Jonathan M. Edge

Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling

There exists a variety of proposals to transform a conventional s-wave superconductor into a topological superconductor, supporting Majorana fermion mid-gap states. A necessary ingredient of these proposals is strong spin-orbit coupling. Here we propose an alternative system consisting of a one-dimensional chain of magnetic nanoparticles on a superconducting substrate. No spin-orbit coupling in the superconductor is needed. We calculate the topological quantum number of a chain of finite length, including the competing effects of disorder in the orientation of the magnetic moments and in the hopping energies, to identify the transition into the topologically nontrivial state (with Majorana fermions at the end points of the chain).

Quantum Critical Origin of the Superconducting Dome in SrTiO3

We expand the well-known notion that quantum criticality can induce superconductivity by proposing a concrete mechanism for superconductivity due to quantum ferroelectric fluctuations. To this end, we investigate the origin of superconductivity in doped SrTiO_{3} using a combination of density functional and strong coupling theories within the framework of quantum criticality. Our density functional calculations of the ferroelectric soft mode frequency as a function of doping reveal a crossover related to quantum paraelectricity at a doping level coincident with the experimentally observed top of the superconducting dome. Thus, we suggest a model in which the soft mode fluctuations provide the pairing interaction for superconductivity carriers. Within our model, the low doping limit of the superconducting dome is explained by the emergence of the Fermi surface, and the high doping limit by departure from the quantum critical regime. We predict that the highest critical temperature will increase and shift to lower carrier doping with increasing ^{18}O isotope substitution, a scenario that is experimentally verifiable. Our model is applicable to other quantum paraelectrics, such as KTaO_{3}.

Wigner-Poisson statistics of topological transitions in a Josephson junction.

The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topological transitions in an N-mode quantum-dot Josephson junction by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topological transitions in a 2π phase interval scales as √[N], and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.

Signature of the Fulde-Ferrell-Larkin-Ovchinnikov phase in the collective modes of a trapped ultracold Fermi gas.

We study theoretically the collective modes of a two-component Fermi gas with attractive interactions in a quasi-one-dimensional harmonic trap. We focus on an imbalanced gas in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Using a mean-field theory, we study the response of the ground state to time-dependent potentials. For potentials with short wavelengths, we find dramatic signatures in the large-scale response of the gas which are characteristic of the FFLO phase. This response provides an effective way to detect the FFLO state in experiments.

Edge-state-enhanced transport in a two-dimensional quantum walk

Quantum walks on translation-invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits or even stops t ...

Z2 peak of noise correlations in a quantum spin Hall insulator.

We investigate the current noise correlations at a quantum point contact in a quantum spin Hall structure, focusing on the effect of a weak magnetic field in the presence of disorder. For the case of two equally biased terminals we discover a robust peak: the noise correlations vanish at B = 0 and are negative for B ≠ 0. We find that the character of this peak is intimately related to the interplay between time reversal symmetry and the helical nature of the edge states and call it the Z2 peak.

Localization, delocalization, and topological transitions in disordered two-dimensional quantum walks

We investigate time-independent disorder on several two-dimensional discrete-time quantum walks. We find numerically that, contrary to claims in the literature, random onsite phase disorder, spin-dependent or otherwise, cannot localize the Hadamard quantum walk; rather, it induces diffusive spreading of the walker. In contrast, split-step quantum walks are generically localized by phase disorder. We explain this difference by showing that the Hadamard walk is a special case of the split-step quantum walk, with parameters tuned to a critical point at a topological phase transition. We show that the topological phase transition can also be reached by introducing strong disorder in the rotation angles. We determine the critical exponent for the divergence of the localization length at the topological phase transition, and find nu = 2.6, in both cases. This places the two-dimensional split-step quantum walk in the universality class of the quantum Hall effect.

Upper Critical Field as a Probe for Multiband Superconductivity in Bulk and Interfacial STO

We investigate the temperature dependence of the upper critical field Hc2 as a tool to probe the possible presence of multiband superconductivity at the interface between LaAlO 3 and SrTiO 3 (LAO/STO). The behaviour of Hc2 can clearly indicate two-band superconductivity through its nontrivial temperature dependence. For the disorder scattering dominated two-dimensional LAO/STO interface, we find a characteristic non- monotonic curvature of the Hc2(T). We also analyse the Hc2 for multiband bulk STO and find similar behaviour.

Metal-topological insulator transition in the quantum kicked rotator with Z(2) symmetry

The quantum kicked rotator is a periodically driven dynamical system with a metal-insulator transition. We extend the model so that it includes phase transitions between a metal and a topological insulator, in the universality class of the quantum spin Hall effect. We calculate the Z2 topological invariant using a scattering formulation that remains valid in the presence of disorder. The scaling laws at the phase transition can be studied efficiently by replacing one of the two spatial dimensions with a second incommensurate driving frequency. We find that the critical exponent does not depend on the topological invariant, in agreement with earlier independent results from the network model of the quantum spin Hall effect.