Effect of long-range structural corrugations on magnetotransport properties of phosphorene in tilted magnetic field

Rippling is an inherent quality of two-dimensional materials playing an important role in determining their properties. Here, we study the effect of structural corrugations on the electronic and transport properties of monolayer black phosphorus (phosphorene) in the presence of tilted magnetic field. We follow a perturbative approach to obtain analytical corrections to the spectrum of Landau levels induced by a long-wavelength corrugation potential. We show that surface corrugations have a non-negligible effect on the electronic spectrum of phosphorene in tilted magnetic field. Particularly, the Landau levels are shown to exhibit deviations from the linear field dependence. The observed effect become especially pronounced at large tilt angles and corrugation amplitudes. Magnetotransport properties are further examined in the low temperature regime taking into account impurity scattering. We calculate magnetic field dependence of the longitudinal and Hall resistivities and find that the nonlinear effects reflecting the corrugation might be observed even in moderate fields (\mbox{$B<10$ T})

Spectral Analysis of Multi-dimensional Self-similar Markov Processes

In this paper we consider a discrete scale invariant (DSI) process $\{X(t), t\in {\bf R^+}\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\alpha^k, k\in {\bf W}$ where $\alpha$ is obtained by the equality $l=\alpha^T$ and ${\bf W}=\{0, 1,...\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\cdot)$ with parameter space $\{\alpha^k, k\in {\bf W}\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We assume that the process $\{X(t), t\in {\bf R^+}\}$ is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally we find the spectral density matrix of such DT-SIM process and show that its associated $T$-dimensional self-similar Markov process is fully specified by $\{R_{j}^H(1),R_{j}^H(0),j=0, 1,..., T-1\}$ where $R_j^H(\tau)$ is the covariance function of $j$th and $(j+\tau)$th observations of the process.Comment: 16 page