arXiv subjects

Yan-Yang Zhang

Publications and source records attributed to Yan-Yang Zhang.

At least 19 recordsLinked to original sources

arXiv2025

Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential

In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the existence of critical states. Our findings show that, unlike in Hermitian cases, the non-Hermiticity of the potential leads to the disappearance of critical states and critical regions. Furthermore, we are able to accurately determine the Lyapunov exponents and the mobility edges. Our results reveal that the mobility edges form mobility lines and mobility rings in the complex energy plane. Within the mobility rings, the eigenstates are extended, while the localized states are located outside the mobility rings. For mobility line cases, only when the eigenenergies lie on the mobility lines, their corresponding eigenstates are extended states.Finally, as the energy approaches the mobility edges, we observe that, differently from Hermitian cases, here the critical index of the localization length is not a constant, but rather varies depending on the positions of the mobility edges.

cond-mat.dis-nn↗

arXiv2024

Two-dimensional topological effect in a transmon qubit array with tunable couplings

We investigate a square-lattice architecture of superconducting transmon qubits with inter-qubit interactions mediated by inductive couplers. Therein, the inductive couling between the qubit and couplers is suggested to be designed into the gradiometer form to intigimate the flux noise orginating from the environment. Via periodically modulating the couplers,the Abelian gauge potential, termed effective magnetic flux, can be synthesized artificially, making the system an excellent platform for simulating two-dimensional topological physics. In the simplest two-dimensional model, the double (or three-leg) ladder, the staggered vortex-Meissner phase transition different from that in the two-leg ladder can be found in the single-particle ground state as the effective magnetic flux varies. Besides, the large coupling ratio between the interleg and intraleg coupling strengths also makes the chiral current resemble squeezed sinusoidal functions. If the row number is further increased, the topological band structure anticipated at massive rows begins to occur even for a relatively small number of rows (ten or so for the considered parameters). This heralds a small circuit scale to observe the topological band. The edge state in the band gap is determined by the topological Chern number and can be calculated through integrating the Berry curvature with respect to the first Brillouin zone. Besides, we present a systematic method on how to measure the topological band structure based on time- and space-domain Frourier transformation of the wave function after properly excited. The result offers an avenue for simulating two-dimensional topological physics on the state-of-the-art superconducting quantum chips.

quant-ph↗

arXiv2023

Orbital Magnetization under an Electric Field and Orbital Magnetoelectric Polarizabilty for a Bilayer Chern System

In the real space formalism of orbital magnetization (OM) for a Chern insulator without an external electric field, it is correct to average the local OM either over the bulk region or over the whole sample. However for a layered Chern insulator in an external electric field, which is directly related to the nontrivial nature of orbital magnetoelectric coupling, the role of boundaries remains ambiguous in this formalism. Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the OM with the above two different average types under a nonzero perpendicular electric field. The result shows that in this case, the nonzero Chern number gives rise to a gauge shift of the OM with the bulk region average, while this gauge shift is absent for the OM with the whole sample average. This indicates that only the whole sample average is reliable to calculate the OM under a nonzero electric field for Chern insulators. On this basis, the orbital magnetoelectric polarizablity (OMP) and the Chern-Simons orbital magnetoelectric polarizablity (CSOMP) with the whole sample average are studied. We also present the relationship between the OMP (CSOMP) and the response of Berry curvature to the electric field. The stronger the response of Berry curvature to electric field, the stronger is the OMP (CSOMP). Besides clarify the calculation methods, our result also provides an effective method to enhance OMP and CSOMP of materials.

cond-mat.mes-hall↗

arXiv2023

Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State

We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until $\sim 10^4$ times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function $β\sim 0$, which is also a marginal phase between the typical metal ($β>0$) and insulating phase ($β<0$). The all-to-all coupling expels one isolated but extended state far out of the band, whose transport is extremely robust against disorder due to absence of backscattering. The bond current picture of this isolated state shows a quantum version of short circuit through long hopping.

