Parabolic-Cylinder Approach to Valley-Polarized Conductance in Tilted Anisotropic Dirac-Weyl Systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917332828291072 |
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| author | Yesilyurt, Can |
| author_facet | Yesilyurt, Can |
| contents | We develop a parabolic-cylinder approach to valley-polarized conductance in tilted anisotropic Dirac-Weyl systems, showing that the smooth-interface scattering problem can be reduced analytically to the Weber equation, which belongs to the same differential-equation class as the quantum harmonic oscillator. This reduction yields closed-form expressions for the angular transmission envelope and clarifies the distinct roles of the tilt components: the perpendicular tilt renormalizes the tunneling-envelope width, while the parallel tilt shifts the Fabry-Perot resonance structure differently in opposite valleys. Combined with the nonlinear mapping between the fixed device frame and the rotated barrier frame, this analytical structure provides a direct route from valley-dependent interface tunneling to net valley-polarized conductance. We apply the formalism to rotated electrostatic barriers and construct phase diagrams over barrier angle, tilt strength, width, height, and Fermi energy. The results reveal a robust optimum near t = 0.2 over the parameter range studied, identify the crossover from oscillatory to monotonic polarization regimes, and delineate practical operating windows for candidate materials including 8-Pmmn borophene and WTe2. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_10490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parabolic-Cylinder Approach to Valley-Polarized Conductance in Tilted Anisotropic Dirac-Weyl Systems Yesilyurt, Can Mesoscale and Nanoscale Physics We develop a parabolic-cylinder approach to valley-polarized conductance in tilted anisotropic Dirac-Weyl systems, showing that the smooth-interface scattering problem can be reduced analytically to the Weber equation, which belongs to the same differential-equation class as the quantum harmonic oscillator. This reduction yields closed-form expressions for the angular transmission envelope and clarifies the distinct roles of the tilt components: the perpendicular tilt renormalizes the tunneling-envelope width, while the parallel tilt shifts the Fabry-Perot resonance structure differently in opposite valleys. Combined with the nonlinear mapping between the fixed device frame and the rotated barrier frame, this analytical structure provides a direct route from valley-dependent interface tunneling to net valley-polarized conductance. We apply the formalism to rotated electrostatic barriers and construct phase diagrams over barrier angle, tilt strength, width, height, and Fermi energy. The results reveal a robust optimum near t = 0.2 over the parameter range studied, identify the crossover from oscillatory to monotonic polarization regimes, and delineate practical operating windows for candidate materials including 8-Pmmn borophene and WTe2. |
| title | Parabolic-Cylinder Approach to Valley-Polarized Conductance in Tilted Anisotropic Dirac-Weyl Systems |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2603.10490 |