Stiffening thermal membranes by cutting

Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon.Comment: 7 page

The quantum phase transition of itinerant helimagnets

We investigate the quantum phase transition of itinerant electrons from a paramagnet to a state which displays long-period helical structures due to a Dzyaloshinskii instability of the ferromagnetic state. In particular, we study how the self-generated effective long-range interaction recently identified in itinerant quantum ferromagnets is cut-off by the helical ordering. We find that for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum phase transition is of second order with mean-field exponents. In contrast, for a weak Dzyaloshinskii instability the transition is analogous to that in itinerant quantum ferromagnets, i.e. it is of first order, as has been observed in MnSi.Comment: 5 pages RevTe

Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

Non-Hookean statistical mechanics of clamped graphene ribbons

Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: large distance elastic parameters are in fact not constant, but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions $W\times L$ (with $L\geq W$), the macroscopic bending rigidity $\kappa_R$ determined from cantilever deformations is independent of the width when $W<\ell_\textrm{th}$, where $\ell_\textrm{th}$ is a thermal length scale, as expected. When $W>\ell_\textrm{th}$, however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on $W$. When the ribbon length $L > \ell_p$, where $\ell_p$ is the $W$-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior

Order parameter symmetry and mode coupling effects at dirty superconducting quantum phase transitions

We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions.Comment: final version as publishe

Anisotropic London Penetration Depth and Superfluid Density in Single Crystals of Iron-based Pnictide Superconductors

In- and out-of-plane magnetic penetration depths were measured in three iron-based pnictide superconducting systems. All studied samples of both 122 systems show a robust power-law behavior, $\lambda (T) T^n$, with the sample-dependent exponent n=2-2.5, which is indicative of unconventional pairing. This scenario could be possible either through scattering in a $s_{\pm }$ state or due to nodes in the superconducting gap. In the Nd-1111 system, the interpretation of data may be obscured by the magnetism of rare-earth ions. The overall anisotropy of the pnictide superconductors is small. The 1111 system is about two times more anisotropic than the 122 system. Our data and analysis suggest that the iron-based pnictides are complex superconductors in which a multiband three-dimensional electronic structure and strong magnetic fluctuations play important roles.Comment: submitted to a special issue of Physica C on superconducting pnictide

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe

Near-degeneracy of several pairing channels in multiorbital models for the Fe-pnictides

Weak-coupling approaches to the pairing problem in the iron pnictide superconductors have predicted a wide variety of superconducting ground states. We argue here that this is due both to the inadequacy of certain approximations to the effective low-energy band structure, and to the natural near-degeneracy of different pairing channels in superconductors with many distinct Fermi surface sheets. In particular, we review attempts to construct two-orbital effective band models, the argument for their fundamental inconsistency with the symmetry of these materials, and the comparison of the dynamical susceptibilities in two- and five-orbital models. We then present results for the magnetic properties, pairing interactions, and pairing instabilities within a five-orbital Random Phase Approximation model. We discuss the robustness of these results for different dopings, interaction strengths, and variations in band structure. Within the parameter space explored, an anisotropic, sign-changing s-wave state and a d_x2-y2 state are nearly degenerate, due to the near nesting of Fermi surface sheets.Comment: 17 pages, 23 figure