We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zero-energy surface state in the $d_{xy}$-wave case becomes a Majorana fermion, in contrast with the situation realized in the topologically trivial high-$T_c$ cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of this field are shown to strongly influence the transport properties, in contrast with the case without TI. We predict an experimental signature of the Majorana states via conductance spectroscopy.

Reaction cross sections (${\sigma }_R$) for ${}^{19}\mathrm{C}$, ${}^{20}\mathrm{C}$ and the drip-line nucleus ${}^{22}\mathrm{C}$ on a liquid hydrogen target have been measured at around $40A\mathrm{MeV}$ by a transmission method. A large enhancement of ${\sigma }_R$ for ${}^{22}\mathrm{C}$ compared to those for neighboring C isotopes was observed. Using a finite-range Glauber calculation under an optical-limit approximation the rms matter radius of ${}^{22}\mathrm{C}$ was deduced to be $5.4\pm 0.9\mathrm{fm}$. It does not follow the systematic behavior of radii in carbon isotopes with $N\le 14$, suggesting a neutron halo. It was found by an analysis based on a few-body Glauber calculation that the two-valence neutrons in ${}^{22}\mathrm{C}$ preferentially occupy the $1s_{1/2}$ orbital.

The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high-field regime, the eightfold degeneracy in the zero-energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding to filling factors $\nu =0$, 1, 2, and 3. Measurements of the activation energy gaps for the $\nu =2$ and 3 filling factors in tilted magnetic fields exhibit no appreciable dependence on the in-plane magnetic field, suggesting that these Landau level splittings are independent of spin. In addition, measurements taken at the $\nu =0$ charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.

We report the observation of vortex nucleation in a rotating optical lattice. A ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.

We report an electron transport study of lithographically fabricated graphene nanoribbons (GNRs) of various widths and lengths. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the GNR width. In this gap, electrons are localized, and charge transport exhibits a transition between thermally activated behavior at higher temperatures and variable range hopping at lower temperatures. By varying the geometric capacitance, we find that charging effects constitute a significant portion of the activation energy.

${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is one of a handful of known topological insulators. Here we show that copper intercalation in the van der Waals gaps between the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ layers, yielding an electron concentration of $\sim 2\times {10}^{20}{\mathrm{cm}}^{-3}$, results in superconductivity at 3.8 K in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ for $0.12\le x\le 0.15$. This demonstrates that Cooper pairing is possible in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ at accessible temperatures, with implications for studying the physics of topological insulators and potential devices.

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are trees. It is shown here that this result is contingent on the assumption of a stationary flow through the network. When time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops. The transitions between different network topologies as the parameters of the problem vary are examined. These results may have strong implications for the structure and formation of natural networks, as is illustrated by the example of leaf venation networks.

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e., loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.

We show that minuscule entropic forces, on the order of 100 fN, can prevent the formation of DNA loops—a ubiquitous means of regulating the expression of genes. We observe a tenfold decrease in the rate of LacI-mediated DNA loop formation when a tension of 200 fN is applied to the substrate DNA, biasing the thermal fluctuations that drive loop formation and breakdown events. Conversely, once looped, the DNA-protein complex is insensitive to applied force. Our measurements are in excellent agreement with a simple polymer model of loop formation in DNA, and show that an antiparallel topology is the preferred LacI-DNA loop conformation for a generic loop-forming construct.

Dynamic fracture experiments were performed in polymethylmethacrylate over a wide range of velocities and reveal that the fracture energy exhibits an abrupt threefold increase from its value at crack initiation at a well-defined critical velocity, below the one associated with the onset of microbranching instability. This transition is associated with the appearance of conics patterns on fracture surfaces that, in many materials, are the signature of damage spreading through the nucleation and growth of microcracks. A simple model allows us to relate both the energetic and fractographic measurements. These results suggest that dynamic fracture at low velocities in amorphous materials is controlled by the brittle-quasibrittle transition studied here.

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We discuss implications for two fundamental and unresolved problems in organismal biology and geomorphology: how basal metabolism scales with body size for homeotherms and the scaling of drainage basin shape on eroding landscapes.

