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Nanometric metallic stripes allow the transmission of optical signals via the excitation and propagation of surface-localized evanescent electromagnetic waves, with important applications in the field of nano-photonics. Whereas this kind of plasmonic phenomena typically exploits noble metals, like Ag or Au, other materials can exhibit viable light-transport efficiency. In this work, we demonstrate the transport of visible light in nanometric niobium stripes coupled with a dielectric polymeric layer, exploiting the remotely-excited/detected Raman signal of black phosphorus (bP) as the probe. The light-transport mechanism is ascribed to the generation of surface plasmon polaritons at the Nb/polymer interface. The propagation length is limited due to the lossy nature of niobium in the optical range, but this material may allow the exploitation of specific functionalities that are absent in noble-metal counterparts., Comment: 18 pages, 6 figures; supporting information 7 pages, 9 figures

By means of single-crystal X-ray diffraction we have revealed the breaking of centrosymmetry when lowering the temperature under T$_s$ = 200 K concomitantly with the setting of a commensurate superstructure in the small A-site quadruple perovskite YMn$_3$Mn$_4$O$_{12}$. This results is in agreement with all data already reported for this compounds and solve the previous inconsistency about the Yttrium position. The superstructure is characterized by the appearing of satellite reflections in the single crystal pattern, consistent with an I-centered pseudo-orthorhombic commensurate supercell with $a \approx \sqrt{a_F} = 10.4352(7)$ \AA, $b \approx 2b_F = 14.6049(9)$ \AA, $c \approx \sqrt{c_F} = 10.6961(7)$ \AA and $\beta = 90.110(3)^\circ$, where F stands for the "fundamental" high-temperature cell ($a_F \approx c_F \approx 7.45$ \AA, $b_F \approx 7.34$ \AA, and $\beta \approx 90^\circ$). The space-group was unequivocally found to be Ia, which is non polar, thus allowing for a non-zero polarization in the material. We then have investigated in detail the pyrocurrent, transport, dielectric and the DC and AC magnetic properties of polycrystalline sample of YMn$_3$Mn$_4$O$_{12}$ over a wide temperature range. These measurements clearly highlight several critical temperatures in the material and correlation between the different orders: i) the centrosymmetry is broken at high temperature (T$_S$ = 200K), ii) then the long-range magnetic order of B-sites occurs at T$_{N,B}$ = 108 K and at this same temperature the compound enters in an insulating dielectric state. iii) Finally, a remnant polarization is stabilized concomitantly with a magnetic anomaly at T* = 70 K. We propose that YMn$_3$Mn$_4$O$_{12}$ is a peculiar magnetic ferroelectric in which the polar state is driven by short-range magnetic order.

We investigated the mixed-stack charge-transfer crystal, N,N'-dimethylphenazine-TCNQ (M$_2$P-TCNQ), which is polar at room temperature and just at the neutral-to-ionic interface (ionicity $\rho \approx 0.5$). We detect the typical dielectric signature of a relaxor ferroelectric and an asymmetric positive-up-negative-down behavior. While relaxor ferroelectricity is usually ascribed to disorder in the crystal, we find no evidence for structural disorder in the investigated crystals. To elucidate the origin of M$_2$P-TCNQ's dielectric properties we perform parallel structural and spectroscopic measurements, associated with theoretical modeling and quantum-mechanical calculations. Our combined effort points to a highly polarizable electronic system that is strongly coupled to lattice vibrations. The found indications for polarization reversal imply flipping of the bent conformation of the M$_2$P molecule with an associated energy barrier of a few tens of an eV, broadly consistent with an Arrhenius fit of the dielectric relaxation times. While the polarization is mostly of electronic origin, its possible reversal implies slow collective motions that are affected by solid-state intermolecular interactions., Comment: 13 pages, 12 figures

We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, \texttt{arXiv:1104.1004}, for the reduced density of states of two disjoint intervals with lattice sites $P=\{1,2,\dots,m\}\cup\{2m+1,2m+2,\dots, 3m\}$, which applies to this model. As a first step in the asymptotic analysis of this system, we consider its simplification to two disjoint intervals separated just by one site, and we rigorously calculate the mutual information between these two blocks and the rest of the chain. In order to compute the entropy we need to study the asymptotic behaviour of an inverse Toeplitz matrix with Fisher-Hartwig symbol using the the Riemann--Hilbert method., Comment: 25 pages, 6 figures, title changed

