Flat polymerized membranes at three-loop order

In this conference report, we present a recent field theoretic renormalization group analysis of flat polymerized membranes at three-loop order by the present authors [Phys. Rev. E 105, L012603 (2022)].Comment: (v1) 5 page

The flat phase of polymerized membranes at two-loop order

We investigate two complementary field-theoretical models describing the flat phase of polymerized - phantom - membranes by means of a two-loop, weak-coupling, perturbative approach performed near the upper critical dimension $D_{uc}=4$, extending the one-loop computation of Aronovitz and Lubensky [Phys. Rev. Lett. 60, 2634 (1988)]. We derive the renormalization group equations within the modified minimal substraction scheme, then analyze the corrections coming from two-loop with a particular attention paid to the anomalous dimension and the asymptotic infrared properties of the renormalization group flow. We finally compare our results to those provided by nonperturbative techniques used to investigate these two models.Comment: 9 pages, 1 figure, published versio

Electrostatics of ions inside the nanopores and trans-membrane channels

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels

RPAE versus RPA for the Tomonaga model with quadratic energy dispersion

Recently the damping of the collective charge (and spin) modes of interacting fermions in one spatial dimension was studied. It results from the nonlinear correction to the energy dispersion in the vicinity of the Fermi points. To investigate the damping one has to replace the random phase approximation (RPA) bare bubble by a sum of more complicated diagrams. It is shown here that a better starting point than the bare RPA is to use the (conserving) linearized time dependent Hartree-Fock equations, i.e. to perform a random phase approximation (with) exchange (RPAE) calculation. It is shown that the RPAE equation can be solved analytically for the special form of the two-body interaction often used in the Luttinger liquid framework. While (bare) RPA and RPAE agree for the case of a strictly linear disperson there are qualitative differences for the case of the usual nonrelativistic quadratic dispersion.Comment: 6 pages, 3 figures, misprints corrected; to appear in PRB7

Dehydration and ionic conductance quantization in nanopores

There has been tremendous experimental progress in the last decade in identifying the structure and function of biological pores (ion channels) and fabricating synthetic pores. Despite this progress, many questions still remain about the mechanisms and universal features of ionic transport in these systems. In this paper, we examine the use of nanopores to probe ion transport and to construct functional nanoscale devices. Specifically, we focus on the newly predicted phenomenon of quantized ionic conductance in nanopores as a function of the effective pore radius - a prediction that yields a particularly transparent way to probe the contribution of dehydration to ionic transport. We study the role of ionic species in the formation of hydration layers inside and outside of pores. We find that the ion type plays only a minor role in the radial positions of the predicted steps in the ion conductance. However, ions with higher valency form stronger hydration shells, and thus, provide even more pronounced, and therefore, more easily detected, drops in the ionic current. Measuring this phenomenon directly, or from the resulting noise, with synthetic nanopores would provide evidence of the deviation from macroscopic (continuum) dielectric behavior due to microscopic features at the nanoscale and may shed light on the behavior of ions in more complex biological channels.Comment: 13 pages, 10 figure

Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction

We study dc-transport and magnetization dynamics in a junction of arbitrary transparency consisting of two spin-singlet superconducting leads connected via a single classical spin precessing at the frequency $\Omega$. The presence of the spin in the junction provides different transmission amplitudes for spin-up and spin-down quasiparticles as well as a time-dependent spin-flip transmission term. For a phase biased junction, we show that a steady-state superconducting charge current flows through the junction and that an out-of-equilibrium circularly polarized spin current, of frequency $\Omega$, is emitted in the leads. Detailed understanding of the charge and spin currents is obtained in the entire parameter range. In the adiabatic regime, $\hbar \Omega \ll 2\Delta$ where $\Delta$ is the superconducting gap, and for high transparencies of the junction, a strong suppression of the current takes place around \vp \approx 0 due to an abrupt change in the occupation of the Andreev bound-states. At higher values of the phase and/or precession frequency, extended (quasi-particle like) states compete with the bound-states in order to carry the current. Well below the superconducting transition, these results are shown to be weakly affected by the back-action of the spin current on the dynamics of the precessing spin. Indeed, we show that the Gilbert damping due to the quasi-particle spin current is strongly suppressed at low-temperatures, which goes along with a shift of the precession frequency due to the condensate. The results obtained may be of interest for on-going experiments in the field of molecular spintronics.Comment: 19 pages, 13 figures (v3) Minor modifications per referee's comments. No change in results. (v2) 2 authors added, 1 reference added (Ref. 25), no change in the text and result

Non-equilibrium effects in a Josephson junction coupled to a precessing spin

We present a theoretical study of a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin. When an external magnetic field is applied, the classical spin will precess with the Larmor frequency. This magnetically active interface results in a time-dependent boundary condition with different tunneling amplitudes for spin-up and spin-down quasiparticles and where the precession produces spin-flip scattering processes. We show that as a result, the Andreev states develop sidebands and a non-equilibrium population which depend on the precession frequency and the angle between the classical spin and the external magnetic field. The Andreev states lead to a steady-state Josephson current whose current-phase relation could be used for characterizing the precessing spin. In addition to the charge transport, a magnetization current is also generated.This spin current is time-dependent and its polarization axis rotates with the same precession frequency as the classical spin.Comment: 20 pages, 26 figure

Variable-range hopping in quasi-one-dimensional electron crystals

We study the effect of impurities on the ground state and the low-temperature dc transport in a 1D chain and quasi-1D systems of many parallel chains. We assume that strong interactions impose a short-range periodicicity of the electron positions. The long-range order of such an electron crystal (or equivalently, a $4 k_F$ charge-density wave) is destroyed by impurities. The 3D array of chains behaves differently at large and at small impurity concentrations $N$. At large $N$, impurities divide the chains into metallic rods. The low-temperature conductivity is due to the variable-range hopping of electrons between the rods. It obeys the Efros-Shklovskii (ES) law and increases exponentially as $N$ decreases. When $N$ is small, the metallic-rod picture of the ground state survives only in the form of rare clusters of atypically short rods. They are the source of low-energy charge excitations. In the bulk the charge excitations are gapped and the electron crystal is pinned collectively. A strongly anisotropic screening of the Coulomb potential produces an unconventional linear in energy Coulomb gap and a new law of the variable-range hopping $-\ln\sigma \sim (T_1 / T)^{2/5}$. $T_1$ remains constant over a finite range of impurity concentrations. At smaller $N$ the 2/5-law is replaced by the Mott law, where the conductivity gets suppressed as $N$ goes down. Thus, the overall dependence of $\sigma$ on $N$ is nonmonotonic. In 1D, the granular-rod picture and the ES apply at all $N$. The conductivity decreases exponentially with $N$. Our theory provides a qualitative explanation for the transport in organic charge-density wave compounds.Comment: 20 pages, 7 figures. (v1) The abstract is abridged to 24 lines. For the full abstract, see the manuscript (v2) several changes in presentation per referee's comments. No change in result

On non-supersymmetric conformal manifolds: field theory and holography

We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from which one can extract restrictions on the spectrum of low spin operators and on the behavior of OPE coefficients involving nearly marginal operators. We then consider conformal field theories admitting a gravity dual description, and as such a large-$N$ expansion. We discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for conformal manifolds beyond the planar limit. Our results do not rely on supersymmetry, and therefore apply also outside the realm of superconformal field theories