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We theoretically study the quantum scattering and transport of electrons with Mexican-hat dispersion through both step and rectangular potential barriers by using the transfer matrix method. Owing to the torus-like iso-energy lines of the Mexican-hat dispersion, we observe the presence of double reflections and double transmissions in both two different barrier scenarios, i.e., the normal reflection (NR), retro-reflection (RR), normal transmission (NT), and specular transmission (ST).For the step potential with electrons incident from the large wavevector, the transmission is primarily governed by NT with nearly negligible ST, while the reflection is dominant by RR (NR) within (outside) the critical angle. Additionally, for electrons incident from the small wavevector, the NT can be reduced to zero by adjusting the barrier, resulting in a significant enhancement of ST and RR. For the rectangular barrier, the transmission and reflection spectra resemble those of the step barrier, but there are two kinds of resonant tunneling which can lead to perfect NT or ST. There exists a negative differential conductance (NDC) effect in the conductance spectrum. The conductance and the peak-to-valley ratio of the NDC effect can be effectively controlled by adjusting the height and width of the barrier as well as the incident energy. Our results provide a deeper understanding of the electron states governed by the Mexican-hat dispersion., Comment: 8 pages, 5 figures

In online learning platforms, particularly in rapidly growing computer programming courses, addressing the thousands of students' learning queries requires considerable human cost. The creation of intelligent assistant large language models (LLMs) tailored for programming education necessitates distinct data support. However, in real application scenarios, the data resources for training such LLMs are relatively scarce. Therefore, to address the data scarcity in intelligent educational systems for programming, this paper proposes a new Chinese question-and-answer dataset for Python learners. To ensure the authenticity and reliability of the sources of the questions, we collected questions from actual student questions and categorized them according to various dimensions such as the type of questions and the type of learners. This annotation principle is designed to enhance the effectiveness and quality of online programming education, providing a solid data foundation for developing the programming teaching assists (TA). Furthermore, we conducted comprehensive evaluations of various LLMs proficient in processing and generating Chinese content, highlighting the potential limitations of general LLMs as intelligent teaching assistants in computer programming courses.

We present a theoretical study on the Landau levels (LLs) and magneto-optical absorption of a two-dimensional semi-Dirac electron system under a perpendicular magnetic field. Based on an effective k.p Hamiltonian, we find that the LLs are proportional to the two-thirds power law of the magnetic field and level index, which can be understood as a hybridization of the LL of Schrodinger and Dirac electrons with new features. With the help of Kubo formula, we find the selection rule for interband (intraband) magneto-optical transition is anisotropic (isotropic). Specifically, the selection rules for interband magneto-optical transitions are $\Delta n$=0, $\pm2$ ($\pm2$, $\pm4$) for linearly polarized light along the linear (parabolic) dispersion direction, while the selection rules for the intraband transition are $\Delta n$=$\pm1$, $\pm3$ regardless of the polarization direction of the light. Further, the magneto-optical conductivity for interband (intraband) transition excited by linearly polarized light along the linear dispersion direction is two (one) orders of magnitude larger than that along the parabolic dispersion direction. This anisotropic magneto-optical absorption spectrum clearly reflects the structure of the LLs, and results in a strong linear dichroism. Importantly, a perfect linear dichroism with magnetic-field tunable wavelength can be achieved by using the interband transition between the two lowest LLs, i.e, from Ev0 to Ec0. Our results shed light on the magneto-optical property of the two dimensional semi-Dirac electron systems and pave the way to design magnetically controlled optical devices., Comment: 8 pages, 5 figures

We theoretically study the power-law decay behavior of the local density of states (LDOS) oscillations near a line defect in system with semi-Dirac points by using a low-energy k.p Hamiltonian. We find that the LDOS oscillations are strongly anisotropic and sensitively depend on the orientation of the line defect. We analytically obtain the decay indexes of the LDOS oscillations near a line defect running along different directions by using the stationary phase approximation. Specifically, when the line defect is perpendicular to the linear dispersion direction, the decay index is -5/4 whereas it becomes -1/4 if the system is gapped, both of which are different from the decay index -3/2 in isotropic Dirac systems. In contrast, when the line defect is perpendicular to the parabolic dispersion direction, the decay index is always -1/2 regardless of whether the system is gapped or not, which is the same as that in a conventional semimetal. In general, when the defect runs along an arbitrary direction, the decay index sensitively depends on the incident energy for a certain orientation of the line defect. It varies from -5/4 to -1/2 due to the absence of strict stationary phase point. Our results indicate that the decay index -5/4 provides a fingerprint to identify semi-Dirac points in 2D electron systems., Comment: Published version: 9 Pages, 6 Figures

