Anderson Disorder Research Articles

Non-linear optical response in disordered 2D materials

Using KITE [1], a quantum transport software developed by ourselves, we explore the effect of disorder in the second-order con¬ductivity, aiming to reproduce mesoscopic samples under more realistic models of disorder. This work will be concerned about our most recent results with KITE. We will showcase and examine how different mod¬els of disorder affect the same system, experimenting with Anderson disorder and vacancies in gapped Graphene.

Topological Anderson insulator in electric circuits

Although topological Anderson insulator has been predicted in 2009, the lasting investigations of this disorder established nontrivial state results in only two experimental observations in cold atoms [Science, {\bf 362 },929 (2018)] and in photonic crystals [Nature, {\bf 560}, 461 (2018)] recently. In this paper, we study the topological Anderson transition in electric circuits. By arranging capacitor and inductor network, we construct a disordered Haldane model. Specially, the disorder is introduced by the grounding inductors with random inductance. Based on non-commutative geometry method and transport calculation, we confirm that the disorder in circuits can drive a transition from normal insulator to topological Anderson insulator. We also find the random inductance induced disorder possessing unique characters rather than Anderson disorder, therefore it leads to distinguishable features of topological Anderson transition in circuits. Different from other systems, the topological Anderson insulator in circuits can be detected by measuring the corresponding quantized transmission coefficient and edge state wavefunction due to mature microelectronic technology.

Topological Anderson insulator phase in a quasicrystal lattice

Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index.

Frequency-dependent transport properties in disordered systems: A generalized coherent potential approximation approach

To predict transport properties of disordered systems, especially ac transport properties, one has to calculate the disorder average of the correlation of the multiple Green's function at different energies. To avoid brute force calculation, diagrammatic perturbation expansion must be used along with the coherent potential approximation (CPA). In this paper, we develop a theoretical formalism based on the nonequilibrium Green's function that maps the average of the correlation of the multiple Green's function into an average over a single generalized Green's function. After the mapping, this formalism is structurally very similar to the CPA and completely eliminates the need to perform diagrammatic expansion. As a demonstration of our theory, the dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias in the presence of Anderson disorder are calculated by directly taking the disorder average of the generating function of full counting statistics (FCS) within the CPA. Our numerical results on dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias show remarkable agreement with that obtained by the brute force calculation. The phase diagram in the frequency versus disorder strength plane has been efficiently calculated using the generalized FCS-CPA method.

First-principles calculation of spin-orbit torque in a Co/Pt bilayer

The angular dependence of spin-orbit torque in a disordered Co/Pt bilayer is calculated using a first-principles nonequilibrium Green's function formalism with an explicit supercell averaging over Anderson disorder. In addition to the usual dampinglike and fieldlike terms, the odd torque contains a sizable planar Hall-like term $(\mathbf{m}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{E})\mathbf{m}\ifmmode\times\else\texttimes\fi{}(\mathbf{z}\ifmmode\times\else\texttimes\fi{}\mathbf{m})$ whose contribution to current-induced damping is consistent with experimental observations. The dampinglike and planar Hall-like torquances depend weakly on disorder strength, while the fieldlike torquance declines with increasing disorder. The torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, but the fieldlike torque does not require it.

Localization Properties of Zig‐Zag Edge States in Disordered Phosphorene

Herein, the spectral and transport properties in the finite phosphorene lattice are investigated using the tight‐binding model in the presence of Anderson disorder potential. The focus is on the zig‐zag edge states localization, provided by the numerically calculated inverse participation number. At low disorder, the zig‐zag states undergo a localization process, keeping their 1D character, while further increasing the disorder leads to delocalization due to hybridization with the extended 2D states. The disorder‐induced changes in the electronic conductance, from one zig‐zag edge to the other, are also discussed.

