We propose a conductance measurement to detect the backscattering of chiral Majorana edge states. Because normal and Andreev processes have equal probability for backscattering of a single chiral Majorana edge state, there is qualitative difference from backscattering of a chiral Dirac edge state, giving rise to half-integer Hall conductivity and decoupling of fluctuation in incoming and outgoing modes. The latter can be detected through thermal noise measurement. These experimental signatures of Majorana fermions are robust at finite temperature and do not require the size of the backscattering region to be mesoscopic.

In a recent paper, Teo and Kane [Phys. Rev. Lett. 104, 046401 (2010)] proposed a three-dimensional (3D) model in which the defects support Majorana fermion zero modes. They argued that exchanging and twisting these defects would implement a set $\mathcal{R}$ of unitary transformations on the zero-mode Hilbert space which is a “ghostly” recollection of the action of the braid group on Ising anyons in two dimensions. In this paper, we find the group ${\mathcal{T}}_{2n}$, which governs the statistics of these defects by analyzing the topology of the space $K_{2n}$ of configurations of $2n$ defects in a slowly spatially varying gapped free-fermion Hamiltonian: ${\mathcal{T}}_{2n}\equiv {\pi }_1(K_{2n})$. We find that the group ${\mathcal{T}}_{2n}=\mathbb{Z}\times {\mathcal{T}}_{2n}^r$, where the “ribbon permutation group” ${\mathcal{T}}_{2n}^r$ is a mild enhancement of the permutation group $S_{2n}$: ${\mathcal{T}}_{2n}^r\equiv {\mathbb{Z}}_2\times E\mathbf{(}({\mathbb{Z}}_2){}^{2n}⋊S_{2n}\mathbf{)}$. Here, $E\mathbf{(}({\mathbb{Z}}_2){}^{2n}⋊S_{2n}\mathbf{)}$ is the “even part” of $({\mathbb{Z}}_2){}^{2n}⋊S_{2n}$, namely, those elements for which the total parity of the element in $({\mathbb{Z}}_2){}^{2n}$ added to the parity of the permutation is even. Surprisingly, $\mathcal{R}$ is only a projective representation of ${\mathcal{T}}_{2n}$, a possibility proposed by Wilczek [e-print arXiv:hep-th/9806228]. Thus, Teo and Kane’s defects realize projective ribbon permutation statistics,” which we show to be consistent with locality. We extend this phenomenon to other dimensions, codimensions, and symmetry classes. We note that our analysis applies to 3D networks of quantum wires supporting Majorana fermions; thus, these networks are not required to be planar. Because it is an essential input for our calculation, we review the topological classification of gapped free-fermion systems and its relation to Bott periodicity.

Using optical two-dimensional Fourier transform spectroscopy, we report temperature- and excitation-density-dependent measurements of the homogeneous linewidth of the exciton ground-state transition in a single layer of interfacial GaAs quantum dots (QDs). We show that the homogeneous linewidth increases nonlinearly with temperature from 6 to 50 K and that the thermal broadening is well described by an activation term and offset. The absence of a phonon-activation peak in the two-dimensional spectra reveals that elastic scattering of excitons with acoustic phonons via virtual transitions between the ground and excited states significantly contributes to the thermal broadening. We find that the combination of increasing virtual activation energy and exciton-phonon coupling strength with decreasing QD size results in greater thermal broadening for excitons localized in smaller QDs. The homogeneous linewidth also exhibits a strong excitation-density dependence and is shown to increase linearly as the photon density increases from $2\times {10}^{11}$ to $1\times {10}^{12}$ photons pulse${}^{-1}$ cm${}^{-2}$ at 6 K. This trend is attributed to strong coupling of excitons within the same QD and is independent of the quantum-well exciton population density.

We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a two-dimensional conformal field theory. The critical theories include the square-lattice quantum dimer model, the quantum Lifshitz theory, and a deformed toric code model. We show that under generic perturbation the latter flows toward the ordinary Lorentz-invariant ($2+1$)-dimensional Ising critical point, illustrating that CQCPs are generically unstable. We exploit a correspondence between the classical and quantum-dynamical behavior in such systems to perform an extensive numerical study of two lines of CQCPs in a quantum eight-vertex model or, equivalently, two coupled deformed toric codes. We find that the dynamical critical exponent $z$ remains 2 along the U(1)-symmetric quantum Lifshitz line, while it continuously varies along the line with only ${\mathbb{Z}}_2$ symmetry. This illustrates how two CQCPs can have very different dynamical properties, despite identical equal-time ground-state correlators. Our results equally apply to the dynamics of the corresponding purely classical models.

