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The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is predicated on the well-known equivalence between the classical equilibrium statistical mechanics of directed polymers in two spatial dimensions and the imaginary-time quantum dynamics of particles in one spatial dimension, originally exploited by P.-G. de Gennes [P.-G. de Gennes, J. Chem. Phys. 48, 2257 (1968)]. Known results concerning two exactly solvable microscopic models of quantum particles moving in one spatial dimension—the Lieb-Liniger model of contact interactions and the Calogero-Sutherland model of long-range interactions—are used to shed light on the behavior of the corresponding polymeric systems. In addition, the technique of bosonization is used to reveal how generic polymer interactions give rise to an emergent polymer fluid that has universal collective excitations. Additionally, the response of the system to topological constraints such as pins though which polymers cannot pass is explored. Immediately on the compressed side of a pin there is a divergent pile-up in polymer density, while on the other side there is a gap of finite area in which polymer density is negligible. Comparison of this response to that of a system of simply noncrossing (i.e., noncrossing but otherwise noninteracting) directed polymers, explored in a companion paper, reveals that generic interactions leave the structure quantitatively unchanged on the line transverse to the pin, and leave it qualitatively unchanged throughout the two dimensions of the system's extent. Furthermore, the free-energy cost associated with a pin that partitions a system having generic interactions is found to be proportional to the pin-partitioning cost for a system of simply noncrossing polymers. [ABSTRACT FROM AUTHOR]

We address the statistical mechanics of randomly and permanently crosslinked networks. We develop a theoretical framework (vulcanization theory) which can be used to systematically analyze the correlation between the statistical properties of random networks and their histories of formation. Generalizing the original idea of Deam and Edwards, we consider an instantaneous crosslinking process, where all crosslinkers (modeled as Gaussian springs) are introduced randomly at once in an equilibrium liquid state, referred to as the preparation state. The probability that two functional sites are crosslinked by a spring exponentially decreases with their distance squared. After formally averaging over network connectivity, we obtained an effective theory with all degrees of freedom replicated 1 + n times. Two thermodynamic ensembles, the preparation ensemble and the measurement ensemble, naturally appear in this theory. The former describes the thermodynamic fluctuations in the state of preparation, while the latter describes the thermodynamic fluctuations in the state of measurement. We classify various correlation functions and discuss their physical significances. In particular, the memory correlation functions characterize how the properties of networks depend on their method of preparation, and are the hallmark properties of all randomly crosslinked materials. We clarify the essential difference between our approach and that of Deam-Edwards, and discuss the saddle-point order parameters and its physical significance. Finally we also discuss the connection between saddlepoint approximation of vulcanization theory, and the classical theory of rubber elasticity as well as the neo-classical theory of nematic elastomers. [ABSTRACT FROM AUTHOR]

The orbital degree of freedom is integral to many exotic phenomenain condensed matter, including colossal magnetoresistance and unconventional superconductivity. The standard model of orbital physics is the Kugel-Khomskii model, which first explained the symmetry of orbital and magnetic order in KCuF3 and has since been applied to virtually all orbitally active materials. Here we present Raman and X-ray scattering measurements showing that KCuF3 exhibits a previously unidentified structural phase transition at T=50?K, involving rotations of the CuF6 octahedra. These rotations are quasi-ordered and exhibit glassy hysteresis, but serve to stabilize Néel spin order at T=39?K. We propose an explanation for these effects by supplementing the Kugel-Khomskii model with a direct, orbital exchange term that is driven by a combination of electron-electron interactions and ligand distortions. The effect of this term is to create a near degeneracy that dynamically frustrates the spin subsystem but is lifted at low temperature by subdominant, orbital-lattice interactions. Our results suggest that direct orbital exchange may be crucial for the physics of many orbitally active materials, including manganites, ruthenates and the iron pnictides. [ABSTRACT FROM AUTHOR]

