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As exemplified by the growing interest in the quantum anomalous Hall effect, the research on topology as an organizing principle of quantum matter is greatly enriched from the interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study on the magnetic Weyl semimetal ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$. Unconventional contribution to the anomalous Hall and anomalous Nernst effects were observed both above and below the magnetic transition temperature of ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$, indicating the existence of significant Berry curvature. ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ represents a rare case in which this unconventional transverse transport emerges both above and below the magnetic transition temperature in the same material. The transport properties evolve with temperature and field in the antiferromagnetic phase in a different manner than in the paramagnetic phase, suggesting different mechanisms to their origin. Our results indicate ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ is a fertile playground for investigating the interplay between magnetism and topology, and potentially a plethora of topologically nontrivial phases rooted in this interplay.

Although superconductivity in the vicinity of an antiferromagnetic (AFM) instability has been extensively explored in the last three decades or so, superconductivity in compounds with a background of ferromagnetic (FM) spin fluctuations is still rare. We report $^{75}\mathrm{As}$ nuclear quadrupole resonance measurements on the ${A}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$ family, which is the first group of Cr-based superconductors at ambient pressure, with $A$ being alkali elements. From the temperature dependence of the spin-lattice relaxation rate ($1/{T}_{1}$), we find that by changing $A$ in the order of $A=\mathrm{Na}$, ${\mathrm{Na}}_{0.75}{\mathrm{K}}_{0.25}$, K, and Rb, the system is tuned to approach a possible FM quantum critical point (QCP). This may be ascribed to the Cr2-As2-Cr2 bond angle that decreases towards 90\ifmmode^\circ\else\textdegree\fi{}, which enhances the FM interaction via the Cr2-As2-Cr2 path. Upon moving away from the QCP, the superconducting transition temperature ${T}_{\mathrm{sc}}$ increases progressively up to 8.0 K in ${\mathrm{Na}}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$, which is in sharp contrast to the AFM case where ${T}_{\mathrm{sc}}$ usually shows a maximum around a QCP. The $1/{T}_{1}$ decreases rapidly below ${T}_{\mathrm{sc}}$ with no Hebel-Slichter peak, and ubiquitously follows a ${T}^{5}$ variation below a characteristic temperature ${T}^{*}\ensuremath{\approx}0.6$ ${T}_{\mathrm{sc}}$, which indicates the existence of point nodes in the superconducting gap function commonly in the family. These results suggest that the ${A}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$ family is a possible solid-state analog of superfluid $^{3}\mathrm{He}$.

The $n$-type ${\text{HgCr}}_{2}{\mathrm{Se}}_{4}$ exhibits a sharp semiconductor-to-metal transition (SMT) in resistivity accompanying the ferromagnetic order at ${T}_{C}=106\text{ }\text{ }\mathrm{K}$. Here, we investigate the effects of pressure and magnetic field on the concomitant SMT and ferromagnetic order by measuring resistivity, dc and ac magnetic susceptibility, as well as single-crystal neutron diffraction under various pressures up to 8 GPa and magnetic fields up to 8 T. Our results demonstrate that the ferromagnetic metallic ground state of $n$-type ${\text{HgCr}}_{2}{\mathrm{Se}}_{4}$ is destabilized and gradually replaced by an antiferromagnetic, most likely a spiral magnetic, and insulating ground state upon the application of high pressure. On the other hand, the application of external magnetic fields can restore the ferromagnetic metallic state again at high pressures, resulting in a colossal magnetoresistance (CMR) as high as $\ensuremath{\sim}\text{ }3\ifmmode\times\else\texttimes\fi{}{10}^{11}%$ under 5 T and 2 K at 4 GPa. The present study demonstrates that $n$-type ${\text{HgCr}}_{2}{\mathrm{Se}}_{4}$ is located at a peculiar critical point where the balance of competition between ferromagnetic and antiferromagnetic interactions can be easily tipped by external stimuli, providing a new platform for achieving CMR in a single-valent system.

The temperature dependence of the excitation spectrum in NaOsO_{3} through its metal-to-insulator transition (MIT) at 410 K has been investigated using resonant inelastic x-ray scattering at the Os L_{3} edge. High-resolution (ΔE∼56 meV) measurements show that the well-defined, low-energy magnons in the insulating state weaken and dampen upon approaching the metallic state. Concomitantly, a broad continuum of excitations develops which is well described by the magnetic fluctuations of a nearly antiferromagnetic Fermi liquid. By revealing the continuous evolution of the magnetic quasiparticle spectrum as it changes its character from itinerant to localized, our results provide unprecedented insight into the nature of the MIT in NaOsO_{3} [J. G. Vale, S. Calder, C. Donnerer, D. Pincini, Y. G. Shi, Y. Tsujimoto, K. Yamaura, M. M. Sala, J. van den Brink, A. D. Christianson, and D. F. McMorrow, Phys. Rev. B 97, 184429 (2018)PRBMDO2469-995010.1103/PhysRevB.97.184429].