We have studied the magnetic structure of the ferroelectric frustrated spin-1/2 chain material LiCuVO${}_4$ in applied electric and magnetic fields using polarized neutrons. A symmetry and mean-field analysis of the data rules out the presence of static Dzyaloshinskii-Moriya interaction, while exchange striction is shown to be negligible by our specific-heat measurements. The experimentally observed magnetoelectric coupling is in excellent agreement with the predictions of a purely electronic mechanism based on spin supercurrents.

Triple junctions (TJ’s), topologically required linear defects of grain boundary structure, are suggested to control the behavior of nanocrystalline material. However, measurements of their properties are rare. With atom probe tomography, reliable analysis of singular features of the grain boundary structure becomes possible. We report microscopic measurements of segregation along individual TJ’s in Fe/Cr. By segregation to TJ’s nanometric tubular objects of distinct properties are formed. The determined segregation enthalpy of 0.076 eV indicates that TJ’s provide considerable free volume similar to free surfaces.

We have used $s$- and $p$-polarized synchrotron radiation to image the electronic structure of epitaxial graphene near the $\stackrel{̲}{K}$ point by angle-resolved photoemission spectroscopy (ARPES). Part of the experimental Fermi surface is suppressed due to the interference of photoelectrons emitted from the two equivalent carbon atoms per unit cell of graphene’s honeycomb lattice. Here we show that, by rotating the polarization vector, we are able to illuminate this dark corridor giving access to the complete experimental Fermi surface. Our measurements are supported by first-principles photoemission calculations, which reveal that the observed effect persists in the low-photon-energy regime.

By means of quantum Monte Carlo simulations implemented with a two-loop update scheme, the finite-temperature phase diagram of a three-body constrained attractive Bose lattice gas is investigated. The nature of the thermal phase transitions around the dimer superfluid and the atomic superfluid is unveiled. We find that the $Z_2$ symmetry breaking transitions between these two superfluid phases are of first order even at nonzero temperatures. More interestingly, the thermal transition from the dimer superfluid to the normal fluid is found to be consistent with the Kosterlitz-Thouless type but giving an anomalous universal stiffness jump. It demonstrates that this transition is driven by unbinding of pairs of fractional vortices.

We have induced ultrafast charge oscillations in the plane of an unbiased and undoped (110)-oriented GaAs quantum well by coherent optical excitation of heavy-hole and light-hole exciton transitions. The oscillations arise from an in-plane charge displacement between heavy-hole and light-hole states, which results from the periodic parts of the Bloch wave functions and the (110) orientation. The observations are evidence for the existence of a substantial far-infrared transition-dipole moment between heavy- and light-hole subbands for in-plane wave vectors, which we estimate to be ∼0.5 $e$Å for the quantum well under study. Our findings might prove important for designs of far-infrared detectors and emitters.

We report comprehensive ${}^{77}\mathrm{Se}$ NMR measurements on a single crystalline sample of the recently discovered FeSe-based high-temperature superconductor ${\mathrm{K}}_x$Fe${}_{2-y}$Se${}_2$ ($T_c=33$ K) in a broad temperature range up to 290 K. Despite deviations from the stoichiometric KFe${}_2$Se${}_2$ composition, we observed ${}^{77}\mathrm{Se}$ NMR line shapes as narrow as 4.5 kHz under a magnetic field applied along the crystal $c$ axis, and found no evidence for co-existence of magnetic order with superconductivity. On the other hand, the ${}^{77}\mathrm{Se}$ NMR line shape splits into two peaks with equal intensities at all temperatures when we apply the magnetic field along the $\mathit{ab}$ plane. This suggests that K vacancies may have a superstructure and that the local symmetry of the Se sites is lower than the tetragonal fourfold symmetry of the average structure. This effect might be a prerequisite for stabilizing the $s$${}_{\pm }$ symmetry of superconductivity in the absence of the hole bands at the Brillouin zone center. From the increase of NMR linewidth below $T_c$ induced by the Abrikosov lattice of superconducting vortices, we estimate the in-plane penetration depth ${\lambda }_{\mathit{ab}}~290$ nm and the carrier concentration $n_e~1\times {10}^{+21}$ cm${}^{-3}$. Our Knight shift ${}^{77}K$ data indicate that the uniform spin susceptibility decreases progressively with temperature, in analogy with the case of FeSe ($T_c~9$ K) as well as other FeAs high-$T_c$ systems. The strong suppression of ${}^{77}K$ observed immediately below $T_c$ for all crystal orientations is consistent with a singlet pairing of Cooper pairs. We do not however observe the Hebel-Slichter coherence peak of the nuclear spin-lattice relaxation rate $1/T_1$ immediately below $T_c$, expected for conventional BCS s-wave superconductors. In contrast with the case of FeSe, we do not observe evidence for an enhancement of low-frequency antiferromagnetic spin fluctuations near $T_c$ in $1/T_{1}T$. Instead, $1/T_{1}T$ exhibits qualitatively the same behavior as overdoped non-superconducting Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ with $x~0.14$ or greater, where hole bands are missing in the Brillouin zone center. We will discuss the implications of our results on the unknown mechanism of high-temperature superconductivity in FeSe and FeAs systems.

The Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ high-temperature superconductor represents a natural layered metamaterial composed of metallic CuO bilayers sandwiched between ionic BiO planes. Each pair of CuO bilayers forms an atomic-scale Josephson junction. Here we employ the intrinsic Josephson effect for in situ generation and self-detection of electromagnetic waves in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ single crystals. We observe that electromagnetic waves form polaritons with several transverse optical phonons. This indicates the presence of unscreened polar response in cuprates, which may lead to unusually strong electron-phonon interaction. Our technique can provide intense local sources of coherent, monochromatic phonon-polaritons with kW/cm${}^2$ power densities.

The correlations between stripe order, superconductivity, and crystal structure in ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ single crystals have been studied by means of x-ray and neutron diffraction as well as static magnetization measurements. The derived phase diagram shows that charge stripe order (CO) coexists with bulk superconductivity in a broad range of doping around $x=1/8$, although the CO order parameter and correlation length fall off quickly for $x\ne 1/8$. Except for $x=0.155$, the onset of CO always coincides with the transition between the orthorhombic and the tetragonal or less orthorhombic low-temperature structures. The CO transition evolves from a sharp drop at low $x$ to a more gradual transition at higher $x$, eventually falling below the structural phase boundary for optimum doping. With respect to the interlayer CO correlations, we find no qualitative change of the stripe stacking order as a function of doping, and in-plane and out-of-plane correlations disappear simultaneously at the transition. Similarly to the CO, the spin stripe order (SO) is also most pronounced at $x=1/8$. Truly static SO sets in below the CO and coincides with the first appearance of in-plane superconducting correlations at temperatures significantly above the bulk transition to superconductivity (SC). Indications that bulk SC causes a reduction of the spin or charge stripe order could not be identified. We argue that CO is the dominant order that is compatible with SC pairing but competes with SC phase coherence. Comparing our results with data from the literature, we find good agreement if all results are plotted as a function of $x^{\prime }$ instead of the nominal $x$, where $x^{\prime }$ represents an estimate of the actual Ba content, extracted from the doping dependence of the structural transition between the orthorhombic phase and the tetragonal high-temperature phase.

The integration of ferroelectric polymer gates on a Mn-doped GaAs magnetic channel provides a promising route for the persistent field-effect control of magnetic properties in high-quality diluted magnetic semiconductors (DMSs) that are otherwise incompatible with traditional oxide ferroelectrics. That control demands the thinnest possible DMS layers, for which to date the Curie temperature ($T_C$) is severely depressed. Here we show that reducing the channel thickness from 7 to 3–4 nm by etching, followed by a brief 135 °C anneal, does not degrade the $T_C$ (∼70 K) of the 7-nm film. The channel thinning results in a dramatic threefold increase of the $T_C$ shift controlled by the ferroelectric polarization reversal. Furthermore, we obtain the same exponent $(\partial \ln \hspace{0.5em}{T}_C/\partial \ln \hspace{0.5em}R)\equiv \gamma \approx -0.3$ for all channels with different thicknesses, regardless of the technique used for $T_C$ determination. These results suggest that the ferromagnetic coupling in an ultrathin 3-nm channel is far from the two-dimensional limit and shows a rather bulklike behavior, similar to well-established 7-nm films.

Evidence for rapid ordering in a supercooled Cu${}_{46}$Zr${}_{54}$ liquid, obtained from high-energy x-ray diffraction in a containerless processing environment, is presented. Relatively sudden changes were observed in the topological and chemical short-range order near 850 °C, a temperature that is 75 °C below the liquidus temperature and 465 °C above the glass transition temperature. A peak in the specific heat was observed with supercooling, with an onset near 850 °C (the same temperature as the onset of ordering) and a maximum near 700 °C, consistent with the prediction of a molecular-dynamics calculation using embedded atom potentials. The chemical and topological ordering measured here are in agreement with predictions of a rapid development of chemically ordered icosahedral clusters in the supercooled liquid.

We use neutron scattering to study the magnetic-field effect on the static antiferromagnetic (AF) order and low-energy spin excitations in the underdoped iron arsenide superconductor BaFe${}_{1.92}$Ni${}_{0.08}$As${}_2$. At zero field, superconductivity that occurs below a critical temperature of $T_c=17$ K coincides with the appearance of a neutron spin resonance and reduction in the static ordered moment. Upon application of a $~$10-T magnetic field in the FeAs plane, the intensity of the resonance is reduced, accompanied by decreasing $T_c$ and enhanced static AF scattering. These results are similar to those for some copper oxide superconductors, and demonstrate that the static AF order is a competing phase to superconductivity in BaFe${}_{1.92}$Ni${}_{0.08}$As${}_2$.

