Topological Kondo effect with Majorana fermions

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" which 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 non-local quantum dynamics of Majorana fermions, and validate their potential for topological quantum computation

Generalization of the Poisson kernel to the superconducting random-matrix ensembles

We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution generalizes the Poisson kernel to the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, our result cannot be obtained by combining the maximum entropy principle with the analyticity-ergodicity constraint. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.Comment: 7 pages, 2 figure

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Z_{n} chiral quantum clock models with strong zero modes related to Z_{n} parafermions. Here, we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z_{3} chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z_{3} chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature

The effect of symmetry class transitions on the shot noise in chaotic quantum dots

Using the random matrix theory (RMT) approach, we calculated the weak localization correction to the shot noise power in a chaotic cavity as a function of magnetic field and spin-orbit coupling. We found a remarkably simple relation between the weak localization correction to the conductance and to the shot noise power, that depends only on the channel number asymmetry of the cavity. In the special case of an orthogonal-unitary crossover, our result coincides with the prediction of Braun et. al [J. Phys. A: Math. Gen. {\bf 39}, L159-L165 (2006)], illustrating the equivalence of the semiclassical method to RMT.Comment: 4 pages, 1 figur

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Zn chiral quantum clock models with strong zero modes related to Zn parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z3 chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z3 chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature

Thermal metal-insulator transition in a helical topological superconductor

Two-dimensional superconductors with time-reversal symmetry have a Z_2 topological invariant, that distinguishes phases with and without helical Majorana edge states. We study the topological phase transition in a class-DIII network model, and show that it is associated with a metal-insulator transition for the thermal conductance of the helical superconductor. The localization length diverges at the transition with critical exponent nu approx 2.0, about twice the known value in a chiral superconductor.Comment: 9 pages, 8 figures, 3 table

Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

We consider the effect of spin-orbit coupling on the low energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor), using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: In zero magnetic field: (1) the narrowing of the distribution of the excitation gap; (2) the appearance of oscillations in the average density of states. In strong magnetic field: (3) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.Comment: 5 pages, 4 figure

Quantum limit of the triplet proximity effect in half-metal - superconductor junctions

We apply the scattering matrix approach to the triplet proximity effect in superconductor-half metal structures. We find that for junctions that do not mix different orbital modes, the zero bias Andreev conductance vanishes, while the zero bias Josephson current is nonzero. We illustrate this finding on a ballistic half-metal--superconductor (HS) and superconductor -- half-metal -- superconductor (SHS) junction with translation invariance along the interfaces, and on HS and SHS systems where transport through the half-metallic region takes place through a single conducting channel. Our calculations for these physically single mode setups -- single mode point contacts and chaotic quantum dots with single mode contacts -- illustrate the main strength of the scattering matrix approach: it allows for studying systems in the quantum mechanical limit, which is inaccessible for quasiclassical Green's function methods, the main theoretical tool in previous works on the triplet proximity effect.Comment: 12 pages, 10 figures; v2: references added, typos correcte