_{h}=4 for the hole-doped cuprates. We investigate the strong-coupling dynamics of this gauge theory, while ignoring the coupling to fermionic excitations. We integrate out the SU(2) gauge field in a strong-coupling expansion, and obtain a lattice action for the Higgs fields alone. We study such a lattice action, with O(N

_{h}) global symmetry, in an analytic large N

_{h }expansion and by Monte Carlo simulations for N

_{h}=4 and find consistent results. We find a confining phase with O(N

_{h}) symmetry preserved (this describes the Fermi liquid phase in the cuprates), and Higgs phases (describing the pseudogap phase of the cuprates) with different patterns of the broken global O(N

_{h}) symmetry. One of the Higgs phases is topologically trivial, implying the absence of any excitations with residual gauge charges. The other Higgs phase has Z

_{2}topological order, with `vison' excitations carrying a Z

_{2}gauge charge. We find consistent regimes of stability for the topological Higgs phase in both our numerical and analytical analyses.

_{7}Rh

_{3}which indicate a fully established superconducting gap and spontaneous time-reversal-symmetry breaking at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in the system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin-fluctuations revealed in susceptibility measurements.

Motivated by recent transport measurements in high-Tc cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field *Ansätze* for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any T>0, also show a similarly enhanced thermal Hall conductivity.

_{3}.” Nano Letters. Publisher's VersionAbstract

_{3}films has broadened this definition, accessing these phase spaces is still typically accomplished through isovalent substitution or heteroepitaxial strain which do not allow for continuous modification of phase composition postsynthesis. Here, we show that it is possible to use low-energy helium implantation to tailor morphotropic phases of epitaxial BiFeO

_{3}films postsynthesis in a continuous and iterative manner. Applying this strain doping approach to morphotropic films creates a new phase space based on internal and external lattice stress that can be seen as an analogue to temperature–composition phase diagrams of classical morphotropic ferroelectric systems.

_{2}and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the Neel state.

_{2}topological order.

_{2}: low-temperature London penetration depth and symmetry analysis.” Phys. Rev. B, 98, 024508. Publisher's VersionAbstract

_{2}by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding \(\lambda(T=0)=230\) nm as the only fit parameter at a fixed \(\Delta(0)/T_c\approx 1.76\), and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-independent normal-state anisotropy. The temperature dependence of resistivity is typical for conventional phonon scattering in metals. We compare these experimental results with expectations from a detailed theoretical symmetry analysis and reduce the number of possible superconducting pairing states in PdTe

_{2}to only three nodeless candidates: a regular, topologically trivial, s-wave pairing, and two distinct odd-parity triplet states that both can be topologically non-trivial depending on the microscopic interactions driving the superconducting instability.

a many-body system. We demonstrate that \(\lambda_{L}\) behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, \(\lambda_{L}\) is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization.

Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.