We investigate the specific influence of structural disorder on the suppression of antiferromagnetic order and on the emergence of cuprate superconductivity. We single out pure disorder, by focusing on a series of Y$_{z}$Eu$_{1-z}$Ba$_2$Cu$_3$O$_{6+y}$ samples at fixed oxygen content $y=0.35$, in the range $0\le z\le 1$. The gradual Y/Eu isovalent substitution smoothly drives the system through the Mott-insulator to superconductor transition from a full antiferromagnet with N\'eel transition $T_N=320$ K at $z=0$ to a bulk superconductor with superconducting critical temperature $T_c=18$ K at $z=1$, YBa$_2$Cu$_3$O$_{6.35}$. The electronic properties are finely tuned by gradual lattice deformations induced by the different cationic radii of the two lanthanides, inducing a continuous change of the basal Cu(1)-O chain length, as well as a controlled amount of disorder in the active Cu(2)O$_2$ bilayers. We check that internal charge transfer from the basal to the active plane is entirely responsible for the doping of the latter and we show that superconductivity emerges with orthorhombicity. By comparing transition temperatures with those of the isoelectronic clean system we deterime the influence of pure structural disorder connected with the Y/Eu alloy., Comment: 10 pages 11 figures, submitted to Journal of Physics: Condensed Matter, Special Issue in memory of Prof. Sandro Massida

We present the discovery and refinement by neutron powder diffraction of a new magnetic phase in the Na1-xCaxMn7O12 quadruple perovskite phase diagram, which is the incommensurate analogue of the well-known pseudo-CE phase of the simple perovskite manganites. We demonstrate that incommensurate magnetic order arises in quadruple perovskites due to the exchange interactions between A and B sites. Furthermore, by constructing a simple mean field Heisenberg exchange model that generically describes both simple and quadruple perovskite systems, we show that this new magnetic phase unifies a picture of the interplay between charge, magnetic and orbital ordering across a wide range of compounds., Comment: Accepted for publication in Physical Review Letters

BiMnO3 (BMO), ferromagnetic (FM) below Tc = 100 K, was believed to be also ferroelectric (FE) due to a non-centro-symmetric C2 structure, until diffraction data indicated that its space group is the centro-symmetric C2/c. Here we present infrared phonon spectra of BMO, taken on a mosaic of single crystals, which are consistent with C2/c at any T > 10 K, as well as room-temperature Raman data which strongly support this conclusion. We also find that the infrared intensity of several phonons increases steadily for decreasing T, causing the relative permittivity of BMO to vary from 18.5 at 300 K to 45 at 10 K. At variance with FE materials of displacive type, no appreciable softening has been found in the infrared phonons. Both their frequencies and intensities, moreover, appear insensitive to the FM transition at Tc.

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion paper (J. Hutchinson, J. P. Keating, and F. Mezzadri, arXiv:1503.05732). In particular, we use three approaches: the Trotter-Suzuki mapping; the method of coherent states; and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in our previous article for the classical systems identified., Comment: 36 pages

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and $Sp(2N)$. In particular we calculate critical exponents $s$, $\nu$ and $z$, corresponding to the energy gap, correlation length and dynamic exponent respectively. We also compute the ground state correlators $\left\langle \sigma^{x}_{i} \sigma^{x}_{i+n} \right\rangle_{g}$, $\left\langle \sigma^{y}_{i} \sigma^{y}_{i+n} \right\rangle_{g}$ and $\left\langle \prod^{n}_{i=1} \sigma^{z}_{i} \right\rangle_{g}$, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question., Comment: 14 pages

We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes beta=1,2,4 of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for beta=1,4, thus proving a number of conjectures of Khoruzhenko et al. (Phys. Rev. B, Vol. 80 (2009), 125301). We derive differential equations that characterize the cumulant generating functions for all beta=1,2,4. Furthermore, we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painleve' III' transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit n -> infinity. Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders., Comment: 46 pages. Minor corrections

