Simultaneous Effects of Temperature and Pressure on the Entropy and the Specific Heat of a Three-Dimensional Quantum Wir
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Simultaneous Effects of Temperature and Pressure on the Entropy and the Specific Heat of a Three‑Dimensional Quantum Wire: Tsallis Formalism R. Khordad1 · Ar. Firoozi1 · H. R. Rastegar Sedehi2 Received: 27 July 2020 / Accepted: 3 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this work, the finite-difference time domain (FDTD) has been employed to calculate the energy levels and wave functions of a three-dimensional (3D) cylindrical quantum wire. The inside of the wire is at zero potential, and the background medium is 4.6 eV. This is a true 3D procedure based on a direct implementation of the time-dependent Schrödinger equation. Here, the dependence on the pressure and the temperature of the electronic effective mass is used. We study the effects temperature and pressure simultaneously on the entropy and the specific heat of the system using the Tsallis formalism. The results show that (i) the specific heat obtained by Tsallis has a peak structure. (ii) The entropy has almost the same values at very low temperatures with different pressures. (iii) The peak value of the specific heat with enhancing the pressure shifts toward lower temperatures. (iv) The peak value of the specific heat and its position depend on the value of the entropic index q. Keywords Quantum wires · FDTD · Entropy · Specific heat
1 Introduction After introducing the concepts of quantum wires and quantum dots in 1975 [1], a lot of theory and experimental work has been devoted to the understanding of energy states in quantum wires and dots [2, 3]. The study of wire-like semiconductor structures with nanometer sizes has been a revolutionary fact in the physics that has allowed for undoubted milestones in the technology of electronic and optoelectronics devices [4–7]. Many investigations have been performed in this
* R. Khordad [email protected] 1
Department of Physics, College of Sciences, Yasouj University, 75914‑353 Yasouj, Iran
2
Department of Physics, Jahrom University, 74137‑66171 Jahrom, Iran
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Vol.:(0123456789)
Journal of Low Temperature Physics
context. So, to get more information, the reader can refer to the book by Harrison (and the number of references therein) [8]. There are some works regarding electronic, magnetic, optical and thermodynamic properties of quantum wires [9–14]. For example, Ghosh et al. [15–17] have studied diamagnetic susceptibility, dielectric function, electro-optic effect and third-order nonlinear optical susceptibility of quantum dot under simultaneous effects of temperature and pressure. Even a report on electron g-factor in quantum wires in the presence of spin–orbit Rashba coupling and magnetic field has been presented in Refs.[18–20]. To determine the eigenenergies and eigenfunctions of quantum wires with considering a given confining potential, one should solve the Schrödinger equation analytically or numerically. To solve numerically the Schrödinger equation, there are several methods such as diagonalization procedure, finite difference met
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