Quantum transmission and tunneling in double ladder barriers

doi:10.3969/j.issn.1007-5461.2026.03.007

Abstract

Abstract: To investigate the quantum tunneling properties in double trapezoidal barriers, this study systematically examines the quantum transmission behavior in double trapezoidal barriers via rigorous theoretical analysis. The exact analytical solutions for the transmission coefficients of trapezoidal barrier structures are derived, and their essential distinctions from those of rectangular barriers are revealed. Firstly, the transmission peaks of trapezoidal barrier structures originate from the resonances of quasi-bound states formed within the gradient barrier structures, and the formation and characteristics of these quasi-bound states are governed by the slope, width, separation, and particle energy of the barriers. Crucially, the nonlinear phase accumulation inherent to the gradient profile prevents the complete destructive interference of reflected waves during resonance, leading to a mechanism fundamentally different from that in conventional rectangular barriers. Secondly, the transmission coefficients of trapezoidal barrier structures exhibit a distinct slope dependence, where positive slopes suppress transmission and negative slopes enhance it. The study also find that for trapezoidal barrier structures, transmission is suppressed when the incident energy lies below the initial barrier height, the transmission coefficient becomes independent of the barrier sequence when the energy significantly exceeds the initial barrier height, and the transmission coefficient of the trapezoidal barrier structure oscillates periodically with barrier spacing while decaying periodically with the increasing barrier width. This work elucidates the multidimensional tuning mechanisms governing quantum transmission in double trapezoidal barriers.

Key words: quantum mechanics, transmission coefficient, transfer matrix method, double trapezoidal barriers, Airy function

CLC Number:

O413.1

References

[1]Yusofvand Z, Naderi D, et al. Competition of proton radioactivity with α- and β+-decays[J]. Indian Journal of Physics,2025,99(2): 631-637.
[2]Mehta K, Dasgupta S, et al. Quantum interference effect in plasmonic transmission in the presence of quantum emitters[J]. Journal of Modern Optics,2022,69(4): 183-191.
[3]Mei G D, Wu D, Ding S H, et al. Optical Tunneling to Improve Light Extraction in Quantum Dot and Perovskite Light-Emitting Diodes[J]. IEEE Photonics Journal,2020,12(6): 1-14.
[4]Matrood W R, Jeji F R, Jeji, et al. Tunneling Effect in Double Quantum Dots Nanostructure[J]. Advanced Physical Research,2024,6(2): 145-158.
[5]Jonsson B. Solving the Schrodinger equation in arbitary quantum-well potential profile using the transfer matrix method[J]. IEEE J. Quantum Electron,1990,26: 2025-2035.
[6]Wang J, et al. Modified Airy function method for modeling of direct tunneling current in metal--oxide--semiconductor structures[J]. Applied Physics Letters,2001,79(12): 1831-1833.
[7]Yan Q Q, Xu H Z, Li J S. Phase times and lateral displacements of particle through rectangular symmetric barrier structure[J]. The European Physical Journal B,2023,96(5): 1-9.
[8]Otero V G L, Villanueva A A D. Contraction of a Wave Packet while Scattering with a Step Potential[J]. Philippine Journal of Science,2025,154(1): 207-216.
[9]Johson C, Sally. Multiphoton effect exists within quantum interference of light.[J]. Laser Focus World,2024,60: 12-13.
[10]Hyllested L O H, Prestholm I, Solomon G C. Intermolecular Interactions and Quantum Interference Effects in Molecular Junctions[J]. ACS Nanoscience Au,2024,4(6): 426-434.
[11] Li X H, Zheng Y, Zhou Y, et al. Supramolecular Transistors with Quantum Interference Effect[J]. Journal of the American Chemical Society,2023,145(39): 21679-21686.
[12]Wang H B. Interplay of Inter-Dot Tunneling and Quantum Interference under Optical Vortex Beams to Induce Spatially Dependent Optical Effects in Quantum Dot Molecules[J]. International Journal of Theoretical Physics,2025,64(3): 57-77.
[13]Asenjo F A, Hojman S A, et al. Exact solutions to the telegraph equation in terms of airy functions[J]. Revista Mexicana de Física,2024,0(4): 1-4.
[14]Sun B X, Cao Q Q, Sun Y T. The possible K -K* and D -D* bound and resonance states by solving the Schrodinger equation[J]. Communications in Theoretical Physics,2024,76(10): 85-91.
[15]Liu C F, Hu K, Hu T, Tang Y. Tunneling of a Bose-Einstein condensate under damping [J]. Journal of Low Temperature Physics, 2020,160:32-40 .
[16]Liu C F, Tang Y. Metastable state and macroscopic quantum tunneling of binary mixtures [J]. Eur. Phys. J. B,2009,70:193–199.
[17]Wang Y, Li D, Sun X Y. Effect of lattice distortion on spin admixture and quantum transport in organic devices with spin-orbit coupling[J]. Chinese Physics B,2024,33(7): 518-527.
[18]Wine J. Achtymichuk J; Marsiglio F. The modified airy function approximation applied to the double-well potential[J]. AIP Advances, 2025, 15(3):035330.
[19]LI X X, Peng H, Wang D. Effect of electron–electron interaction on polarization process of exciton and biexciton in conjugated polymer[J]. Chinese Physics B,2024,33(3): 556-566.
[20]Bal M E, Cheah E B, Maurice E C, et al. Quantum Hall effect in InAsSb quantum wells at elevated temperatures[J]. Physical Review Research,2024,6(2): 32-59.