cond-mat.dis-nn↗

arXiv2023

Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at $g\sim 0$ of the critical distribution and the large $g$ limit of the universal scaling function $β$ resemble those behaviors of three-dimensional disordered systems.

cond-mat.mes-hall↗

arXiv2022

Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch

We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in two layers), the inter-layer coupling results in resonant traversing between forward propagating waves in two layers. In the case of generic ratios, there is a quantized conductance plateau originated from two Chern numbers associated with two layers. However, the phase boundary of this quantization plateau consists of a fractal transitional region (instead of a clear transition line) of interpenetrating edge states (with quantized conductance) and bulk states (with unquantized conductance). We attribute these bulk states as mismatch induced in-gap bulk states. Different from in-gap localized states induced by random disorder, these in-gap bulk states are extended in the limit of vanishing random disorder. However, the detailed fine structure of this transitional region is sensitive to disorder, lattice structure, sample size, and even the configuration of leads connecting to it, due to the bulk and topologically trivial nature of these in-gap bulk states.

cond-mat.mes-hall↗

arXiv2022

Effects of Boundary on Orbital Magnetization for a Bilayer System with Different Chern Numbers

The real space formalism of orbital magnetization (OM) is an average of the local OM over some appropriate region of the system. Previous studies prefer a bulk average (i.e., without including boundaries). Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the effects from boundaries on the real space expressions of OM. The size convergence processes of its three constituent terms $M_{\mathrm{LC}}$, $M_{\mathrm{IC}}$, $M_{\mathrm{BC}}$ are analysed. The topological term $M_{\mathrm{BC}}$ makes a nonnegligible contribution from boundaries as a manifestation of edge states, especially in the case of nonzero Chern numbers. However, we show that the influence of the boundary on $M_{\mathrm{LC}}$ and $M_{\mathrm{IC}}$ exactly compensates that on $M_{\mathrm{BC}}$. This compensation effect leads to the conclusion that the whole sample average is also a correct algorithm in the thermodynamic limit, which gives the same value as those from the bulk average and the $k$ space formula. This clarification will be beneficial to further studies on orbitronics, as well as the orbital magnetoelectric effects in higher dimensions.

cond-mat.mes-hall↗

arXiv2022

Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential

In this work, we investigate the Anderson localization problems of the generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasi-periodic potential where the parameter $|α|\geq1$. The Lyapunov exponent $γ(E)$ and the mobility edges $E_c$ are exactly obtained for the unbounded quasi-periodic potential. With the Lyapunov exponent, we find that there exists a critical region in the parameter $λ-E$ plane. The critical region consists of critical states. In comparison with localized and extended states, the fluctuation of spatial extensions of the critical states is much larger. The numerical results show that the scaling exponent of inverse participation ratio (IPR) of critical states $x\simeq0.5$. Furthermore, it is found that the critical indices of localized length $ν=1$ for bounded ($|α|<1$) case and $ν=1/2$ for unbounded ($|α|\geq1$) case. The above distinct critical indices can be used to distinguish the localized-extended from localized-critical transitions. At the end, we show that the systems with different $E$ for both cases of $|α|<1$ and $|α|\geq1$ can be classified by the Lyapunov exponent $γ(E)$ and Avila's quantized acceleration $ω(E)$.

