There are compounds whose structures support superconductivity at high temperatures. They have intra and inter-band interactions which occur within their bands. However there has been no hybrid Hamiltonian developed so far for a lattice structure that can support conduction by both D-waves and other waves on the same Fermi surface. These waves interact or change from one type to another on the same Fermi surface as they travel. The occurrences of interactions within and across bands with different waves lead to variations in transition temperature and resistance. To address these effects, theories that have been developed consider only S-wave and do not adequately account for the differences when compared with experimental observations. Therefore there was a need to advance efforts towards formulation of a theory that would explain differences in the characteristics of compounds that have D-waves and other waves on the same Fermi surface. In advancing these efforts a hybrid system has been developed that takes into consideration intra and inter-band interactions that have introduced new interaction dimensions. These efforts have helped in the understanding of how to achieve a high transition temperature superconductor, which a two band hybrid Hamiltonian has been determined for a Fermi surface with varying fermions density and hybridization terms. It is from it that thermodynamic properties have been obtained by use of the Green’s function. Where the correlation function has been substituted in the second quantized Hamiltonian form and the energy gap derived. This enabled us to calculate the thermodynamic potential and energy density. These properties have helped not only in the understanding of multi-component type II superconductors, but more so in the development of high transition temperature superconductors needed for magnetic resonance imaging, high speed data transmission and energy transfers. In this research, inter-band interaction has been considered on a new dimension. Consequently a new Hamiltonian has been formulated and thermodynamic properties derived using the Green’s function. These properties show the possibility of attaining high transition temperature superconductivity.
| Published in | World Journal of Applied Physics (Volume 1, Issue 2) |
| DOI | 10.11648/j.wjap.20160102.16 |
| Page(s) | 67-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Energy Gap, Phase Transition, Coupling, D-Wave, Hybrid, Superconductivity, Hamiltonian
| [1] | Agarrwal, B., & Eisner, M. (1991). Statistical Mechanics. Delhi: Wiley Eastern Limited. |
| [2] | Callaway, J. (1958). Energy band theory. New York: academic press. |
| [3] | Gopalakrishnan, J., Chintamani, N., & Ramachandra, R. (1997). New DIrections in chemistry. london: cambridge university press. |
| [4] | Ostrovoski. (2010). Kinetic Equations for a Dirty Two-Band Superconductor. Karmiel 21982. |
| [5] | Artjom and Kullike. (2013). Two gap superconductivity:interband interaction in the role of an external field.teetord Iop Publishing, 1-10. |
| [6] | Rout, G., & Das, S. (2000). Temperature Dependance of superconducting gap of heavy fermions system. American journal of Science, 17-26. |
| [7] | Maskalenko, D., & Mat, C. (1959). Superconductivity interband and intraband interactions. mettaloved,503, 45-49 |
| [8] | Okoye, C. (1998). Greens functions and gap equation in hybridization two band model of superconductivity. chinese journal of physics, 204-211. |
| [9] | Komendova, Yajiang, & Shenenko. (2012). Two band superconductors;hidden critically deep in superconducting state. physical revew letter, 408-416. |
| [10] | Shannon and Milosevic. (2011). Gauge invariance in superconductivity. phys.rev.letter. |
| [11] | Alexander, L., & Walecka, D. (2002). Quantum theory of many particle systems. Mineola New York: Dover publications. |
| [12] | Lubashevsky, Y., Lahoud, E., Chaska, K., Podolsky, D., & Kanigel, A. (2001). Fermi energy levels. American journal of physics, 1107-1487. |
| [13] | Suhl, H., Mathias, T., & Walker, L. R. (1959). Superconductivity. physical Review Letter 3552, 552-555. |
| [14] | Johan Carlstrom, EgorBabaev and Martin Speight. (2010). Type 1.5 superconductivity in multiband systems;the effects of interband couplings. physics.Rev let 105,067003. |
| [15] | Chen, Y., Huang, P. H., Wang, C. R., Y. D. Yao, & Lee, T. K. (2007). Kondo Interactions and Magnetic Correlations in CePt2 Nanocrystals. physical review letters, 1-4. |
| [16] | Babis, A. (2010). Quantum Field Theory. zurinch: Institute of theoretical physics. |
APA Style
Otimo Solomon, Thomas Sakwa, Ayodo Yudah Kennedy, James Sifuna. (2017). Quantum Phase Transition: Intra and Inter-Band Interaction on D- Wave Superconductivity. World Journal of Applied Physics, 1(2), 67-82. https://doi.org/10.11648/j.wjap.20160102.16