We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-B\"utticker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of Random Matrix Theory (RMT). The starting points are the finite-n formulae that we recently discovered (Mezzadri and Simm, J. Math. Phys. 52 (2011), 103511). Our analysis includes all the symmetry classes beta=1,2,4; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer (J. Math. Phys. 37 (1996), 4986-5018) and Altland and Zirnbauer (Phys. Rev. B. 55 (1997), 1142-1161). Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. (J. Phys. A.: Math. Theor. 41 (2008), 365102) and Berkolaiko and Kuipers (J. Phys. A: Math. Theor. 43 (2010), 035101 and New J. Phys. 13 (2011), 063020). Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion explicitly., Comment: 45 pages; typos corrected and 6 references added

By means of neutron powder diffraction, we investigated the effect of the polar Bi$^{3+}$ ion on the magnetic ordering of the Mn$^{3+}$ ions in BiMn$_3$Mn$_4$O$_{12}$, the counterpart with \textit{quadruple} perovskite structure of the \textit{simple} perovskite BiMnO$_3$. The data are consistent with a \textit{noncentrosymmetric} spacegroup $Im$ which contrasts the \textit{centrosymmetric} one $I2/m$ previously reported for the isovalent and isomorphic compound LaMn$_3$Mn$_4$O$_{12}$, which gives evidence of a Bi$^{3+}$-induced polarization of the lattice. At low temperature, the two Mn$^{3+}$ sublattices of the $A'$ and $B$ sites order antiferromagnetically (AFM) in an independent manner at 25 and 55 K, similarly to the case of LaMn$_3$Mn$_4$O$_{12}$. However, both magnetic structures of BiMn$_3$Mn$_4$O$_{12}$ radically differ from those of LaMn$_3$Mn$_4$O$_{12}$. In BiMn$_3$Mn$_4$O$_{12}$ the moments $\textbf{M}_{A'}$ of the $A'$ sites form an anti-body AFM structure, whilst the moments \textbf{M}$_{B}$ of the $B$ sites result from a large and \textit{uniform} modulation $\pm \textbf{M}_{B,b}$ along the b-axis of the moments \textbf{M}$_{B,ac}$ in the $ac$-plane. The modulation is strikingly correlated with the displacements of the Mn$^{3+}$ ions induced by the Bi$^{3+}$ ions. Our analysis unveils a strong magnetoelastic coupling between the internal strain created by the Bi$^{3+}$ ions and the moment of the Mn$^{3+}$ ions in the $B$ sites. This is ascribed to the high symmetry of the oxygen sites and to the absence of oxygen defects, two characteristics of quadruple perovskites not found in simple ones, which prevent the release of the Bi$^{3+}$-induced strain through distortions or disorder. This demonstrates the possibility of a large magnetoelectric coupling in proper ferroelectrics and suggests a novel concept of internal strain engineering for multiferroics design., Comment: 9 pages, 7 figures, 5 tables

We study the rate of convergence to a normal random variable of the real and imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a deterministic complex matrix. We show that the rate of convergence is O(N^{-2 + b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the singular values of A; for example, if the singular values are non-degenerate, different from zero and O(1) as N -> infinity, then b=0. The proof uses a Berry-Esse'en inequality for linear combinations of eigenvalues of random unitary, matrices, and so appropriate for strongly dependent random variables., Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3 references

We investigate the matrix model with weight $w(x):=\exp(-z^2/2x^2 + t/x - x^2/2)$ and unitary symmetry. and unitary symmetry. In particular we study the double scaling limit as $N \to \infty$ and $(\sqrt{N} t, Nz^2 ) \to (u_1,u_2)$, where $N$ is the matrix dimension and the parameters $(u_1,u_2)$ remain finite. Using the Deift-Zhou steepest descent method we compute the asymptotics of the partition function when $z$ and $t$ are of order $O\bigl(N^{-1/2}\bigr)$. In this regime we discover a phase transition in the $(z,N)$-plane characterised by the Painleve' III equation. This is the first time that Painleve' III appears in studies of double scaling limits in Random Matrix Theory and is associated to the emergence of an essential singularity in the weighting function. The asymptotics of the partition function is expressed in terms of a particular solution of the Painleve' III equation. We derive explicitly the initial conditions in the limit $Nz^2\rightarrow u_2$ of this solution., Comment: 50 pages and 6 figures. Minor corrections

