There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite wi...There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.展开更多
For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） e...For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.展开更多
The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin-...The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.展开更多
For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior ...For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior can appear only when the number of agents in the model takes a finite value.Those changes of behavior can be related to the apparent phase transitions that appear in some physical models.We show examples in the Galam's model of opinion transmission and the Axelrod's model of culture formation stressing the role that the network of interactions has on the main results of both models.Finally,we present the phenomenon of system-size stochastic resonance by which a forcing signal(identified as an advertising agent)is optimally amplified by a population of the right(intermediate)size.Our work stresses the role that the system size has in the dynamics of social systems and the inappropriateness of taking the thermodynamic limit for these systems.展开更多
Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of th...Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.展开更多
With the device size gradually approaching the physical limit, the small changes of the Si(001)/SiO 2 interface in silicon-based devices may have a great impact on the device characteristics. Based on this, the bridge...With the device size gradually approaching the physical limit, the small changes of the Si(001)/SiO 2 interface in silicon-based devices may have a great impact on the device characteristics. Based on this, the bridge-oxygen model is used to construct the interface of different sizes, and the finite size effect of the interface between fine electronic structure silicon and silicon dioxide is studied. Then, the influence of the finite size effect on the electrical properties of nanotransistors is calculated by using the first principle. Theoretical calculation results demonstrate that the bond length of Si-Si and Si-O shows a saturate tendency when the size increases, while the absorption capacity of visible light and the barrier of the interface increase with the decrease of size. Finally, the results of two tunneling current models show that the finite size effect of Si(001)/SiO 2 interface can lead to a larger change in the gate leakage current of nano-scale devices, and the transition region and image potential, which play an important role in the calculation of interface characteristics of large-scale devices, show different sensitivities to the finite size effect. Therefore, the finite size effect of the interface on the gate leakage current cannot be ignored in nano-scale devices.展开更多
The gas-liquid phase coexistence in a two-dimensional Lennard-Jones system is investigated using Maxwell construction method together with molecular dynamics simulations.The results of phase coexistence in different t...The gas-liquid phase coexistence in a two-dimensional Lennard-Jones system is investigated using Maxwell construction method together with molecular dynamics simulations.The results of phase coexistence in different truncations of the potential are compared with data obtained from the literature,and the corresponding critical properties calculated.The crossover from Ising-like to mean field behavior is observed and confirmed as the temperature approaches the critical point from below.Performing simulations on systems with different sizes,we find that a finite size effect is more significant than those shown in most of the previous results,and a lower critical temperature is obtained when the full extent of this finite size effect is considered.展开更多
Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the cha...Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the channel walls, minimal incorporation of these interaction factors in the models to describe the flow phenomena accurately has been done. In this paper, we aim at formulating a modified PNP equation which constitutes finite size effects to capture ions interactions in the channel using Lennard Jonnes (LJ) potential theory. Particularly, the study examines existence and uniqueness of the approximate analytical solutions of the mPNP equations, First, by obtaining the priori energy estimate and providing solution bounds, and finally constructing the approximate solutions and establishing its convergence in a finite dimensional subspace in <em>L</em><sup>2</sup>, the approximate solution of the linearized mPNP equations was found to converge to the analytical solution, hence proof of existence.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in Universities,China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20134208110001)
文摘There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in University of the Ministry of Education of China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of the Higher Education of China(Grant No.20134208110001)
文摘For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in University of the Ministry of Education of China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20134208110001)
文摘The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.
基金support from MCyT(Spain)and FEDER(EU)through projects FIS2004-5073 and FIS2004-953.
文摘For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior can appear only when the number of agents in the model takes a finite value.Those changes of behavior can be related to the apparent phase transitions that appear in some physical models.We show examples in the Galam's model of opinion transmission and the Axelrod's model of culture formation stressing the role that the network of interactions has on the main results of both models.Finally,we present the phenomenon of system-size stochastic resonance by which a forcing signal(identified as an advertising agent)is optimally amplified by a population of the right(intermediate)size.Our work stresses the role that the system size has in the dynamics of social systems and the inappropriateness of taking the thermodynamic limit for these systems.
基金National Natural Science Foundation of China and the China Academy of Engineering Physics under Grant No.10676025(NSAF)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Ministry of Education
文摘Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.
基金The National Natural Science Foundation of China(No.61774014)Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYZZ15_0331)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.19KJB510060)
文摘With the device size gradually approaching the physical limit, the small changes of the Si(001)/SiO 2 interface in silicon-based devices may have a great impact on the device characteristics. Based on this, the bridge-oxygen model is used to construct the interface of different sizes, and the finite size effect of the interface between fine electronic structure silicon and silicon dioxide is studied. Then, the influence of the finite size effect on the electrical properties of nanotransistors is calculated by using the first principle. Theoretical calculation results demonstrate that the bond length of Si-Si and Si-O shows a saturate tendency when the size increases, while the absorption capacity of visible light and the barrier of the interface increase with the decrease of size. Finally, the results of two tunneling current models show that the finite size effect of Si(001)/SiO 2 interface can lead to a larger change in the gate leakage current of nano-scale devices, and the transition region and image potential, which play an important role in the calculation of interface characteristics of large-scale devices, show different sensitivities to the finite size effect. Therefore, the finite size effect of the interface on the gate leakage current cannot be ignored in nano-scale devices.
基金supported by the National Natural Science Foundation of China(20903112,10972217)the Knowledge Innovation Program of Chinese Academy of Sciences(KJCX2-YW-L08)
文摘The gas-liquid phase coexistence in a two-dimensional Lennard-Jones system is investigated using Maxwell construction method together with molecular dynamics simulations.The results of phase coexistence in different truncations of the potential are compared with data obtained from the literature,and the corresponding critical properties calculated.The crossover from Ising-like to mean field behavior is observed and confirmed as the temperature approaches the critical point from below.Performing simulations on systems with different sizes,we find that a finite size effect is more significant than those shown in most of the previous results,and a lower critical temperature is obtained when the full extent of this finite size effect is considered.
文摘Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the channel walls, minimal incorporation of these interaction factors in the models to describe the flow phenomena accurately has been done. In this paper, we aim at formulating a modified PNP equation which constitutes finite size effects to capture ions interactions in the channel using Lennard Jonnes (LJ) potential theory. Particularly, the study examines existence and uniqueness of the approximate analytical solutions of the mPNP equations, First, by obtaining the priori energy estimate and providing solution bounds, and finally constructing the approximate solutions and establishing its convergence in a finite dimensional subspace in <em>L</em><sup>2</sup>, the approximate solution of the linearized mPNP equations was found to converge to the analytical solution, hence proof of existence.
