Screening, Friedel oscillations and low-temperature conductivity in topological insulator thin films

In thin topological insulator films, the top and bottom surfaces are coupled by tunneling, which restores backscattering and strongly affects screening. We calculate the dielectric function in the random phase approximation obtaining a closed-form result. Unlike independent TI surfaces, the dielectric function of thin films exhibits a valley as a function of wavenumber $q$ and tunneling, as well as a cusp at $q=2k_F$, with $k_F$ the Fermi wave vector. As a result of the cusp, Friedel oscillations decay with distance $r$ as $\sin(2k_Fr)/(2k_Fr)^2$. We determine the longitudinal conductivity $\sigma$ in the first Born approximation at low temperatures where screened impurities provide the dominant scattering mechanism. At high electron densities $n_e$, $\sigma \propto n_e$, while at low densities $\sigma \propto n_e^{3/2}$

Coulomb drag in topological insulator films

We study Coulomb drag between the top and bottom surfaces of topological insulator films. We derive a kinetic equation for the thin-film spin density matrix containing the full spin structure of the two-layer system, and analyze the electron-electron interaction in detail in order to recover all terms responsible for Coulomb drag. Focusing on typical topological insulator systems, with film thicknesses d up to 6 nm, we obtain numerical and approximate analytical results for the drag resistivity $\rho_\text{D}$ and find that $\rho_\text{D}$ is proportional to $T^2d^{-4}n^{-3/2}_{\text{a}}n^{-3/2}_{\text{p}}$ at low temperature T and low electron density $n_{\text{a,p}}$, with a denoting the active layer and p the passive layer. In addition, we compare $\rho_{\text{D}}$ with graphene, identifying qualitative and quantitative differences, and we discuss the multi valley case, ultra thin films and electron-hole layers

Average Transition Conditions for Electromagnetic Fields at a Metascreen of Nonzero Thickness

Using a dipole interaction model, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen consisting of an array of arbitrarily shaped apertures in a perfectly conducting screen of nonzero thickness. The simple analytical formulas obtained are validated through comparison with full-wave numerical simulations.Comment: 8 pages, 8 figure

Photon Fluence and Dose Estimation in Computed Tomography using a Discrete Ordinates Boltzmann Solver

In this study, cone-beam single projection and axial CT scans are modeled with a software package - DOCTORS, which solves the linear Boltzmann equation using the discrete ordinates method. Phantoms include a uniform 35 cm diameter water cylinder and a non-uniform abdomen phantom. Series simulations were performed with different simulation parameters, including the number of quadrature angles, the order of Legendre polynomial expansions, and coarse and fine mesh grid. Monte Carlo simulations were also performed to benchmark DOCTORS simulations. A quantitative comparison was made between the simulation results obtained using DOCTORS and Monte Carlo methods. The deterministic simulation was in good agreement with the Monte Carlo simulation on dose estimation, with a root-mean-square-deviation (RMSD) difference of around 2.87 percent. It was found that the contribution of uncollided photon fluence directly from the source dominates the local absorbed dose in the diagnostic X-ray energy range. The uncollided photon fluence can be calculated accurately using a ray-tracing algorithm. The accuracy of collided photon fluence estimation is largely affected by the pre-calculated multigroup cross-sections. The primary benefit of DOCTORS lies in its rapid computation speed. Using DOCTORS, parallel computing using GPU enables the cone-beam CT dose estimation nearly in real-time

The Instanton-Dyon Liquid Model V: Twisted Light Quarks

We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with equal number of colors $N_c$ and flavors $N_f$. We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2, 3$. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry but supports finite and unequal quark condensates.Comment: 12 pages, 2 figure

The Instanton-Dyon Liquid Model III: Finite Chemical Potential

We discuss an extension of the instanton-dyon liquid model that includes light quarks at finite chemical potential in the center symmetric phase. We develop the model in details for the case of SU_c(2)\times SU_f(2) by mapping the theory on a 3-dimensional quantum effective theory. We analyze the different phases in the mean-field approximation. We extend this analysis to the general case of SU_c(N_c)\times SU_f(N_f) and note that the chiral and diquark pairings are always comparable.Comment: 10 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1503.0914

Dense Instanton-Dyon Liquid Model: Diagrammatics

We revisit the instanton-dyon liquid model in the confined phase by using a non-linear Debye-Huckel (DH) resummation for the Coulomb interactions induced by the moduli, followed by a cluster expansion. The organization is shown to rapidly converge and yields center symmetry at high density. The dependence of these results on a finite vacuum angle are also discussed. We also formulate the hypernetted chain (HCN) resummation for the dense instanton-dyon liquid and use it to estimate the liquid pair correlation functions in the DH limit. At very low temperature, the dense limit interpolates between chains and rings of instanton-anti-instanton-dyons and a bcc crystal, with strong topological and magnetic correlations.Comment: 12 pages, 9 figure

Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV

We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\times Z_{4N_f}\rightarrow O(N_f)$. As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.Comment: 22 pages, 6 figure

Light Quarks in the Screened Dyon-Anti-Dyon Coulomb Liquid Model II

We discuss an extension of the dyon-anti-dyon liquid model that includes light quarks in the dense center symmetric Coulomb phase. In this work, like in our previous one, we use the simplest color SU(2) group. We start with a single fermion flavor $N_f=1$ and explicitly map the theory onto a 3-dimensional quantum effective theory with a fermion that is only U$_V(1)$ symmetric. We use it to show that the dense center symmetric plasma develops, in the mean field approximation, a nonzero chiral condensate, although the ensuing Goldstone mode is massive due to the U$_A(1)$ axial-anomaly. We estimate the chiral condensate and $\sigma,\eta$ meson masses for $N_f=1$. We then extend our analysis to several flavors $N_f>1$ and colors $N_c>2$ and show that center symmetry and spontaneous chiral symmetry breaking disappear simultaneously when $x=N_f/N_c\geq 2$ in the dense plasma phase. A reorganization of the dense plasma phase into a gas of dyon-antidyon molecules restores chiral symmetry, but may preserve center symmetry in the linearized approximation. We estimate the corresponding critical temperature.Comment: 16 pages, 5 figure

On the calculation of diffusion coefficients in confined fluids and interfaces with an application to the liquid-vapor interface of water

We propose a general methodology for calculating the self-diffusion tensor from molecular dynamics for a liquid with a liquid-gas or liquid-solid interface. The standard method used in bulk fluids, based on computing the mean square displacement as a function of time and extracting the asymptotic linear time dependence from this, is not valid for systems with interfaces or for confined fluids. The method proposed here is based on imposing virtual boundary conditions on the molecular system and computing survival probabilities and specified time correlation functions in different layers of the fluid up to and including the interfacial layer. By running dual simulations, one based on MD and the other based on Langevin dynamics, using the same boundary conditions, one can fit the Langevin survival probability at long times to the MD computed survival probability, thereby determining the diffusion coefficient as a function of distance of the layers from the interface. We compute the elements of the diffusion tensor of water as a function of distance from the liquid vapor interface of water. Far from the interface the diffusion tensor is found to be isotropic, as expected, and the diffusion coefficient has the value $D\approx$ .22\AA$^2$/psec in agreement with what is found in the bulk liquid. In the interfacial region the diffusion tensor is axially anisotropic, with values of $D_{\parallel}\approx$. 8\AA$^2$/psec and $D_{\perp}\approx$. 5\AA$^2$/psec for the components parallel and normal the interface surface respectively. We also show that diffusion in confined geometries can be calculated by imposing appropriate boundary conditions on the molecular system and computing time correlation functions of the eigenfunctions of the diffusion operator corresponding to the same boundary conditions