Tunable hybridization of Majorana bound states at the quantum spin Hall edge

Confinement at the helical edge of a topological insulator is possible in the presence of proximity-induced magnetic (F) or superconducting (S) order. The interplay of both phenomena leads to the formation of localized Majorana bound states (MBS) or likewise (under certain resonance conditions) the formation of ordinary Andreev bound states (ABS). We investigate the properties of bound states in junctions composed of alternating regions of F or S barriers. Interestingly, the direction of magnetization in F regions and the relative superconducting phase between S regions can be exploited to hybridize MBS or ABS at will. We show that the local properties of MBS translate into a particular nonlocal superconducting pairing amplitude. Remarkably, the symmetry of the pairing amplitude contains information about the nature of the bound state that it stems from. Hence, this symmetry can in principle be used to distinguish MBS from ABS, owing to the strong connection between local density of states and nonlocal pairing in our setup.Comment: 10 pages, 6 figure

Creation of spin-triplet Cooper pairs in the absence of magnetic ordering

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction--the Dirac surface states of a strong topological insulator (TI)--out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin triplet filter across the SC generating equal-spin Cooper pairs via crossed Andreev reflection.Comment: 12 pages, 8 figure

Microscopic theory of the proximity effect in superconductor-graphene nanostructures

We present a theoretical analysis of the proximity effect at a graphene-superconductor interface. We use a tight-binding model for the electronic states in this system which allows to describe the interface at the microscopic level. Two different interface models are proposed: one in which the superconductor induces a finite pairing in the graphene regions underneath, thus maintaining the honeycomb structure at the interface and one that assumes that the graphene layer is directly coupled to a bulk superconducting electrode. We show that properties like the Andreev reflection probability and its channel decomposition depend critically on the model used to describe the interface. We also study the proximity effect on the local density of states on the graphene. For finite layers we analyze the induced minigap and how it is reduced when the length of the layer increases. Results for the local density of states profiles for finite and semi-infinite layers are presented.Comment: 9 pages, 7 figures, submitted to Phys. Rev.

Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters

Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell inequality is within the reach of current experimental setups.Comment: 8 pages, 5 figure

Advisory Opinions and the Problem of Legal Authority

The prohibition against advisory opinions is fundamental to our understanding of federal judicial power, but we have misunderstood its origins. Discussions of the doctrine begin not with a constitutional text or even a court case, but a letter in which the Jay Court rejected President Washington’s request for legal advice. Courts and scholars have offered a variety of explanations for the Jay Court’s behavior. But they all depict the earliest Justices as responding to uniquely American concerns about advisory opinions. This Article offers a different explanation. Drawing on previously untapped archival sources, it shows that judges throughout the anglophone world—not only in the United States, but also in England and British India—became opposed to advisory opinions in the second half of the eighteenth century. The death of advisory opinions was a global phenomenon, rooted in a crisis of common-law authority. Early modern English judges had routinely advised the Crown. This advisory role was politically fraught but doctrinally unproblematic thanks to a jurisprudential orthodoxy that treated judges’ opinions as evidence of a preexisting common law. Although this declaratory theory survived into the nineteenth century (and beyond), it began to fragment after 1750, as lawyers began to disagree about the nature of precedent. Those disagreements generated new pressure to clarify the weight of different kinds of legal authority. Most lawyers intuited that advisory opinions were less authoritative than decisions arising from litigation. But because bench and bar lacked a common theory of legal authority, they were unable to articulate a shared understanding of what respect was due to judges’ extrajudicial pronouncements. As a result, advisory opinions became dangerous, because the judges who issued them could not control how future readers might treat them. In response, judges sought to limit their advisory activity—first in England, then in British-controlled Bengal, and finally in the United States, whose judges inherited Britain’s contested and dynamic understanding of judicial power

Microscopic theory of Cooper pair beam splitters based on carbon nanotubes

We analyze microscopically a Cooper pair splitting device in which a central superconducting lead is connected to two weakly coupled normal leads through a carbon nanotube. We determine the splitting efficiency at resonance in terms of geometrical and material parameters, including the effect of spin-orbit scattering. While the efficiency in the linear regime is limited to 50% and decay exponentially as a function of the width of the superconducting region we show that it can rise up to $\sim 100$ in the non-linear regime for certain regions of the stability diagram.Comment: 5 pages, 5 figure