cond-mat.dis-nn↗

arXiv2020

Spin-dependent electron transport along hairpin-like DNA molecules

The chirality-induced spin selectivity (CISS), demonstrated in diverse chiral molecules by numerous experimental and theoretical groups, has been attracting extensive and ongoing interest in recent years. As the secondary structure of DNA, the charge transfer along DNA hairpins has been widely studied for more than two decades, finding that DNA hairpins exhibit spin-related effects as reported in recent experiments. Here, we propose a setup to demonstrate directly the CISS effect in DNA hairpins contacted by two nonmagnetic leads at both ends of the stem. Our results indicate that DNA hairpins present pronounced CISS effect and the spin polarization could be enhanced by using conducting molecules as the loop. In particular, DNA hairpins show several intriguing features, which are different from other chiral molecules. First, the local spin currents can flow circularly and assemble into a number of vortex clusters when the electron energy locates in the left/right electronic band of the stem. The chirality of vortex clusters in each band is the same and will be reversed by switching the electron energy from the left band to the right one, inducing the sign reversal of the spin polarization. Interestingly, the local spin currents can be greater than the corresponding spin component of the source-drain current. Second, both the conductance and the spin polarization can increase with molecular length as well as dephasing strength, contrary to the physical intuition that the transmission ability of molecular wires should be poorer when suffering from stronger scattering. Third, we unveil the optimal contact configuration of efficient electron transport and that of the CISS effect, which are distinct from each other and can be controlled by dephasing strength. The underlying physical mechanism is illustrated.

cond-mat.mes-hall↗

arXiv2020

Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures

Landauer-Büttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, Chebyshev polynomial method has attracted intense interests in numerical simulations of quantum systems due to the high efficiency in parallelization, because the only matrix operation it involves is just the product of sparse matrices and vectors. Many progresses have been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer-Büttiker formula for the conductance of quantum transports in nanostructures. We first describe the full algorithm based on the standard bath kernel polynomial method (KPM). Then, we present two simple butefficient improvements. One of them has a time consumption remarkably less than the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.

cond-mat.mes-hall↗

arXiv2020

Numerical Study of Disorder on the Orbital Magnetization in Two Dimensions

The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistent T-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.

cond-mat.mes-hall↗

arXiv2019

Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall Systems

Quantum anomalous Hall (QAH) multilayers provide a platform of topological materials with high Chern numbers. We investigate the localization routes of bilayer QAH systems with Chern number C = 2 under strong disorder, by numerical simulations on their quantum transport properties and the Chern-Simons axion coupling. Compared to the single layer counterpart with C = 2, the localization trajectories present much richer behaviors, for example, the existence of the stable intermediate state with C = 1 can be tuned by model parameters. This state was always unstable in the single layer case. Furthermore, the two parameter scaling trajectories also exhibit multiple patterns, some of which were not captured by the standard Pruisken picture. During the process towards localization, the Chern-Simons axion coupling shows a surprisingly remarkable peak which is even higher and sharper in the large size limit. Therefore the disordered bilayer QAH system can be a good candidate for this nontrivial magnetoelectric coupling mediated by orbital motions.

cond-mat.mes-hall↗

arXiv2018

Barrier tunneling of the Loop-Nodal Semimetal in the Hyperhoneycomb lattice

We theoretically investigate the barrier tunneling in the three-dimensional model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for different injecting states around the nodal loop are calculated, by using analytical treatments of the effective model, as well as numerical simulations of the tight binding model. In the low energy regime, states with remarkable transmissions are only concentrated in a small range around the loop plane. When the momentum of the injecting electron is coplanar with the nodal loop, nearly perfect transmissions can occur for a large range of injecting azimuthal angles if the potential is not high. For higher potential energies, the transmission shows a resonant oscillation with the potential, but still with peaks being perfect transmissions that do not decay with the potential width. These robust transports of the loop-nodal semimetal can be approximately explained by a momentum dependent Dirac Hamiltonian.

cond-mat.mes-hall↗

arXiv2016

Spin-filtered and Spatially Distinguishable Crossed Andreev Reflection in a Silicene-Superconductor Junction

We theoretically investigate the quantum transports in a junction between a superconductor and a silicene nanoribbon, under the effect of a magnetic exchange field. We find that for a narrow nanoribbon of silicene, remarkable crossed Andreev reflection (with a fraction $>50\%$) can be induced in the energy window of the elastic cotunneling, by destroying some symmetries of the system. Since the energy responses of electrons to the exchange field are opposite for opposite spins, these transport channels can be well spin polarized. Moreover, due to the helicity conservation of the topological edge states, these three transport channels are spatially separated in three different locations of the device, making them experimentally distinguishable. This crossed Andreev reflection is a nonlocal quantum interference between opposite edges through evanescent modes. If two superconducting leads with different phases are connected to two edges of the silicene nanoribbon, the crossed Andreev reflection can present Josephson type oscillations, with a maximal fraction $\sim 100\%$.