For the pristine phosphorene nanoribbons (PNRs) with edge states, there exist two categories of edge bands near the Fermi energy (EF), i.e., the shuttle-shaped twofold-degenerate and the near-flat simple degenerate edge bands. However, the usual experimental measurement may not distinguish the difference between the two categories of edge bands. Here we study the varying rule for the edge bands of PNRs under an external electrostatic field. By using the KWANT code based on the tight-binding approach, we find that the twofold-degenerate edge bands can be divided into two separated shuttles until the degeneracy is completely removed and a gap near EFis opened under a sufficiently strong in-plane electric field. Importantly, each shuttle from the ribbon upper or lower edge outmost atoms is identified according to the local density of states. However, under a small off-plane field the shuttle-shaped bands are easily induced into two near-flat bands contributed from the edge atoms of the top and bottom sublayers, respectively. The evidence provides the edge and sublayer degrees of freedom (DOF) for the PNRs with shuttle-shaped edge bands, of which is obviously different from another category PNRs intrinsically with near-flat edge bands. This is because that the former category of ribbons solely have four zigzag-like atomic configurations at the edges in each unit cell, which also results in that the property is robust against the point defect in the ribbon center area. As an application, furthermore, based on this issue we propose a homogenous junction of a shuttle-edge-band PNR attached by two electric gates. Interestingly, the transport property of the junction with field manipulation well reflects the characteristics of the two DOFs. These findings may provide a further understanding on PNRs and initiate new developments in PNR-based electronics.

The central question in the field of 2D materials is how a material behaves when it is patterned at nanometer scale with different edge geometries. Due to the anisotropy inherent in the puckered structure, black phosphorene nanostructures may have more varieties of edge geometries. Here, we present a comprehensive 2D planar crystallographic characterization of phosphorene uniformly by a chiral vector (angle), from which a new type of edge atomic configuration, the slope edge geometry is discovered. The phosphorene nanoribbons (PNRs) with slope edges, like previously noticed zigzag and skewed-armchair PNRs, also own interesting twofold-degenerate edge states. These three marginal directions, together with the skewed-zigzag and armchair directions without edge states, divide a phosphorene into four regions among which the electronic property is different from each other. Further, for a PNR cutting along any possible direction, by taking into account the z-direction in structure, whether or not it owns edge states depends on the periodic zigzag-like morphology along the edges. Moreover, we propose a PNR-based z-shaped homogenous junction with scale $\sim$100 nm, where the central scattering region between two PNR electrodes is a phosphorene quantum dot (PQD) of PNR segment with various edge morphologies. Interestingly, the calculated conductance of the junction relies sensitively on the central PQD edge states, which exhibits a terrace with resonant oscillations near Fermi energy, otherwise the electron transport is blocked due to the absence of edge states. Remarkably, the number of oscillating peaks exactly matches to the number of sawtooth along an edge of PQD, since the discrete energy levels of the zigzag-like edge provide the transporting channels for electrons. The results here may be extended to the group-VA 2D materials for observing the electronic property of nanostructures.

We analytically study the electronic structures and optical properties of zigzag-edged black phosphorene nanoribbons (ZPNRs) utilizing the tight-binding (TB) Hamiltonian and Kubo formula. By solving the discrete Schordinger equation directly, we obtain the energy spectra and wavefunctions for a $N$-ZPNR with $N$ number of transverse zigzag atomic chains, and classify the eigenstates according to the lattice symmetry. We then obtain the optical transition selection rule of ZPNRs based on the symmetry analysis and the analytical expressions of the optical transition matrix elements. Under an incident light linearly-polarized along the ribbon, importantly, we find that the optical transition selection rule for the $N$-ZPNR with even- or odd-$N$ is qualitatively different. In specification, for even-$N$ ZPNRs the inter- (intra-) band selection rule is $\Delta n=$odd (even), since the parity of the wavefunction corresponding to the $n$th subband in the conduction (valence) band is $(-1)^{n}[(-1)^{(n+1)}]$ due to the presence of the $C_{2x}$ symmetry. In contrast, all optical transitions are possible among all subbands due to the absence of the $C_{2x}$ symmetry. Our findings provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful in the explanation of the optical experiment data on ZPNR samples., Comment: 13 pages, 9 figures

The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region with a prepatterned graphite local gate. The graphite local gate screens the impurity potential in the 2DEG. More importantly, it electrostatically defines the edge of the 2DEG, which facilitates the formation of well-defined edge channels in the quantum Hall regime. The improvements enable us to observe precisely quantized Hall plateaus in electron-doped black phosphorus FET. Magneto-transport measurements under high magnetic fields further revealed a large effective mass and an enhanced Land\'e g-factor, which points to strong electron-electron interaction in black phosphorus 2DEG. Such strong interaction may lead to exotic many-body quantum states in the fractional quantum Hall regime., Comment: Accepted in Nano Letters

Black phosphorus (BP) has emerged as a promising material candidate for next generation electronic and optoelectronic devices due to its high mobility, tunable band gap and highly anisotropic properties. In this work, polarization resolved ultrafast mid-infrared transient reflection spectroscopy measurements are performed to study the dynamical anisotropic optical properties of BP under magnetic fields up to 9 T. The relaxation dynamics of photoexcited carrier is found to be insensitive to the applied magnetic field due to the broadening of the Landau levels and large effective mass of carriers. While the anisotropic optical response of BP decreases with increasing magnetic field, its enhancement due to the excitation of hot carriers is similar to that without magnetic field. These experimental results can be well interpreted by the magneto-optical conductivity of the Landau levels of BP thin film, based on an effective k*p Hamiltonian and linear response theory. These findings suggest attractive possibilities of multi-dimensional controls of anisotropic response (AR) of BP with light, electric and magnetic field, which further introduces BP to the fantastic magnetic field sensitive applications.