Perfect valley filter based on a topological phase in a disordered Sb monolayer heterostructure

The hydrogenated $\rm{Sb}$ monolayer epitaxially grown on a $\rm{LaFeO_3}$ substrate is a novel type of two-dimensional material hosting quantum spin-quantum anomalous Hall (QS-QAH) states. For a device formed by $\rm{Sb}$ monolayer ribbon, the QAH edge states, belong to a single valley, are located at opposite edges of the ribbon. The QSH edge states, on the other hand, belong to the other valley and are distributed in a very narrow region at the same edge. In this paper, we find such material can be used to fabricate perfect valley filter. Adopting scattering matrix method and Green's function method, the valley resolved transport and spatial distribution of local current are calculated, in the present of Anderson disorder, edge defects and edge deformations. The numerical results demonstrate that, in the presence of above three types of disorder with moderate strength, the carriers can flow disspationless with nearly perfect valley polarization. Moreover, when the device becomes longer, the transport current does not decrease while the valley filter works even better. The origin is that the disorder can destroy the QSH edge states, but the valley-polarized QAH edge states can well hold.

Disordered Potential Landscapes for Anomalous Delocalization and Superdiffusion of Light

The prominent distinction between order and disorder in optics has been understood in terms of the spatial spreading of waves. In the Anderson picture of optical disorder, light localization has been elucidated by the interference of multiple scatterings from disorders, thus implying a natural correspondence between the localization and disordered potentials. Here, we focus on the disorder of a wave itself to achieve a new class of disordered optical potentials with continuous landscapes, distinguished from conventional Anderson disorder or abnormal disorders in discrete systems. Starting from the disordered but extended ground state for the Schrodinger-like wave equation, we inversely develop the landscape of an optical potential, the disorder pattern of which is similar to Brownian random-walk motion. We then demonstrate that the modes in such a structure can extend over an anomalously large region of space, and also exhibit superdiffusive wave transport. Such behaviors are in contrast to the wavelength...

Disorder-induced topological phase transitions on Lieb lattices

Motivated by the very recent experimental realization of electronic Lieb lattices and research interest on topological states of matter, we study the topological phase transitions driven by Anderson disorder on spin-orbit coupled Lieb lattices in the presence of spin-independent and dependent potentials. By combining the numerical transport and self-consistent Born approximation methods, we found that both time-reversal invariant and broken Lieb lattices can host disorder-induced gapful topological phases, including the quantum spin Hall insulator (QSHI) and quantum anomalous Hall insulator (QAHI) phases. For the time-reversal invariant case, this disorder can induce a topological phase transition directly from normal insulator (NI) to the QSHI. While for the time-reversal broken case, the disorder can induce either a QAHI-QSHI phase transition or a NI-QAHI-QSHI phase transition. Remarkably, the time-reversal broken QSHI phase can be induced by Anderson disorder on the spin-orbit coupled Lieb lattices without time-reversal symmetry.

Spin-dependent Seebeck effects in a graphene superlattice p–n junction with different shapes

We theoretically calculate the spin-dependent transmission probability and spin Seebeck coefficient for a zigzag-edge graphene nanoribbon p–n junction with periodically attached stubs under a perpendicular magnetic field and a ferromagnetic insulator. By using the nonequilibrium Green’s function method combining with the tight-binding Hamiltonian, it is demonstrated that the spin-dependent transmission probability and spin Seebeck coefficient for two types of superlattices can be modulated by the potential drop, the magnetization strength, the number of periods of the superlattice, the strength of the perpendicular magnetic field, and the Anderson disorder strength. Interestingly, a metal to semiconductor transition occurs as the number of the superlattice for a crossed superlattice p–n junction increases, and its spin Seebeck coefficient is much larger than that for the T-shaped one around the zero Fermi energy. Furthermore, the spin Seebeck coefficient for crossed systems can be much pronounced and their maximum absolute value can reach 528 μV by choosing optimized parameters. Besides, the spin Seebeck coefficient for crossed p–n junction is strongly enhanced around the zero Fermi energy for a weak magnetic field. Our results provide theoretical references for modulating the thermoelectric properties of a graphene superlattice p–n junction by tuning its geometric structure and physical parameters.

