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M. Amini

Publications and source records attributed to M. Amini.

At least 19 recordsLinked to original sources
arXiv2024

Vacancy-Induced Topological Fano Resonance in Kane-Mele Nanoribbons: Design, Control, and Sensing Applications

The concept of topological Fano resonance, characterized by an ultrasharp asymmetric line shape, is a promising candidate for robust sensing applications due to its sensitivity to external parameters and immunity to structural disorder. In this study, the vacancy-induced topological Fano resonance in a nanoribbon made up of a hexagonal lattice with armchair sides is examined by introducing several on-site vacancies, which are deliberately created at regular distances, along a zigzag chain that stretches across the width of the ribbon. The presence of the on-site vacancies can create localized energy states within the electronic band structure, leading to the formation of an impurity band, which can result in Fano resonance phenomena by forming a conductivity channel between the edge modes on both armchair sides of the ribbon. Consequently, an ultracompact tunable on-chip integrated topological Fano resonance derived from the graphene-based nanomechanical phononic crystals is proposed. The Fano resonance arises from the interference between topologically protected even and odd edge modes at the interface between trivial and nontrivial insulators in a nanoribbon structure governed by the Kane-Mele model describing the quantum spin Hall effect in hexagonal lattices. The simulation of the topological Fano resonance is performed analytically using the Lippmann-Schwinger scattering formulation. One of the advantages of the present study is that the related calculations are carried out analytically, and in addition to the simplicity and directness, it reproduces the results obtained from the Landauer-B\"{u}ttiker formulation very well both quantitatively and qualitatively. The findings open up possibilities for the design of highly sensitive and accurate robust sensors for detecting extremely tiny forces, masses, and spatial positions.

cond-mat.mes-hall↗
arXiv2023

Tensor Network Representation and Entanglement Spreading in Many-Body Localized Systems: A Novel Approach

A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to diagonalize the Hamiltonian of the specified system. To construct the tensor network, we utilize the eigenstates of the subsystems Hamiltonian to attain the desired unitary transformations. Subsequently, we optimize the eigenstates and acquire appropriate unitary localized operators that will represent the LIOMs tensor network. The efficiency of the method was assessed and found to be both fast and almost accurate. In framework of the introduced tensor-network representation, we examine how the entanglement spreads along the considered many-body localized system and evaluate the outcomes of the approximations employed in this approach. The important and interesting result is that in the proposed tensor network approximation, if the length of the blocks is greater than the length of localization, then the entropy growth will be linear in terms of the logarithmic time. Also, it has been demonstrated that, the entanglement can be calculated by only considering two blocks next to each other, if the Hamiltonian has been diagonalized using the unitary transformation made by the provided tensor-network representation.

quant-ph↗
arXiv2022

Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?

The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin-$\frac12$ Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like.

cond-mat.dis-nn↗
arXiv2022

Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction

Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such macroscopically LIOMs, we explore and study some of their structural properties across the MBL transition. We first, consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a non-perturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert-space. Our cluster size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert-space. By performing finite-size scaling, we compare the critical disorder and correlation exponent $\nu$ both in the presence and absence of interaction. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition.

cond-mat.dis-nn↗
arXiv2022

Enhanced thermoelectric efficiency of zigzag bilayer phosphorene nanoribbon; edge states engineering

We theoretically investigate the thermoelectric properties of zigzag bilayer phosphorene nanoribbons (ZBPNR). We first, draw an analogy between the extended Su-Schrieffer-Heeger (SSH) ladder and ZBPNR edge states and obtain their corresponding band structure and wave functions analytically. Then, by applying the energy filtering method, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by applying periodic point potentials at the boundaries.

cond-mat.mes-hall↗
arXiv2021

Thermoelectric properties of armchair phosphorene nanoribbons in the presence of vacancy-induced impurity band

