We present a powerful and general approach to describe the coupling of Majorana fermions to external leads, of interacting or noninteracting electrons. Our picture has the Klein factors of ...bosonization appearing as extra Majorana fermions hybridizing with the physical ones. We demonstrate the power of this approach, analyzing a highly nontrivial SO(M) Kondo problem arising in topological superconductors with M Majorana-lead couplings, allowing for arbitrary M and for conduction electron interactions. Mapping the problem on a quantum Brownian motion model we find robust non-Fermi liquid behavior, even for Fermi liquid leads, and a quantum phase transition between insulating and Kondo regimes when the leads form Luttinger liquids. In particular, for M=4 we find a stable realization of the two-channel Kondo fixed point. Obtaining the linear conductance at low temperatures, we predict transport signatures of this Majorana-Kondo-Luttinger physics.
A leading candidate for the experimental confirmation of the nonlocal quantum dynamics of Majorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected ...to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function and fractional charge quantization observable via the Fano factor. In the universal regime, our results apply for generic anisotropy and even away from the Kondo limit as long as the system supports an emergent topological Kondo fixed point. Our approach thus provides key new qualitative insights and exact expressions for quantitative comparisons to future experimental data.
Background In the last two decades, the world experienced two overlapping global shocks – that is, the 2008–2009 financial crisis and the COVID-19 lockdowns – with severe social and economic ...consequences on African economies that have, once again, brought to the fore the intricate role that globalisation plays in economic growth because of grave risks that often accompany it.Aim We consider three research questions about globalisation: (i) does globalisation heighten economic growth? (ii) is there a statistically significant threshold level of globalisation above which globalisation affects growth differently than at lower levels? (iii) what factors moderate the globalisation-economic growth nexus?Setting A panel of 47 selected countries from Africa from 2001 to 2018 is under scrutiny.Method To begin, it applies an overlapping five-year moving average (MA) to smoothen the data. In addition, we employ the revised globalisation index and the two-step systems generalised method of the moment (GMM) in its empirical strategy.Results We find a largely insignificant relationship between globalisation and economic growth. We attribute these results to Africa’s infinitesimal share – less than 5% – in foreign direct investment (FDI) and global trade, acute infrastructure deficit and the lack of relevant skills that lead to productivity losses and weak performance within the international business ecosystem. We also find, among others, that globalisation is more effective in countries with more gross capital formation, higher population and urban growth rates.Conclusion For Africa to maximise its growth potential from globalisation, sound policies should be put in place to promote trade, FDI, domestic capital formation and urbanisation. We suggest that future studies investigate the long-run equilibrium relationship between globalisation and economic growth.
The Kondo effect is a striking consequence of the coupling of itinerant electrons to a quantum spin with degenerate energy levels. While degeneracies are commonly thought to arise from symmetries or ...fine-tuning of parameters, the recent emergence of Majorana fermions has brought to the fore an entirely different possibility: a topological degeneracy that arises from the nonlocal character of Majorana fermions. Here we show that nonlocal quantum spins formed from these degrees of freedom give rise to a novel topological Kondo effect. This leads to a robust non-Fermi liquid behavior, known to be difficult to achieve in the conventional Kondo context. Focusing on mesoscopic superconductor devices, we predict several unique transport signatures of this Kondo effect, which would demonstrate the nonlocal quantum dynamics of Majorana fermions and validate their potential for topological quantum computation.
We study the multichannel Kondo impurity dynamics realized in a mesoscopic superconducting island connected to metallic leads. The effective "impurity spin" is nonlocally realized by Majorana bound ...states and strongly coupled to lead electrons by non-Fermi liquid correlations. We explore the spin dynamics and its observable ramifications near the low-temperature fixed point. The topological protection of the system raises the perspective to observe multichannel Kondo impurity dynamics in experimentally realistic environments.
Conduction electrons coupled to a mesoscopic superconducting island hosting Majorana bound states have been shown to display a topological Kondo effect with robust non-Fermi liquid correlations. With ...M bound states coupled to M leads, this is an SO(M) Kondo problem, with the asymptotic high and low-energy theories known from bosonization and conformal field theory studies. Here we complement these approaches by analyzing the Bethe ansatz equations describing the exact solution of these models at all energy scales. We apply our findings to obtain nonperturbative results on the thermodynamics of M → M − 2 crossovers induced by tunnel couplings between adjacent Majorana bound states.
We describe how optical dressing can be used to generate band structures for ultracold atoms with nontrivial Z(2) topological order. Time-reversal symmetry is preserved by simple conditions on the ...optical fields. We first show how to construct optical lattices that give rise to Z(2) topological insulators in two dimensions. We then describe a general method for the construction of three-dimensional Z(2) topological insulators. A central feature of our approach is a new way to understand Z(2) topological insulators starting from the nearly free electron limit.
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of Z or X rotations of individual qubits. We find that, similar to the case of incoherent bit and ...phase flips, a trade-off between resilience against coherent X and Z rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into three distinct classes, each resulting in qualitatively distinct final-state distributions. In particular, we show that a graph class exists where the logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold. In these classes, therefore, the logical level noise above the error-correction threshold can retain a significant amount of coherence even for large-distance codes. To perform our analysis, we develop a Majorana-fermion representation of planar-graph surface codes and describe the characterization of logical-state storage using fermion-linear-optics-based simulations. We thereby generalize the approach introduced for the square lattice by Bravyi et al. npj Quantum Inf. 4, 55 (2018)10.1038/s41534-018-0106-y to surface codes on general planar graphs.
PDF
