Mats Horsdal

Enhancing triplet superconductivity by the proximity to a singlet superconductor in oxide heterostructures

We show how in principle a coherent coupling between two superconductors of opposite parity can be realized in a three-layer oxide heterostructure. Due to strong intraionic spin-orbit coupling in the middle layer, singlet Cooper pairs are converted into triplet ones and vice versa. This results in a large enhancement of the triplet superconductivity, persisting well above the native triplet critical temperature.

Proposed detection of the topological phase in ring-shaped semiconductor-superconductor nanowires using Coulomb blockade transport.

In semiconductor-superconductor hybrid structures a topological phase transition is expected as a function of the chemical potential or magnetic field strength. We show that signatures of this transition can be observed in nonlinear Coulomb blockade transport through a ring shaped structure. In particular, on the scale of the superconducting gap and for a fixed electron parity of the ring, the excitation spectrum is independent of flux in the topologically trivial phase but acquires a characteristic h/e periodicity in the nontrivial phase. We relate the h/e periodicity to the recently predicted 4π periodicity of the Josephson current across a junction formed by two topological superconductors.

Charge fractionalization on quantum Hall edges

We discuss the propagation and fractionalization of localized charges on the edges of quantum Hall bars of variable widths, where interactions between the edges give rise to Luttinger liquid behavi ...

Sharp fractional charges in Luttinger liquids

We examine charge fractionalization by chiral separation in a one-dimensional fermion system described by Luttinger liquid theory. The focus is on the question of whether the fractional charges are quantum-mechanically sharp, and in the analysis we make a distinction between the global charge, which is restricted by boundary conditions, and the local charge where a background contribution is subtracted. We show, by way of examples, that fractional charges of arbitrary values, all which are quantum-mechanically sharp, can be introduced by different initial conditions. Since the system is gapless, excitations of arbitrary low frequency contribute to the fluctuations, it is important to make a precise definition of sharp charges, and this we we do by subtraction of the ground-state contribution. We very briefly comment on the relevance of our analysis for proposed experiments.

Explicit mapping between a two-dimensional quantum Hall system and a one-dimensional Luttinger liquid. I. Luttinger parameters

We study a model of a quantum Hall system with the electrons confined to a narrow, linear channel. This system is mapped to a one-dimensional (1D) system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. The mapping is studied at the microscopic level, and we show in detail how the form of the 1D Luttinger liquid is detemined by interactions with particles at the edges and in the bulk of the quantum Hall system. We focus, in particular, on how the parameters are renormalized by the interactions between the two edges and show that the velocity parameter of the current is not modified. The paper is Paper I in a sequence of two papers, where Paper II [M. Horsdal and J. M. Leinaas, Phys. Rev. B 76, 195322 (2007)] gives a derivation of the two-dimensional electron correlation function.

Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems

Semi-Dirac fermions are known to exist at the critical points of topological phase transitions requiring fine-tuning of the parameters. We show that robust semi-Dirac points can appear in a heterostructure consisting of superconducting Sr2IrO4 and a t2g electron system (t2g-ES) without fine-tuning. They are topologically stable in the presence of the symmetries of the model, metallic t2g-ES and a single active band in Sr2IrO4. If the t2g metal is coupled to two different layers of Sr2IrO4 (effectively a multiband superconductor) in a three-layer-structure the semi-Dirac points can split into two stable Dirac points with opposite chiralities. A similar transition can be achieved if the t2g-ES supports intrinsic triplet superconductivity. By considering Sr2RuO4 as an example of a t2g-ES we predict a rich topological phase diagram as a function of various parameters.

Robustness of topological order in semiconductor?superconductor nanowires in the Coulomb blockade regime

Semiconductor?superconductor hybrid systems are promising candidates for the realization of Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the non-trivial phase. The transition between the trivial and non-trivial phase is reflected in the closing and reopening of an excitation gap. We show that the signatures of topological order are robust against details of the geometry, electrostatic disorder and the existence of additional subbands and only rely on the topology of the nanowire and the existence of a superconducting gap. Finally, we show that the coherence length in the non-trivial phase is much longer than in the trivial phase. This opens the possibility to coat the nanowire with superconducting nanograins and thereby significantly reduce the current due to cotunnelling of Cooper pairs and to enhance the Coulomb charging energy without destroying the superconducting gap.

Explicit mapping between a two-dimensional quantum Hall system and a one-dimensional Luttinger liquid. II. Correlation functions

We study a model of a quantum Hall system with the electrons confined to a narrow, linear channel. The system is mapped to a one-dimensional (1D) system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. In a previous paper (Part I) [M. Horsdal and J. M. Leinaas, Phys. Rev. B 76, 195321 (2007)], we studied this mapping at the microscopic level, and examined how the interaction in the two-dimensional (2D) system renormalizes 1D Luttinger liquid parameters. We follow up this study here and derive the low-energy form of the 2D electron correlation function by applying the mapping from the 1D correlation function. The derived expression has a natural separation in a bulk part, which is not modified by interactions, and an edge part, which is modified. We study the effect of interactions on the electron density and on the asymptotic form of the correlation function. The asymptotic parameter is found to be consistent with the expected value from the Luttinger liquid theory, but deviations from the asymptotic form are found in a rather wide intermediate interval. We suggest some questions of interest for further study.

Effects of interaction-induced second Landau level mixing in the ν = 1 quantum Hall effect

The work by Mandal and Jain [Solid State Commun. 118, 503 (2001)] suggests that interaction-induced mixing with the second composite fermion Landau level can lead to renormalization of the electron correlation function exponent in the fractional quantum Hall effect. In the work reported here, a similar mixing with the second electronic Landau level is studied in the

Coulomb blockade signatures of the topological phase transition in semiconductor-superconductor nanowires

\ensuremath{\nu}=1