Armchair phosphorene nanoribbons (APNRs) are known to be semiconductors with an indirect bandgap. Here, we propose to introduce new states in the gap of APNRs by creating a periodic structure of vacancies (antidots). Based on the tight-binding model, we show that a periodic array of vacancies or nanopores leads to the formation of an impurity band inside the gap region. We first present an analytical expression for the dispersion relation of an impurity band induced by hybridization of bound states associated with each single vacancy defect. Then, we increase the size of vacancy defects to include a bunch of atoms and theoretically investigate the effect of nanopores size and their spacing on electronic band structure, carrier transmission function, and thermoelectric properties. Our analysis of the power generation rate and thermoelectric efficiency of these structures reveals that an ANPR can be used as a superb thermoelectric power generation module.

cond-mat.mes-hall↗
arXiv2020

Marshall-Olkin exponential shock model covering all range of dependence

In this paper, we present a new Marshall-Olkin exponential shock model. The new construction method gives the proposed model further ability to allocate the common joint shock on each of the components, making it suitable for application in fields like reliability and credit risk. The given model has a singular part and supports both positive and negative dependence structure. Main dependence properties of the model is given and an analysis of stress-strength is presented. After a performance analysis on the estimator of parameters, a real data is studied. Finally, we give the multivariate version of the proposed model and its main properties.

stat.ME↗
arXiv2020

A General Class of Weighted Rank Correlation Measures

In this paper we propose a class of weighted rank correlation coefficients extending the Spearman's rho. The proposed class constructed by giving suitable weights to the distance between two sets of ranks to place more emphasis on items having low rankings than those have high rankings or vice versa. The asymptotic distribution of the proposed measures and properties of the parameters estimated by them are studied through the associated copula. A simulation study is performed to compare the performance of the proposed statistics for testing independence using asymptotic relative efficiency calculations.

math.ST↗
arXiv2019

Two-spin entanglement induced by scattering of backscattering-free chiral electrons in a chern insulator

The existence of robust chiral edge states in a finite topologically nontrivial chern insulator is a consequence of the bulk-boundary correspondence. In this paper, we present a theoretical framework based on lattice Green's function to study the scattering of such chiral edge electrons by a single localized impurity. To this end, in the first step, we consider the standard topological Haldane model on a honeycomb lattice with strip geometry. We obtain analytical expressions for the wave functions and their corresponding energy dispersion of the low-energy chiral states localized at the edge of the ribbon. Then, we employ the $T$-matrix Lippmann-Schwinger approach to explicitly show the robustness of chiral edge states against the impurity scattering. This backscattering-free process has an interesting property that the transmitted wave function acquires an additional phase factor. Although this additional phase factor does not affect quantum transport through the chiral channel it can carry quantum information. As an example of such quantum information transport, we investigate the entanglement of two magnetic impurities in a chern insulator through the dissipation-less scattering of chiral electrons.

cond-mat.mes-hall↗
arXiv2019

Gorenstein $\pi[T]$-projectivity with respect to a tilting module

Let $T$ be a tilting module. In this paper, Gorenstein $\pi[T]$-projective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein $\pi[T]$-projective are given. For instance, on the $T$-cocoherent rings, it is proved that the Gorenstein $\pi[T]$-projectivity of all $R$-modules is equivalent to the $\pi[T]$-projectivity of $\sigma[T]$-injective as a module.

math.AC↗
arXiv2018

Vacancy-induced Fano resonances in zigzag phosphorene nanoribbons

Motivated by recent scanning tunneling microscopy/spectroscopy experiments on probing single vacancies in black phosphorus, we present a theory for Fano antiresonances induced by coupling between vacancy states and edge states of zigzag phosphorene nanoribbons (zPNRs). To this end, in the first step, using the tight-binding Hamiltonian, we obtain an analytic solution on the lattice for the state associated to a single vacancy located in the bulk phosphorene which shows a highly anisotropic localization in real space. For a finite zigzag ribbon, in the absence of particle-hole symmetry, the localized state induced by vacancies can couple to the wave functions of the edge states which results in the formation of a new bound state. The energy of vacancy bound state lies inside the quasi-flat band composed of edge states when the vacancy locates sufficiently far away from the edge. Then, we employ the T-matrix Lippmann-Schwinger approach to obtain an explicit analytical expression for the scattering amplitude of the edge electrons of a zPNR by the presence of a single vacancy which shows a Fano resonance profile with a tunable dip. We demonstrate that varying the position of the vacancy produces substantially different effects on the resonance width, resonance energy position, and the asymmetry parameter of Fano line shape. Furthermore, the validity of the theoretical descriptions is verified numerically by using the Landauer approach.

