Tunable Rapid Electron Transport in Titanium Oxide Thin Films

Rapid electron transport in the quantum well triggers many novel physical phenomena and becomes a critical point for the high-speed electronics. Here, we found electrical properties of the titanium oxide changed from semiconducting to metallic as the degree of oxidation decreased and Schottky quantum well was formed at the interface. We take the asymmetry interface electron scattering effect into consideration when studying the electrical transport properties of the multilayer thin films. A novel physical conductivity model for the multilayer thin films was developed. We found electron would be transferred from the low-mobility semiconducting and metallic conductive channels to the high-mobility Schottky quantum well conductive channel with an in-plane applied electric field. Electron concentration and mobility of the forming 2DEG in the Schottky quantum well could be tuned thus the nano-devices exhibited non-linear voltage-current curves. The differential resistivity of the nano-devices could decrease by two orders with increasing electric field at room temperature. Weak electron localization of electrons has been experimentally observed in our nano-devices at low temperature, which further demonstrated the existence of 2DEG in the Schottky quantum well. Our work will provide us new physics about the rapid electron transport in the multilayer thin films, and bring novel functional devices for the modern microelectronic industry

Tailoring energy barriers of Bloch-point-mediated transitions between topological spin textures

Magnetic skyrmions are nanoscale spin textures that their thermal stability originates from the nontrivial topology in nature. Recently, a plethora of topological spin textures have been theoretically predicted or experimentally observed, enriching the diversity of the skyrmionic family. In this work, we theoretically demonstrate the stabilities of various topological spin textures against homochiral states in chiral magnets, including chiral bobbers, dipole strings, and skyrmion tubes. They can be effectively classified by the associated topological Hall signals. Multiple transition paths are found among these textures, mediated by Bloch-point singularities, and the topological protection property here can be manifested by a finite energy barrier with the saddle point corresponding to the Bloch-point creation/destruction. By carefully modulating the local property of a surface, such as interfacial DMI induced by breaking the structural symmetry, the energy landscape of a magnetic system can be tailored decisively. Significantly, the proposed scenario also enables the manipulation of stabilities and transition barriers of these textures, even accompanied by the discovery of ground-state chiral bobbers. This study may raise great expectations on the coexistence of topological spin textures as spintronics-based information carriers for future applications

Luttinger Liquid phase in the Aubry-Andr\'e Hubbard chain

We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half-filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and localized gapless Aubry- Andr\'e insulator at strong quasiperiodic potential. Away from half-filing, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the non-interacting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy

2D excitation information by MPS method on infinite helixes

Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems

An analysis on the sensibility of casing vibration signal and its application to aero-hydraulic pump

Aero-hydraulic pump is a central part of hydraulic system in an aircraft. Acceleration sensors are installed in the axis, tangential and vertical direction for identifying the weak imbalance fault, and meanwhile analysis is made for the sensibility of weak imbalance fault from different direction acceleration signal. The result shows that the signal from vertical acceleration sensor is the most sensitive and the one from axis acceleration sensor is the least sensitive to identify and diagnose weak imbalance fault of aero-hydraulic pump

Hardness of Graph-Structured Algebraic and Symbolic Problems

In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in $\mathbb{Z}_p$ to solving unit-weight low-degree graph Laplacians over $\mathbb{Z}_p$ with a polylogarithmic overhead on the number of non-zeros. Given the hardness of solving general linear systems in $\mathbb{Z}_p$ [Casacuberta-Kyng 2022], this result shows that it is unlikely that we can generalize Laplacian solvers over $\mathbb{R}$, or finite-element based methods over $\mathbb{R}$ in general, to a finite-field setting. We also reduce solving general linear systems over $\mathbb{Z}_p$ to solving linear systems whose coefficient matrices are walk matrices (matrices with all ones on the diagonal) and normalized Laplacians (Laplacians that are also walk matrices) over $\mathbb{Z}_p$. We often need to apply linear system solvers to random linear systems, in which case the worst case analysis above might be less relevant. For example, we often need to substitute variables in a symbolic matrix with random values. Here, a symbolic matrix is simply a matrix whose entries are in a polynomial ring $\mathbb{F}[x_1, \ldots, x_t]$. We formally define the reducibility between symbolic matrix classes, which are classified in terms of the degrees of the entries and the number of occurrences of the variables. We show that the determinant identity testing problem for symbolic matrices with polynomial degree $1$ and variable multiplicity at most $3$ is at least as hard as the same problem for general matrices over $\mathbb{R}$.Comment: 57 pages, submitted version to STOC2

Anomalous shift in Andreev reflection from side incidence

Andreev reflection at a normal-superconductor interface may be accompanied with an anomalous spatial shift. The studies so far are limited to the top incidence configuration. Here, we investigate this effect in the side incidence configuration, with the interface parallel to the principal axis of superconductor. We find that the shift exhibits rich behaviors reflecting the character of pair potential. It has two contributions: one from the $k$-dependent phase of pair potential, and the other from the evanescent mode. For chiral $p$-wave pairing, the pairing phase contribution is proportional to the chirality of pairing and is independent of excitation energy, whereas the evanescent mode contribution is independent of chirality and is nonzero only for excitation energy below the gap. The two contributions also have opposite parity with respect to the incident angle. For $d_{x^{2}-y^{2}}$-wave pairing, only the evanescent mode contribution exists, and the shift exhibits suppressed zones in incident angles, manifesting the superconducting nodes. The dependence of the shift on other factors, such as the angle of incident plane and Fermi surface anisotropy, are discussed