Topological Anderson insulator phase in a Dirac-semimetal thin film

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from normal band insulator to topological Anderson insulator in Dirac semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na$_{3}$Bi shows that in the topological Anderson insulator phase a quantized conductance plateau occurs in the bulk gap of band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on Born approximation fits the numerical data.

Stability of topological properties of bismuth (1 1 1) bilayer

We investigate the electronic and transport properties of the bismuth (1 1 1) bilayer in the context of the stability of its topological properties against different perturbations. The effects of spin–orbit coupling variations, geometry relaxation and interaction with a substrate are considered. The transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within the multi-orbital tight-binding model and density functional theory methods. A band inversion process in the bismuth (1 1 1) infinite bilayer and an evolution of the edge state dispersion in ribbons as a function of spin–orbit coupling strength are analyzed. A significant change in the orbital composition of the conduction and valence bands is observed during a topological phase transition. The topological edge states are shown to be weakly affected by the effect of ribbon geometry relaxation. The interaction with a substrate is considered for narrow ribbons on top of another bismuth (1 1 1) bilayer. This corresponds to a weakly interacting case and the effect is similar to an external perpendicular electric field. Robust quantized conductance is observed when the Fermi energy lies within the energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, scattering is possible between the channels lying close in the k-space. When the energy of the edge states overlaps the valence states, no topological protection is observed.

Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors.

Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological superconductors.

Electronic spin polarization in the Majorana bound state in one-dimensional wires

We have studied the effect of magnetic field and disorder on the electronic z-spin polarization at the ends of the one-dimensional wire with strong Rashba spin–orbit coupling deposited on an s-wave superconductor. It was shown that in the topologically nontrivial phase the polarization as well as the energy of the Majorana bound state oscillate as a function of the magnetic field. Despite being substantially nonzero in the low transversal and longitudinal fields the polarization at one of the wire's ends is significantly suppressed at a certain range of the magnitudes and angles of the canted magnetic field. Thus, in this case the polarization cannot be regarded as a local order parameter. However, the sum of the absolute values of the polarization at both ends remains significantly nonzero. It was demonstrated that Anderson disorder does not seriously affect observed properties but leads to the appearance of the additional areas with weak spin polarization at the high magnetic fields.

Thermoelectric effects in a rectangular Aharonov-Bohm geometry

The thermoelectric transport properties of a rectangular Aharonov-Bohm ring at low temperature are investigated using a theoretical approach based on Green's functions. The oscillations in the transmission coefficient as the field is varied can be used to tune the thermoelectric response of the ring. Large magnitude thermopowers are obtainable which, in conjunction with low conductance, can result in a high thermoelectric figure of merit. The effects of single site impurities and more general Anderson disorder are considered explicitly in the context of evaluating their effect on the Fano-type resonances in the transmission coefficient. Importantly, it is shown that even for moderate levels of disorder, the thermoelectric figure of merit can remain significant, increasing the appeal of such structures from the perspective of specialist thermoelectric applications.

Superdiffusive transport and energy localization in disordered granular crystals.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to differ fundamentally from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder-an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements)-and for two types of initial conditions (displacement excitations and velocity excitations). We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics depend strongly on the type of initial condition. In particular, for displacement excitations, the long-time asymptotic behavior of the second moment m̃(2) of the energy has oscillations that depend on the type of disorder, with a complex trend that differs markedly from a power law and which is particularly evident for an Anderson-like disorder. By contrast, for velocity excitations, we find that a standard scaling m̃(2)∼t(γ) (for some constant γ) applies for all three types of disorder. For weakly precompressed (i.e., strongly nonlinear) chains, m̃(2) and the inverse participation ratio P(-1) satisfy scaling relations m̃(2)∼t(γ) and P(-1)∼t(-η), and the dynamics is superdiffusive for all of the cases that we consider. Additionally, when precompression is strong, the inverse participation ratio decreases slowly (with η<0.1) for all three types of disorder, and the dynamics leads to a partial localization around the core and the leading edge of a propagating wave packet. For an Anderson-like disorder, displacement perturbations lead to localization of energy primarily in the core, and velocity perturbations cause the energy to be divided between the core and the leading edge. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar (roughly γ≈1.7 and η≈1) for all three types of disorder and for both types of initial conditions.