The Thorne hoop conjecture is an attempt to make precise the notion that gravitational collapse occurs if enough energy is compressed into a small enough volume, with the “size” being defined by the circumference. We can make a precise statement of this form, in spherical symmetry, using the Brown-York mass as our measure of the energy. Consider a spherical 2-surface in a spherically symmetric spacetime. If the Brown-York mass $M_{\mathrm{BY}}$ and the circumference $C$ satisfy $C<2\pi M_{\mathrm{BY}}$, then the system must either have emerged from a white hole or will collapse into a black hole. We show that no equivalent result can hold true using either the Liu-Yau mass $M_{\mathrm{LY}}$ or the Wang-Yau mass $M_{\mathrm{WY}}$. This forms a major obstacle to any attempt to establish a Thorne-type hoop theorem in the general case based on either the Liu-Yau or the Wang-Yau mass.

We compare the azimuthal correlations arising from three and two hadron production in $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$. We show that in $\mathrm{Au}+\mathrm{Au}$, the two away side partons in two-to-three processes have in average a smaller and a greater path length than the average path length of the away-side parton in two-to-two processes. Since in average the particle with the shortest path length in two-to-three processes loses less energy, with respect to the away-side particle in two-to-two processes, this effect leads to a relative enhancement of the ratio of two-to-three to two-to-two processes in $\mathrm{Au}+\mathrm{Au}$ compared to $p+p$ collisions. We argue that this phenomenon may be responsible for the shape of the away side in azimuthal correlations at the Relativistic Heavy-Ion Collider.

Excited states in ${}^{212}\mathrm{Po}$ were populated by $\alpha$ transfer using the ${}^{208}\mathrm{Pb}({}^{18}\mathrm{O},{}^{14}\mathrm{C})$ reaction, and their deexcitation $\gamma$ rays were studied with the Euroball array. Several levels were found to decay by a unique $E1$ transition ($E_{\gamma }<1\mathrm{MeV}$) populating the yrast state with the same spin value. Their lifetimes were measured by the Doppler-shift attenuation method. The values, found in the range 0.1–1.4 ps, lead to very enhanced transitions, $B(E1)=2\times {10}^{-2}–1\times {10}^{-3}\mathrm{W}.\mathrm{u}.$ These results are discussed in terms of an $\alpha$-cluster structure which gives rise to states with non-natural-parity values, provided that the composite system cannot rotate collectively, as expected in the “$\alpha +{}^{208}\mathrm{Pb}$” case. Such states due to the oscillatory motion of the $\alpha$-core distance are observed for the first time.

In the gravity field, density changes triggered by a kinetic scheme as simple as $A+B\to C$ can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars $A$ and $B$. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns. This is demonstrated both numerically and experimentally on the specific example of a simple acid-base neutralization reaction.

We show that three dimensional superconductors, described within a Bogoliubov–de Gennes framework, can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A feature of three dimensional systems is that there are “braidless” operations in which it is possible to manipulate the ground state associated with a set of defects without moving or measuring them. To illustrate these effects, we analyze specific architectures involving topological insulators and superconductors.

It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (${\mathrm{H}}_2$) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.

We report the preparation of a rovibronic ground-state molecular quantum gas in a single hyperfine state and, in particular, the absolute lowest quantum state. This addresses the last internal degree of freedom remaining after the recent production of a near quantum degenerate gas of molecules in their rovibronic ground state, and provides a crucial step towards full control over molecular quantum gases. We demonstrate a scheme that is general for bialkali polar molecules and allows the preparation of molecules in a single hyperfine state or in an arbitrary coherent superposition of hyperfine states. The scheme relies on electric-dipole, two-photon microwave transitions through rotationally excited states and makes use of electric nuclear quadrupole interactions to transfer molecular population between different hyperfine states.

We propose a method to measure the superfluid fraction of an atomic gas. The method involves the use of a vector potential generated by optical beams with nonzero angular momenta to simulate uniform rotation. The induced change in angular momentum of the atomic gas can be measured spectroscopically. This allows a direct determination of the superfluid fraction.