Recently, there have been intense efforts in searching for new topological insulator (TI) materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial Z2 number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial Z2 topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant k-points and associated with the intermediate inter-bilayer coupling of the multi-bilayer Bi film. Our calculations further indicate that the presence of metallic surface states in thick Bi(111) films can be effectively removed by surface adsorption., 5 pages, 3 figures

In this paper we propose a new assignment for mutual exclusion statistics between quasielectrons and quasiholes in the fractional quantum Hall effect. In addition to providing numerical evidence for this assignment, we show that the physical origin of this mutual statistics is a novel hard-core constraint due to correlation between the distinguishable vortex-like quasiparticles., Comment: 4 pages, REVTex, 3 Postscript figures, 4 tables; a new paragraph is added (the third from the end)

We derive the occupation-number distribution in a generalized ideal gas of particles obeying fractional statistics, including mutual statistics, by adopting a state-counting definition. When there is no mutual statistics, the statistical distribution interpolates between bosons and fermions, and respects a fractional exclusion principle (except for bosons). Anyons in a strong magnetic field at low temperatures constitute such a physical system. Applications to the thermodynamic properties of quasiparticle excitations in the Laughlin quantum Hall fluid are discussed.

application/pdf, For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1 / Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q→∞, the wave function is, ψ(x), 2=(2 / sin πx), which is critical and unnormalizable. For the golden-mean flux, the distribution of roots has exact self-similarity and the distribution function is nowhere differentiable. The corresponding wave function also shows a clear self-similar structure.

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group, giving rise to a unified algebraic structure that characterizes the ground-state subspace and fractionally charged, anyonic quasiparticles. Minimal ground state degeneracy is derived without assuming any relation between quasiparticle charge and statistics. We also point out that noncommutativity between large gauge transformations is essential for the topological order in the fractional quantum Hall effect., 5pages, 2 figures; reference added

We show that in the world-sheet SL(2,{ital R})/U(1) coset model there exists a hidden nonlinear {ital {cflx W}}{sub {infinity}} current algebra, which incorporates all higher-spin ({ital s}{ge}2) currents including the energy-momentum tensor. Our proof is based on a free-field realization of {ital {cflx W}}{sub {infinity}} in terms of two scalars, as well as an elegant generating function for the {ital {cflx W}}{sub {infinity}} currents in the classical model. After quantization, the deformed {ital {cflx W}}{sub {infinity}} current algebra still results in an infinite set of commuting charges, which might be related to a space-time {ital W} symmetry for the 2D black hole arising in the corresponding string theory.

A path-integral quantization is presented for the chiral Schwinger model on a Riemann surface. Gauge invariance is maintained by integrating over all gauge potentials without the usual gauge fixing. All local degrees of freedom of the gauge field are suppressed after the integration of the anomalous effective action over a gauge orbit. The resulting theory is a topological one for the surviving global gauge excitations. The general implications for consistent quantization of chiral gauge theories are also discussed.

In this Letter a recently proposed gravity dual of noncommutative Yang-Mills theory is derived from the relations between closed string moduli and open string moduli recently suggested by Seiberg and Witten. The only new input one needs is a simple form of the running string tension as a function of energy. This derivation provides convincing evidence that string theory integrates with the holographical principle and demonstrates a direct link between noncommutative Yang-Mills theory and holography.

Transitions between two quantum Hall states or between a quantum Hall state and a Mott insulator induced by periodic potentials are studied in the 1/N expansion. The transitions are found to be continuous in the large-N limit and are described by a critical point that depends on a real parameter \ensuremath{\theta}, which is determined by the topological orders in the quantum Hall states involved in the transition. Some critical exponents and universal quantities are calculated in the large-N limit and shown to be \ensuremath{\theta} dependent.

Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological {ital Z}{sub {ital n}} symmetry with associated quantum number and unavoidable occurrence of level crossings for many-body eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.

A general concept of holonomy scattering is defined. It applies, among other things, to imply a nontrivial (generally, inelastic) scattering amplitude for the scattering of pure flux tubes off one another, when these fluxes are non-Abelian and do not commute. The amplitudes for such processes, as well as the original Aharonov-Bohm cross section, are calculated directly from an expression for the propagator with a definite winding number.

The present time variation of coupling constants in superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of internal space. If the potential is almost flat, as in perturbation theory to all orders, the value of G-italic-dot/G for Newton's gravitational constant is calculable and estimated to be -1 x 10/sup -11//sup +- //sup 1/ yr/sup -1/. If the potential has a minimum with finite curvature due to unknown nonperturbative effects, G-italic-dot/G will become unobservably small. Improvement of the measurement of G-italic-dot/G would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.

Because of complicated topology of the configuration space for indistinguishable particles in two dimensions, Feynman's path-integral formulation allows exotic statistics. All possible quantum statistics in two-space are characterized by an angle parameter $\ensuremath{\theta}$ which interpolates between bosons and fermions. The current formalisms in terms of topological action of multivalued wave functions can be derived in a model-independent way.

We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found.

The phase change of the wave function of a superfluid film as a vortex moves around a closed path counts the number of superfluid particles enclosed by that path. This result is used to investigate whether such vortices obey ``fractional statistics.'' We conclude that this is not the case in compressible superfluids such as $^{4}\mathrm{He}$ films.

Recently, Berry recognized in quantum mechanics a topological phase factor arising from the adiabatic transport of a system around a closed circuit, which is essentially the Aharonov-Bohm effect in parameter space. Here we consider manifestations of this phase factor for a photon in a state of adiabatically invariant helicity. An interferometer is suggested to see this phase. Also, an effective optical activity for a helical optical fiber is predicted. These effects emerge on a classical level as topological features of Maxwell's theory.

We formulate a geometrical theory of self-dual scalar fields in two dimensions with a local Lorentz-invariant action. Path-integral quantization is used to derive chiral Bosonization by demonstrating equivalence of correlation functions of currents and energy-momentum tensors in our theory with those for Weyl fermions.

We argue that the ..beta.. function for the statistics parameter in (2+1)-dimensional electrodynamics is zero to all orders in perturbation theory beyond one loop. We show that there can be finite radiative corrections from massless charged scalar fields.