cond-mat.mes-hall↗

arXiv2016

Resonant impurities states-driven topological transition in quantum well

We demonstrate theoretically that a new system quantum well can realize the topological transition based on the 16-band kp model. Utilizing the strain introduced by the doped impurities, the band anti crossing induced by the doped nitrogen and valence band anti crossing induced by the doped bismuth, the band gap of the quantum well is rapidly decreased and even becomes negative. As a result, the topological transitions arise. Furthermore, the band gap as a function of the concentration of nitrogen and bismuth is calculated, where the negative gap corresponds to the topological phase. Noting the cancel of strain resulting from the combination of tensile strain introduced by N and strain introduced by Bi, we can easily tune the ratio of the N and Bi to meet the requirement of strain in the crystal growth procedure. Our proposal provides a promising approach for topological insulator in traditional semiconductor system utilizing the semiconductor fabrication technologies.

cond-mat.mes-hall↗

arXiv2015

Route towards Localization for Quantum Anomalous Hall Systems with Chern Number 2

The quantum anomalous Hall system with Chern number 2 can be destroyed by sufficiently strong disorder. During its process towards localization, it was found that the electronic states will be directly localized to an Anderson insulator (with Chern number 0), without an intermediate Hall plateau with Chern number 1. Here we investigate the topological origin of this phenomenon, by calculating the band structures and Chern numbers for disordered supercells. We find that on the route towards localization, there exists a hidden state with Chern number 1, but it is too short and too fluctuating to be practically observable. This intermediate state cannot be stabilized even after some "smart design" of the model and this should be a universal phenomena for insulators with high Chern numbers. By performing numerical scaling of conductances, we also plot the renormalization group flows for this transition, with Chern number 1 state as an unstable fixed point. This is distinct from known results, and can be tested by experiments and further theoretical analysis.

cond-mat.mes-hall↗

arXiv2014

Robustness of Quantum Spin Hall Effect in an External Magnetic Field

The edge states in the quantum spin Hall effect are expected to be protected by time reversal symmetry. The experimental observation of the quantized conductance was reported in the InAs/GaSb quantum well {[}Du et al, arXiv:1306.1925{]}, up to a large magnetic field, which raises a question on the robustness of the edge states in the quantum spin Hall effect under time reversal symmetry breaking. Here we present a theoretical calculation on topological invariants for the Benevig-Hughes-Zhang model in an external magnetic field, and find that the quantum spin Hall effect retains robust up to a large magnetic field. The critical value of the magnetic field breaking the quantum spin Hall effect is dominantly determined by the band gap at the $Γ$ point instead of the indirect band gap between the conduction and valence bands. This illustrates that the quantum spin Hall effect could persist even under time reversal symmetry breaking.

cond-mat.str-el↗

arXiv2014

The Coexistence and Decoupling of Bulk and Edge States in Disordered Two-dimensional Topological Insulators

We investigate the scattering and localization properties of edge and bulk states in a disordered two-dimensional topological insulator when they coexist at the same fermi energy. Due to edge-bulk backscattering (which is not prohibited \emph{a priori} by topology or symmetry), Anderson disorder makes the edge and bulk states localized indistinguishably. Two methods are proposed to effectively decouple them and to restore robust transport. The first kind of decouple is from long range disorder, since edge and bulk states are well separated in $k$ space. The second one is from an edge gating, owing to the edge nature of edge states in real space. The latter can be used to electrically tune a system between an Anderson insulator and a topologically robust conductor, i.e., a realization of a topological transistor.

cond-mat.mes-hall↗