ASYMMETRIC SPECIAL POTENTIALS IN LOW-DIMENSIONAL SYSTEMS
B.G. Ibragimov1,2, Z.S. Agayev1
   download pdf   

ABSTRACT

Asymmetric Special Potentials arise when spatial inversion symmetry is broken, leading to profound changes in confinement, spectra, tunneling, and transport. This review summarizes the theoretical foundations and mathematical structure of Asymmetric Special Potentials, highlights their impact on quantum wells, wires, and dots, and explores experimental realizations in semiconductor and photonic platforms. Key results—parity mixing, asymmetric tunneling, non-reciprocal propagation, and activated forbidden transitions—are highlighted. Asymmetric Special Potentials provide a unified framework for a new generation of quantum and optoelectronic devices.

Keywords: Asymmetric special potentials, quantum wells, wires, and dots, optical selection rules.
DOI:10.70784/azip.1.2025431

Received: 02.12.2025
Internet publishing: 19.12.2025    AJP Fizika E 2025 04 en p.31-39

AUTHORS & AFFILIATIONS

1. Institute of Physics, Ministry of Science and Education of Azerbaijan, H. Javid av.131, Baku
2. Azerbaijani-French University
E-mail: behbud.ibrahimov@ufaz.az

 [1]   P.M. Morse. 1929. Diatomic molecules according to the wave mechanics. Physical Review, 34(1), 57–64.
[2]   G. Rosen, & P.M. Morse. 1932. On the vibrations of polyatomic molecules. Physical Review, 42(2), 210–217.
[3]   M. Razavy. 1980. Double-well potentials and quasisolutions to the Schrödinger equation. American Journal of Physics, 48(4), 285–288.
[4]   L.D. Landau, & E.M. Lifshitz. 1977. Quantum Mechanics: Non-relativistic Theory. Pergamon Press.
[5]   C. Kittel. 2005. Introduction to Solid State Physics (8th ed.). Wiley.
[6]   G. Bastard. 1988. Wave Mechanics Applied to Semiconductor Heterostructures. Wiley.
[7]   M. Grifoni, & P. Hänggi. 1998. Driven quantum tunneling. Physics Reports, 304(5), 229–354.
[8]   P. Reimann. 2002. Brownian motors: noisy transport far from equilibrium. Physics Reports, 361(2), 57–265.
[9]   A. Smerzi, A. Trombettoni, P.G. Kevrekidis, & A.R. Bishop. 2002. Dynamical superfluid-insulator transitions in asymmetric double-well potentials. Physical Review Letters, 89(17), 170402.
[10]  I. Bloch, J. Dalibard, & W. Zwerger. 2008. Many-body physics with ultracold gases. Reviews of Modern Physics, 80(3), 885.
[11]  V.M. Fomin. 2018. Physics of Quantum Rings. Springer.
[12]  R. Tsu. 2010. Superlattice to Nanoelectronics. Elsevier.
[13]  A.O. Caldeira, & A.J. Leggett. 1983. Quantum tunneling in dissipative systems. Annals of Physics, 149(2), 374–456.
[14]  U. Weiss. (2012). Quantum Dissipative Systems. World Scientific.
[15]  P. Hanggi, F. Marchesoni. 2009. Artificial Brownian motors: Controlling transport on the nanoscale. Reviews of Modern Physics, 81, 387–442.
[16]  H. Jensen. 1981. Quantum mechanical tunneling in asymmetric potentials. Journal of Physics A, 14(12), 3231.
[17]  P.F. Bagwell. 1990. Suppression of Josephson tunneling by asymmetric potentials. Physical Review B, 41(14), 10354.
[18]  Z. Yu, & S. Fan. 2009. Complete optical isolation created by indirect interband photonic transitions. Nature Photonics, 3(2), 91–94.
[19]  S. Longhi. 2010. Quantum-optical analogies using photonic lattices. Laser & Photonics Reviews, 3(3), 243–261.
[20]  M. Holthaus. 1992. Collapse of minibands in AC-driven superlattices. Physical Review Letters, 69(6), 351.
[21]  E.L. Ivchenko. 2005. Optical Spectroscopy of Semiconductor Nanostructures. Springer.
[22]  G. Bastard, E.E. Mendez, L.L. Chang, & L. Esaki. 1983. Electric field induced localization in superlattices. Physical Review B, 28(6), 3241.
[23]  A. Wacker. 2002. Semiconductor superlattices: a model system for nonlinear transport. Physics Reports, 357, 1–111.
[24]  B.P. Anderson, & M.A. Kasevich. 1998. Macroscopic quantum interference from asymmetric optical lattices. Science, 282(5394), 1686–1689. Cold-atom optik latticelərdə asymmetric interference patterns göstərilir.
[25]  D. Leibfried. 2003. Quantum dynamics of trapped ions. Reviews of Modern Physics, 75, 281–324.
[26]  L. Salasnich. 2011. Nonlinear Schrödinger equation with asymmetric potentials. Physical Review A, 84, 033620.
[27]  Y. Zhai. 2012. Asymmetric double-well solitons in nonlinear media. Optics Letters, 37(15), 3003–3005.
[28]  V. Peano, M. Houde, F. Marquardt, & A. Clerk. 2015. Topological phase transitions induced by asymmetric potentials. Nature Communications, 6, 5961.
[29]  A.H. Nayfeh, & D.T. Mook. 2008. Nonlinear Oscillations. Wiley.
[30]  P.S. Landa. 1996. Nonlinear oscillations and waves in dissipative systems.
[31]  Chen, Z., Segev, M., & Christodoulides, D. (2012). Optical spatial solitons and photonic lattices. Reports on Progress in Physics, 75(8), 086401.
[32]  L. Esaki. (1974). Superlattice and negative differential conductivity. IBM Journal of Research and Development.
[33]  M. Segev, & D. Christodoulides. 1994. Observation of self-trapped asymmetric beams. Physical Review Letters, 73(26), 3211.
[34]  W. Kohn. 1959. Analytic properties of Bloch waves in asymmetric periodic potentials. Physical Review, 115(4), 809.
[35]  M. Holthaus, & D.W. Hone. 1994. Tunneling in tilted periodic potentials. Physical Review B, 49(23), 16605.
[36]  Y. Lin, J.J. García-Ripoll, & C. Monroe. 2009. Quantum simulation of tunable asymmetric potentials. Physical Review Letters, 103(3), 030502.
[37]  R. Peierls. 1955. Quantum Theory of Solids. Oxford University Press.
[38]  H. Dekker. 1987. Classical and quantum mechanics in asymmetric double-well potentials. Physics Reports, 80(1), 1–112
[39]  S. Flach, O. Yevtushenko, & Y. Zolotaryuk. 2000. Directed current due to broken time-space symmetry. Physical Review Letters, 84, 2358.