We present neutron-scattering measurements of Bose-Einstein condensation, the atomic momentum distribution, and final-state effects in liquid ${}^4\mathrm{He}$ under pressure. The condensate fraction at low temperature is found to decrease from $n_0=7.25\pm 0.75\%$ at saturated vapor pressure ($p\simeq$ 0) to $n_0=3.2\pm 0.75\%$ at pressure $p=24$ bar. This indicates an $n_0=3.0\%$ in the liquid at the liquid/solid coexistence line ($p=25.3$ bar). The atomic momentum distribution $n(\mathbf{k})$ has high occupation of low-$k$ states and differs significantly from a Gaussian [e.g., a classical $n(\mathbf{k})$]. Both $n(\mathbf{k})$ and the final-state function broaden with increasing pressure, reflecting the increased localization of the ${}^4\mathrm{He}$ in space under increased pressure.

The variations of in- and inter-plane London penetration depths, $\Delta \lambda (T)$, were measured using a tunnel diode resonator in single crystals of the intrinsic pnictide superconductor LiFeAs. This compound appears to be in the clean limit with a residual resistivity of 4 ($T\to 0$) to 8 ($T_c$) $\mu \Omega \hspace{0.5em}$cm and a residual resistivity ratio of 65 to 35, respectively. The superfluid density ${\rho }_s(T)={\lambda }^2(0)/{\lambda }^2(T)$ is well described by the self-consistent two-gap $\gamma$ model. Together with the previous data, our results support the universal evolution of the superconducting gap from nodeless to nodal upon departure from optimal doping even in clean systems. We also conclude that pair-breaking scattering plays an important role in the deviation of the low-temperature behavior of $\lambda (T)$ from the exponential in Fe-based compounds.

A detailed muon spin relaxation ($\mu$SR) and magnetization study is presented of the paramagnetic-to-ferromagnetic transition in the compound ${\mathrm{SrFe}}_{0.80}{\mathrm{Co}}_{0.20}{\mathrm{O}}_3$. The critical exponents derived from the static critical analysis are close to the theoretical predictions for the Heisenberg model in three dimensions. However, a small drift toward mean-field values is interpreted as arising from the presence of long-range dipolar interactions between the Fe(IV) centers. The evolution of spin dynamics across the transition determined from the $\mu$SR study is consistent with this interpretation. $\mu$SR and magnetization data also provide evidence of an inhomogeneous magnetic state both above and below $T$${}_c$, placing this system in line with other double-exchange materials such as manganites and cobaltites where spontaneous electronic and magnetic phase separation appears conspicuous and explains much of the encountered experimental phenomenology.

Transport measurements on few-layer graphene (FLG) are important because they interpolate between the properties of single-layer graphene (SLG) as a true two-dimensional material and the three-dimensional bulk properties of graphite. In this article we present four-probe local charge transport and nonlocal spin-valve and spin-precession measurements on lateral spin field-effect transistors on FLG. We study systematically the charge- and spin-transport properties depending on the number of layers and the electrical back gating of the device. We explain the charge-transport measurements by taking the screening of scattering potentials into account and use the results to understand the spin data. The measured samples are between 3 and 20 layers thick, and we include in our analysis our earlier results of the measurements on SLG for comparison. In our room-temperature spin-transport measurements we manage to observe spin signals over distances up to 10 $\mathrm{\mu }\mathrm{m}$ and measure enhanced spin-relaxation times with an increasing number of layers, reaching ${\tau }_s~500$ ps as a maximum, about $4$ times higher than in SLG. The increase of ${\tau }_s$ can result from the screening of scattering potentials due to additional intrinsic charge carriers in FLG. We calculate the density of states of FLG using a zone-folding scheme to determine the charge-diffusion coefficient $D_C$ from the square resistance $R_S$. The resulting $D_C$ and the spin-diffusion coefficient $D_S$ show similar values and depend only weakly on the number of layers and gate-induced charge carriers. We discuss the implications of this on the identification of the spin-relaxation mechanism.

We report the observation of a remarkably strong microwave photoresistivity effect in a high-mobility two-dimensional electron system subject to a weak magnetic field and low temperature. The effect manifests itself as a giant microwave-induced resistivity peak which, in contrast to microwave-induced resistance oscillations, appears only near the second harmonic of the cyclotron resonance and only at sufficiently high microwave frequencies. Appearing in the regime linear in microwave intensity, the peak can be more than an order of magnitude stronger than the microwave-induced resistance oscillations and can not be explained by existing theories.