Electronic and thermoelectric transport properties for a zigzag graphene–silicene–graphene heterojunction modulated by external field

we investigate the electronic and thermoelectric transport properties for a graphene–silicene–graphene (GSG) heterojunction with zigzag-edge nanoribbons under the modulation of the effective spin–orbit coupling (SOC) and potential energy. Using the nonequilibrium Green's function method, it is demonstrated that both the transmission coefficient T and the charge Seebeck coefficient SC display the oscillatory behavior and can be effectively modulated by effective SOC λSO and the potential energy V0. Furthermore, the even–odd difference in transport and thermoelectric properties disappears in the GSG heterojunction. Additionally, the dependence of the transmission coefficient and the charge Seebeck coefficient on Anderson disorder strength has been studied.

Tunable electronic and transport properties for ultranarrow armchair-edge silicene nanoribbons under spin–orbit coupling and perpendicular electric field

The electronic and transport properties for armchair-edge silicene nanoribbons (ASiNR) with effective spin–orbit coupling and potential energy were investigated by using the non-equilibrium Green's function method. The energy gaps and the conductance for ASiNRs can be effectively modulated by effective spin–orbit coupling λSO and the potential energy V0. With increasing λSO, the energy gap for 6-ASiNR and 7-ASiNR decreases, while it remains zero for metallic 8-ASiNR. Interestingly, an energy gap appears for 8-ASiNR in presence of V0, which results in the appearance of a conductance gap for 8-ASiNR system. Additionally, the dependence of conductance on Anderson disorder strength has been studied.

Influence of [0001] tilt grain boundaries on the destruction of the quantum Hall effect in graphene

The half-integer quantum Hall effect (QHE) is often suppressed in graphene grown by chemical vapor deposition on metals. The reason behind the suppression is unclear, and we hypothesize that it might be connected to extended defects in the material. In this paper we present results for the quantum Hall effect in graphene with [0001] tilt grain boundaries connecting opposite sides of Hall bar devices. Such grain boundaries contain 5-7 ring complexes that host defect states that hybridize to form bands with varying degree of metallicity depending on grain-boundary defect density. In a magnetic field, edge states on opposite sides of the Hall bar can be connected by the defect states along the grain boundary. This destroys Hall resistance quantization and leads to nonzero longitudinal resistance. Anderson disorder can partly recover quantization, where current instead flows along returning paths along the grain boundary depending on defect density in the grain boundary and on disorder strength. Since grain sizes in graphene made by chemical vapor deposition are usually small, this may help explain why the quantum Hall effect is usually poorly developed in devices made of this material.

Controllable spin polarization and spin filtering in a zigzag silicene nanoribbon

Using non-equilibrium Green's function, we study the spin-dependent electron transport properties in a zigzag silicene nanoribbon. To produce and control spin polarization, it is assumed that two ferromagnetic strips are deposited on the both edges of the silicene nanoribbon and an electric field is perpendicularly applied to the nanoribbon plane. The spin polarization is studied for both parallel and anti-parallel configurations of exchange magnetic fields induced by the ferromagnetic strips. We find that complete spin polarization can take place in the presence of perpendicular electric field for anti-parallel configuration and the nanoribbon can work as a perfect spin filter. The spin direction of transmitted electrons can be easily changed from up to down and vice versa by reversing the electric field direction. For parallel configuration, perfect spin filtering can occur even in the absence of electric field. In this case, the spin direction can be changed by changing the electron energy. Finally, we investigate the effects of nonmagnetic Anderson disorder on spin dependent conductance and find that the perfect spin filtering properties of nanoribbon are destroyed by strong disorder, but the nanoribbon retains these properties in the presence of weak disorder.