Systems of superconducting islands placed on normal metal films offer tunable realizations of two-dimensional (2D) superconductivity; they can thus elucidate open questions regarding the nature of 2D superconductors and competing states. In particular, island systems have been predicted to exhibit zero-temperature metallic states. Although evidence exists for such metallic states in some 2D systems, their character is not well understood: the conventional theory of metals cannot explain them, and their properties are difficult to tune. Here, we characterize the superconducting transitions in mesoscopic island-array systems as a function of island thickness and spacing. We observe two transitions in the progression to superconductivity. Both transition temperatures exhibit unexpectedly strong depression for widely spaced islands, consistent with the system approaching zero-temperature (T=0) metallic states. In particular, the first transition temperature seems to linearly approach T=0 for finite island spacing. The nature of the transitions is explained using a phenomenological model involving the stabilization of superconductivity on each island via a coupling to its neighbours. [ABSTRACT FROM AUTHOR]

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment. [ABSTRACT FROM AUTHOR]

The orbital degree of freedom is integral to many exotic phenomenain condensed matter, including colossal magnetoresistance and unconventional superconductivity. The standard model of orbital physics is the Kugel-Khomskii model, which first explained the symmetry of orbital and magnetic order in KCuF3 and has since been applied to virtually all orbitally active materials. Here we present Raman and X-ray scattering measurements showing that KCuF3 exhibits a previously unidentified structural phase transition at T=50?K, involving rotations of the CuF6 octahedra. These rotations are quasi-ordered and exhibit glassy hysteresis, but serve to stabilize Néel spin order at T=39?K. We propose an explanation for these effects by supplementing the Kugel-Khomskii model with a direct, orbital exchange term that is driven by a combination of electron-electron interactions and ligand distortions. The effect of this term is to create a near degeneracy that dynamically frustrates the spin subsystem but is lifted at low temperature by subdominant, orbital-lattice interactions. Our results suggest that direct orbital exchange may be crucial for the physics of many orbitally active materials, including manganites, ruthenates and the iron pnictides. [ABSTRACT FROM AUTHOR]

We report experiments on quantum dot single-electron-tunneling (SET) transistors made from short multiwall nanotubes and threaded by magnetic flux. Such systems allow us to probe the electronic energy spectrum of the nanotube and its dependence on the magnetic field. Evidence is provided for the interconversion between gapped (semiconducting) and ungapped (metallic) states. Our tubes exhibit h/e-period magnetic flux dependence, in agreement with simple tight-binding calculations. [ABSTRACT FROM AUTHOR]

When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume while maintaining its toroidal shape. By contrast, if the gel is heated quickly, an impermeable layer of collapsed polymer forms and traps solvent within the gel, arresting the volume change. The ensuing evolution of the gel then happens at fixed volume, leading to phase separation and the development of inhomogeneous stress that deforms the toroidal shape. We observe that this stress can cause the torus to buckle out of the plane, via a mechanism analogous to the bending of bimetallic strips upon heating. Our results demonstrate that thermodynamic instabilities, i.e., phase transitions, can be used to actuate mechanical deformation in an extreme thermodynamics of materials. [ABSTRACT FROM AUTHOR]

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent cross-links are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerge upon sufficient cross-linking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of cross-linking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellas or random structures with a unique wavelength, can be energetically favorable.

The application of single molecules as templates for nanodevices is a promising direction for nanotechnology. We used a pair of suspended DNA molecules as templates for superconducting two-nanowire devices. Because the resulting wires are very thin, comparable to the DNA molecules themselves, they are susceptible to thermal fluctuations typical for one-dimensional superconductors and exhibit a nonzero resistance over a broad temperature range. We observed resistance oscillations in these two-nanowire structures that are different from the usual Little-Parks oscillations. Here, we provide a quantitative explanation for the observed quantum interference phenomenon, which takes into account strong phase gradients created in the leads by the applied magnetic field.