cond-mat.mes-hall↗
arXiv2018

Tunable transmission due to defects in zigzag phosphorene nanoribbons

Transport of the edge-state electrons along zigzag phosphorene nanoribbons in presence of two impurities/vacancies is analytically investigated. Considering the places of the defects, a number of different situations are examined. When both defects are placed on the edge zigzag chain, as is expected, with changing the energy of the traveling electrons the electrical conductance exhibits a resonance behavior. In this case, for two vacancies the observed resonant peaks become extremely sharp. An amazing behavior is seen when the second vacancy is located along an armchair chain while the first is placed at the intersection of the edge zigzag and this armchair chains. In this case, in a considerable range of energy, the conductance is strongly strengthened. In fact the presence of the second vacancy create a shielded region around the first vacancy, consequently, the traveling wave bypasses this region and enhances the conductivity. The analytical results are compared with numerical simulations showing a very good agreement.

cond-mat.mtrl-sci↗
arXiv2018

Two-impurity-entanglement generation by electron scattering in zigzag phosphorene nanoribbons

In this paper, we investigate how two on-side doped impurities with net magnetic moments in an edge chain of a zigzag phosphorene nanoribbon~(zPNR) can be entangled by scattering of the traveling edge-state electrons. To this end, in the first step, we employ the Lippmann-Schwinger equation as well as the Green's function approach to study the scattering of the free traveling electrons from two magnetic impurities in a one-dimensional tight-binding chain. Then, following the same formalism, that is shown that the behavior of two on-side spin impurities in the edge chain of a zPNR in responding to the scattering of the edge-state traveling electrons is very similar to what happens for the one-dimensional chain. In both cases, considering a known incoming wave state, the reflected and transmitted parts of the final wave state are evaluated analytically. Using the obtained results, the related partial density matrices and the reflection and transmission probabilities are computable. Negativity as a measure of the produced entanglement in the final state is calculated and the results are discussed. Our theoretical model actually proposes a method, which is perhaps experimentally performable to create the entanglement in the state of the impurities.

quant-ph↗
arXiv2018

Quantum transport through the edge states of Zigzag phosphorene nanoribbons in presence of a single point defect: analytic Green's function method

Zigzag phosphorene nanoribbons have quasi-flat band edge modes entirely detached from the bulk states. We analytically study the electronic transport through such edge states in the presence of a localized defect for semi-infinite and finite ribbons. Using the tight-binding model, we derive analytical expressions for the Green's function and transmission amplitude of both pristine and defective nanoribbons. We find that the transmission of both semi-infinite and finite ribbons is sensitive to the location of a single impurity defect with respect to the edge. By the presence of an impurity on the outermost edge site of the ribbon, the transmission through the edge channel, similar to a one-dimensional chain, strongly suppresses for the entire energy spectrum of the quasi-flat band. In contrast, the transmission of low-energy $(E\approx 0)$ states, is robust as the impurity is moved one position far away from the edge on the same sub-lattice. The analytical calculations are also complemented by exact numerical transport computations using the Landauer approach.

cond-mat.dis-nn↗
arXiv2018

Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probability of finding the initial state after time $t$. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of $R(t)$ with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of $R(t\to\infty)=k$, finite in the thermodynamic limit $N\rightarrow\infty$, which approaches $k=R(t\to 0)$ in this limit.

cond-mat.dis-nn↗
arXiv2016

Casimir torque between two inhomogeneous semi-transparent concentric cylinders

Motivated by the problem of Casimir energy, we investigate the idea of using inhomogeneity of surfaces instead of their corrugation, which leads to Casimir interaction between two inhomogeneous semi-transparent concentric cylinders. Using the multiple scattering method, we study the Casimir energy and torque between the cylinders with different potentials subjected to Dirichlet boundary conditions, both in weak and strong coupling regimes. We also extend our formalism to the case of two inhomogeneous dielectrics in a weak coupling regime.

cond-mat.other↗