Research Output
Articles
Publication Date: 2025
Physical Review Research (26431564)7(3)
A Dirac electron passing through a heterojunction with spatially variable tilt experiences an effective curved spacetime. In this work, we show how this experience is manifested in its conductance. We investigate the propagation of electron waves in a two-dimensional tilted Dirac cone heterostructure where tilt depends on the coordinate z along the junction. The resulting Dirac equation in an emergent curved spacetime for the spinor ψ(z) can be efficiently solved using a fourth-order Runge-Kutta numerical method by a transformation to a suitable spinor φ where the resulting Dirac cone looks locally upright. The spatial texture of the tilt induces oscillatory behaviors in key physical quantities such as the norm |φ(z)|2 of the wave function, polar and azimuthal angles Θ(z) and Φ(z) of the pseudospin, and the integrated transmission τ where oscillation wavelengths get shorter (longer) in stronger (weaker) tilt regions. Such an oscillatory behavior that is reminiscent of gigantic gravitational redshift is an indicator of an underlying spacetime metric that can be probed in tunneling experiments. We derive analytical approximations for the position-depdendent wave numbers Δkz(z) that explain the redshift patterns and corroborate it with numerical simulations. For a tilt bump spread over length scale ℓ, upon increasing ℓ, the amplitude of redshifted oscillations reduces whereas the number of peaks increases. The scale invariance of the Dirac equation allows us to probe these aspects of ℓ dependence by a voltage sweep in transmission experiments. Smooth variations of the tilt reduces impedance mismatch of the electron waves, thereby giving rise to very high transmission rates. This concept can be used in combination with a sigmoid-shaped tilt texture for a gigantic redshift or blueshift engineering of the transmitted waves, depending on whether the sigmoid is downswing or upswing. © 2025 authors. Published by the American Physical Society.
Publication Date: 2025
Solid State Communications (00381098)401
In this study, the Haldane model's edge states are utilized to illustrate that a zero-energy localized state forms around a single vacancy in the model. In order to complete this task, the conventional unit cell associated to the Haldane hexagonal structure is transferred onto a two-leg ladder in momentum space, effectively forming an extended Su–Schrieffer–Heeger (SSH) lattice through a one-dimensional Fourier transform. Through the application of a suitable unitary transformation, the two-leg SSH ladder in momentum space is converted into an equivalent lattice with two distinct on-site states with different momentum that are suitable for the calculations. Ultimately, the desired zero-energy localized mode formed around the vacant-site is represented by a combination of the armchair edge states. Furthermore, the scenario involving two vacant sites is investigated and it is revealed that an effective hopping interaction exists between the localized states formed around the on-site vacancies created along a zigzag chain in the lattice. This structure can be likened to the structure of a quantum dot with two none-degenerate energy levels. Such a hopping interaction is absent for the same vacancies created on the armchair chains. Finally, it is shown that introducing vacancies periodically on the sites of a zigzag row along a finite-width ribbon with the Haldane structure leads to the emergence of an impurity band within the energy gap. © 2025
Publication Date: 2024
Physical Review B (24699950)109(2)
The quantization of conductance in the presence of nonmagnetic point defects is a consequence of topological protection and the spin-momentum locking of helical edge states in two-dimensional topological insulators. This protection ensures the absence of backscattering of helical edge modes in the quantum Hall phase of the system. However, in this paper, we focus on exploring an approach to spoil such conductance quantization. We propose that a linear arrangement of (nonmagnetic) on-site impurities can effectively cause deviations from the conductance quantization of the edge states in the Kane-Mele model. To investigate this phenomenon, we consider an armchair ribbon containing a line defect spanning its width. Utilizing the tight-binding model and nonequilibrium Green's function method, we calculate the transmission coefficient of the system. Our results reveal a suppression of conductance at energies near the lower edge of the bulk gap for positive on-site potentials. To further comprehend this behavior, we perform analytical calculations and discuss the formation of an impurity channel. This channel arises due to the overlap of in-gap bound states, linking the bottom edge of the ribbon to its top edge, consequently facilitating backscattering. Our explanation is supported by the analysis of the local density of states at sites near the position of impurities. © 2024 American Physical Society.
Publication Date: 2024
Physica Scripta (00318949)99(9)
The concept of topological Fano resonance, characterized by an ultrasharp asymmetric line shape, is a promising candidate for robust sensing applications due to its sensitivity to external parameters and immunity to structural disorder. In this study, the vacancy-induced topological Fano resonance in a nanoribbon made up of a hexagonal lattice with armchair sides is examined by introducing several on-site vacancies, which are deliberately created at regular distances, along a zigzag chain that stretches across the width of the ribbon. The presence of the on-site vacancies can create localized energy states within the electronic band structure, leading to the formation of an impurity band, which can result in Fano resonance phenomena by forming a conductivity channel between the edge modes on both armchair sides of the ribbon. Consequently, an ultracompact tunable on-chip integrated topological Fano resonance derived from the graphene-based nanomechanical phononic crystals is proposed. The Fano resonance arises from the interference between topologically protected even and odd edge modes at the interface between trivial and nontrivial insulators in a nanoribbon structure governed by the Kane-Mele model describing the quantum spin Hall effect in hexagonal lattices. The simulation of the topological Fano resonance is performed analytically using the Lippmann-Schwinger scattering formulation. One of the advantages of the present study is that the related calculations are carried out analytically, and in addition to the simplicity and directness, it reproduces the results obtained from the Landauer-Büttiker formulation very well both quantitatively and qualitatively. The findings open up possibilities for the design of highly sensitive and accurate robust sensors for detecting extremely tiny forces, masses, and spatial positions. © 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