We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We compute the leading order term of the partition function and of the coefficients of its Taylor expansion. Our results are valid in the range N^(-1/2) < z < N^(1/4). Such partition function contains all the information on a new statistics of the eigenvalues of matrices in the Gaussian Unitary Ensemble (GUE) that was introduced by Berry and Shukla (J. Phys. A: Math. Theor., Vol. 41 (2008), 385202, arXiv:0807.3474). It can also be interpreted as the moment generating function of a singular linear statistics., Comment: 28 pages, 3 figures

We report on the high pressure synthesis of BiMn$_7$O$_{12}$, a manganite displaying a "quadruple perovskite" structure. Structural characterization of single crystal samples shows a distorted and asymmetrical coordination around the Bi atom, due to presence of the $6s^{2}$ lone pair, resulting in non-centrosymmetric space group Im, leading to a permanent electrical dipole moment and ferroelectric properties. On the other hand, magnetic characterization reveals antiferromagnetic transitions, in agreement with the isostructural compounds, thus evidencing two intrinsic properties that make BiMn$_7$O$_{12}$ a promising multiferroic material., Comment: 4 pages, 3 figures

We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L tends to infinity of the determinant of a block-Toeplitz matrix whose symbol belongs to a general class of 2 x 2 matrix functions. The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve of genus g >= 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for thes systems are characterized by the branch points of the hyperelliptic curve approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin (2004) for the XX model and Its, Jin and Korepin (2005,2006) for the XY model., Comment: 75 pages, 10 figures. Revised version with minor corrections

We propose a new correlator in one-dimensional quantum spin chains, the $s-$Emptiness Formation Probability ($s-$EFP). This is a natural generalization of the Emptiness Formation Probability (EFP), which is the probability that the first $n$ spins of the chain are all aligned downwards. In the $s-$EFP we let the spins in question be separated by $s$ sites. The usual EFP corresponds to the special case when $s=1$, and taking $s>1$ allows us to quantify non-local correlations. We express the $s-$EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale., Comment: 6 pages, 1 figure

Bipartite entanglement in the ground state of a chain of $N$ quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is usually a single spin or a block of adjacent spins and the entanglement differentiates between critical and non-critical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem $S_A$ consists of a {\it comb} of $L$ spins, spaced $p$ sites apart. Our results are thus not restricted to a simple `area law', but contain non-local information, parameterized by the spacing $p$. For the XX model we calculate the von-Neumann entropy analytically when $N\to \infty$ and investigate its dependence on $L$ and $p$. We find that an external magnetic field induces an unexpected length scale for entanglement in this case., Comment: 6 pages, 4 figures

We compute the entropy of entanglement between the first $N$ spins and the rest of the system in the ground states of a general class of quantum spin-chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like $\kappa\log_2 N + {\tilde \kappa}$ as $N\to\infty$, where $\kappa$ and ${\tilde \kappa}$ are determined explicitly. In an important class of systems, $\kappa$ is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for $\kappa$ therefore provides an explicit formula for the central charge., Comment: 4 pages

We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the limit of infinite total chain length. We show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given Hamiltonian and those characterizing the Haar measure of the associated group. These averages are either Toeplitz determinants or determinants of combinations of Toeplitz and Hankel matrices. Recent generalizations of the Fisher-Hartwig conjecture are used to compute the leading order asymptotics of the entropy as N --> infinity . This is shown to grow logarithmically with N. The constant of proportionality is determined explicitly, as is the next (constant) term in the asymptotic expansion. The logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal-field-theoretic calculations. In these calculations the constant of proportionality was determined in terms of the central charge of the Virasoro algebra. Our results therefore lead to an explicit formula for this charge. We also show that the entropy is related to solutions of ordinary differential equations of Painlev\'e type. In some cases these solutions can be evaluated to all orders using recurrence relations., Comment: 39 pages, 1 table, no figures. Revised version: minor corrections

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88 (2002), 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps., Comment: 7 pages, 2 figures. Second version: minor corrections