Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding

In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is directly related to global transformations of the ground-state wavefunctions on a torus (the modular transformations). On the other hand, there are theoretical descriptions of various topologically ordered states in 3+1D, which exhibit both point-like and loop-like excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of loop-like excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a non-trivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work we consider realizations of topological order in 3+1D using cohomological gauge theory in which the loops have Abelian statistics, and explicitly demonstrate our results on examples with $Z_2\times Z_2$ topological order

Topological superconductivity with deformable magnetic skyrmions

Magnetic skyrmions are nanoscale spin configurations that can be efficiently created and manipulated. They hold great promises for next-generation spintronics applications. In parallel to these developments, the interplay of magnetism, superconductivity and spin-orbit coupling has proved to be a versatile platform for engineering topological superconductivity predicted to host non-abelian excitations, Majorana zero modes. We show that topological superconductivity can be induced by proximitizing magnetic skyrmions and conventional superconductors, without need for additional ingredients. Apart from a previously reported Majorana zero mode in the core of the skyrmion, we find a more universal chiral band of Majorana modes on the edge of the skyrmion. We show that the chiral Majorana band is effectively flat in the physically relevant regime of parameters, leading to interesting robustness and scaling properties. In particular, the number of Majorana modes in the (nearly-)flat band scales with the perimeter length of a deformed skyrmion configuration, while being robust to local disorder.Comment: 16 + 3 pages, 3 figures + Supplementary Material

Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice

Recently two interesting candidate quantum phases --- the chiral spin density wave state featuring anomalous quantum Hall effect and the d+id superconductor --- were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and t-J model on the honeycomb lattice at 1/4-doping. The main advantage of our approach is the use of symmetry quantum numbers of ground state wavefunctions on finite size systems (up to 32 sites) to sharply distinguish different quantum phases. Our results show that for $1\lesssim U/t< 40$ in the Hubbard model and for $0.1< J/t<0.80(2)$ in the t-J model, the quantum ground state is either a chiral spin density wave state or a spin-charge-Chern liquid, but not a d+id superconductor. However, in the t-J model, upon increasing $J$ the system goes through a first-order phase transition at $J/t=0.80(2)$ into the d+id superconductor. Here the spin-charge-Chern liquid state is a new type of topologically ordered quantum phase with Abelian anyons and fractionalized excitations. Experimental signatures of these quantum phases, such as tunneling conductance, are calculated. These results are discussed in the context of 1/4-doped graphene systems and other correlated electronic materials on the honeycomb lattice.Comment: Some parts of text revised for clarity of presentatio

Straining the Identity of Majorana Fermions

We propose an experimental setup of an interferometer for the observation of neutral Majorana fermions on topological insulator - superconductor - ferromagnet junctions. We show that the extended lattice defects naturally present in materials, dislocations, induce spin currents on the edges while keeping the bulk time-reversal symmetry intact. We propose a simple two terminal conductance measurement in an interferometer formed by two edge point contacts, which reveals the nature of Majorana states through the effect of dislocations. The zero temperature magneto-conductance changes from even oscillations with period phi/2 (phi is the flux quantum hc/e) to odd oscillations with period phi, when non-trivial dislocations are present and the Majorana states are sufficiently strongly coupled. Additionally, the conductance acquires a notable asymmetry as a function of the incident electron energy, due to the topological influence of the dislocations, while resonances appear at the coupling energy of Majorana states.Comment: 5 pages, 3 figures, three-point bending setup with Hg(Cd)Te analyze

Activation of Stat3 Signaling in AgRP Neurons Promotes Locomotor Activity

Over the last years, much of the research on obesity has focused on the study of leptin. This adipocyte-derived hormone circulates in proportion to fat mass and functions as an adiposity signal to decrease energy intake and increase energy expenditure in order to maintain energy homeostasis. Leptin signals informations on body energy stores to hypothalamic neurons located in the arcuate nucleus (ARC) of the hypothalamus. One of the leptin-regulated neuronal subtypes in the ARC are the orexigenic agouti-related peptide (AgRP)-producing neurons, which are directly inhibited by leptin. A key pathway downstream of the leptin receptor involves activation of the signal transducer and activator of transcription 3 (Stat3), but the role of Stat3 in the regulation of AgRP neurons remains controversial. In this study, analysis of Stat3-CAgRP mice expressing a constitutively active version of the Stat3 protein (Stat3-C) selectively in AgRP neurons reveals a crucial role for Stat3 in AgRP neurons in the regulation of energy expenditure in vivo. Stat3-CAgRP mice are lean and develop a relative resistance to diet-induced obesity accompanied by improved glucose homeostasis. The lean phenotype of Stat3-CAgRP mice appears in the presence of unaltered AgRP expression and caloric intake as a consequence of increased energy expenditure evoked by elevated locomotor activity. Consistent with the phenotype observed in Stat3-CAgRP mice, expression of Stat3-C in AgRP neurons of leptin deficient ob/ob mice diminishes the obese phenotype of ob/ob mice as a result of increased energy expenditure and locomotor activity in the presence of unaltered food intake. Analysis of brain catecholamines in Stat3-CAgRP mice revealed a trend towards elevated dopamine concentrations in the striatum and frontal cortex, which potentially account for the increased locomotor activity in those mice. Nevertheless, the anatomical interaction of AgRP neurons with neuronal centers that control locomotor activity and the exact molecular mechanism in AgRP neurons leading to Stat3-dependent activation of locomotor activity have to be defined further. Taken together, this thesis introduces a novel model according to which leptin-stimulated Stat3 activation in AgRP neurons directly regulates locomotor activity independent of the regulation of AgRP mRNA expression