Study on Physical Characteristics and Quantum Transport Law in Low-dimensional Quantum System

Chunhang Qiu

doi:10.6911/WSRJ.202609_12(9).0001

Authors

Chunhang Qiu Shandong University, Jinan, China

DOI:

https://doi.org/10.6911/WSRJ.202609_12(9).0001

Keywords:

Low-dimensional quantum system; Quantum transport; Quantum confinement effect; Topological edge state; Coulomb blockage.

Abstract

As electronic devices continue to shrink to nanometer scale, low-dimensional quantum systems have become the core platform for condensed matter physics and the development of next-generation technology. In this paper, the physical properties and quantum transport laws of low-dimensional quantum systems are systematically reviewed. Firstly, the low-dimensional structures are classified according to the effective dimension (0D/1D/2D), and their characteristic electronic structures, density differences of states and key physical phenomena are summarized. Next, the main theoretical tools of quantum transport are introduced, including the Landauer–Büttiker formula and the non-equilibrium Green's function method, along with discussions on representative mechanisms such as ballistic transport, quantum tunneling, Coulomb blockade, Kondo effect, and topological edge state transport. Further analyze the dimension-dependent transport characteristics, external field regulation behavior, topology and spin-related transport, and the latest progress of molecular-scale quantum interference effect. This paper aims to provide concise reference for researchers entering this field and stimulate interdisciplinary exploration.

Downloads

Download data is not yet available.

References

[1] Lin, Q., Yu, X., Jiyuan, B., & others. (2023). Electron transport properties through a two-dimensional quantum dot array. Moscow University Physics Bulletin, 78(3), 368–375. https://doi.org/10.3103/S0027134923030165.

[2] Andrea, T., & Luca, S. (2023). Low-dimensional quantum gases in curved geometries. Nature Reviews Physics, 5(7), 398–406. https://doi.org/10.1038/s42254-023-00591-2

[3] Z., I. A. (2022). Controlled self-assembly of low-dimensional supramolecular systems based on double-decker lanthanide phthalocyaninates. Colloid Journal, 84(5), 633–641. https://doi.org/10.1134/S1061933X22700090

[4] T., R., L., L., O., A., & others. (2018). Experimental study of magneto-structural correlations in low-dimensional quantum magnets Cu(en)Cl₂ and Cu(tn)Cl₂. Acta Physica Polonica A, 133(3), 420–422. https://doi.org/10.12693/aphyspola.133.420

[5] Hee, L. Y., Sangil, H., Eunhae, K., & others. (2018). Structure optimization of low-dimensional quantum dots via anisotropic surface energy. Journal of the Korean Physical Society, 72(5), 582–587. https://doi.org/10.3938/jkps.72.582

[6] Dandan, M., Haisheng, R., & Jianyi, M. (2018). Full-dimensional quantum mechanics calculations for the spectroscopic characterization of the isomerization transition states of HOCO/DOCO systems. Physical Chemistry Chemical Physics, 20(7), 4732–4738. https://doi.org/10.1039/c7cp07673h

[7] Evgeniya, K., K., K. S., Dmitry, P., & others. (2023). Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures. Monte Carlo Methods and Applications, 29(4), 307–322. https://doi.org/10.1515/MCMA-2023-2019

[8] O., L. M., & O., K. L. (2021). Features of electron transport in two-dimensional quantum superlattices with the non-associative dispersion law. Semiconductors, 55(3), 319–327. https://doi.org/10.1134/S1063782621030143

[9] Kamelander, G. (1990). Alpha-particle transport studies using a modified Fokker-Planck equation and semiempirical transport laws. Fusion Technology, 18(3), 384–388. https://doi.org/10.13182/FST90-A29271

[10] Saeedi, S., & Faizabadi, E. (2020). Lead position and lead-ring coupling effects on the spin-dependent transport properties in a two-dimensional network of quantum nanorings in the presence of Rashba spin–orbit interaction. Journal of Computational Electronics, 19(3), 1–17. https://doi.org/10.1007/s10825-020-01506-5

[11] An, D., & Lin, L. (2020). Quantum dynamics with the parallel transport gauge. Multiscale Modeling & Simulation, 18(2), 612–645. https://doi.org/10.1137/18M1179304

[12] Yuqiao, G., Baohu, D., Jing, P., & others. (2019). Electron transport in low dimensional solids: A surface chemistry perspective. Journal of the American Chemical Society, 141(2), 723–732. https://doi.org/10.1021/jacs.8b09821

[13] Bell, T. M., Douçot, B., Gershenson, E. M., & others. (2018). Josephson ladders as a model system for 1D quantum phase transitions. Comptes Rendus - Physique, 19(6), 484–497. https://doi.org/10.1016/j.crhy.2018.09.002

[14] C., W. M., L., Y. J., W., L. K., & others. (2021). Low-dimensional modelling of n-type doped silicene and its carrier transport properties for nanoelectronic applications. Advances in Nano Research, 10(5), 415–422. https://doi.org/10.12989/ANR.2021.10.5.415

[15] Hongwei, S., Anyang, L., Minghui, Y., & others. (2017). Competition between the H- and D-atom transfer channels in the H₂O⁺ + HD reaction: reduced-dimensional quantum and quasi-classical studies. Physical Chemistry Chemical Physics, 19(26), 17396–17403. https://doi.org/10.1039/c7cp02889j

[16] S., E. S., S., R., M., C., & others. (2019). Band-like electron transport in 2D quantum dot periodic lattices: the effect of realistic size distributions. Physical Chemistry Chemical Physics, 21(46), 25872–25879. https://doi.org/10.1039/c9cp04465e

[17] Grasselli, F. (2017). Variational approach to the soft-Coulomb potential in low-dimensional quantum systems. American Journal of Physics, 85(11), 834–839. https://doi.org/10.1119/1.4994809