ACS Style
Otimo Solomon; Thomas Sakwa; Ayodo Yudah Kennedy; James Sifuna. Quantum Phase Transition: Intra and Inter-Band Interaction on D- Wave Superconductivity. World J. Appl. Phys. 2017, 1(2), 67-82. doi: 10.11648/j.wjap.20160102.16
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.wjap.20160102.16,
author = {Otimo Solomon and Thomas Sakwa and Ayodo Yudah Kennedy and James Sifuna},
title = {Quantum Phase Transition: Intra and Inter-Band Interaction on D- Wave Superconductivity},
journal = {World Journal of Applied Physics},
volume = {1},
number = {2},
pages = {67-82},
doi = {10.11648/j.wjap.20160102.16},
url = {https://doi.org/10.11648/j.wjap.20160102.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20160102.16},
abstract = {There are compounds whose structures support superconductivity at high temperatures. They have intra and inter-band interactions which occur within their bands. However there has been no hybrid Hamiltonian developed so far for a lattice structure that can support conduction by both D-waves and other waves on the same Fermi surface. These waves interact or change from one type to another on the same Fermi surface as they travel. The occurrences of interactions within and across bands with different waves lead to variations in transition temperature and resistance. To address these effects, theories that have been developed consider only S-wave and do not adequately account for the differences when compared with experimental observations. Therefore there was a need to advance efforts towards formulation of a theory that would explain differences in the characteristics of compounds that have D-waves and other waves on the same Fermi surface. In advancing these efforts a hybrid system has been developed that takes into consideration intra and inter-band interactions that have introduced new interaction dimensions. These efforts have helped in the understanding of how to achieve a high transition temperature superconductor, which a two band hybrid Hamiltonian has been determined for a Fermi surface with varying fermions density and hybridization terms. It is from it that thermodynamic properties have been obtained by use of the Green’s function. Where the correlation function has been substituted in the second quantized Hamiltonian form and the energy gap derived. This enabled us to calculate the thermodynamic potential and energy density. These properties have helped not only in the understanding of multi-component type II superconductors, but more so in the development of high transition temperature superconductors needed for magnetic resonance imaging, high speed data transmission and energy transfers. In this research, inter-band interaction has been considered on a new dimension. Consequently a new Hamiltonian has been formulated and thermodynamic properties derived using the Green’s function. These properties show the possibility of attaining high transition temperature superconductivity.},
year = {2017}
}
TY - JOUR T1 - Quantum Phase Transition: Intra and Inter-Band Interaction on D- Wave Superconductivity AU - Otimo Solomon AU - Thomas Sakwa AU - Ayodo Yudah Kennedy AU - James Sifuna Y1 - 2017/01/18 PY - 2017 N1 - https://doi.org/10.11648/j.wjap.20160102.16 DO - 10.11648/j.wjap.20160102.16 T2 - World Journal of Applied Physics JF - World Journal of Applied Physics JO - World Journal of Applied Physics SP - 67 EP - 82 PB - Science Publishing Group SN - 2637-6008 UR - https://doi.org/10.11648/j.wjap.20160102.16 AB - There are compounds whose structures support superconductivity at high temperatures. They have intra and inter-band interactions which occur within their bands. However there has been no hybrid Hamiltonian developed so far for a lattice structure that can support conduction by both D-waves and other waves on the same Fermi surface. These waves interact or change from one type to another on the same Fermi surface as they travel. The occurrences of interactions within and across bands with different waves lead to variations in transition temperature and resistance. To address these effects, theories that have been developed consider only S-wave and do not adequately account for the differences when compared with experimental observations. Therefore there was a need to advance efforts towards formulation of a theory that would explain differences in the characteristics of compounds that have D-waves and other waves on the same Fermi surface. In advancing these efforts a hybrid system has been developed that takes into consideration intra and inter-band interactions that have introduced new interaction dimensions. These efforts have helped in the understanding of how to achieve a high transition temperature superconductor, which a two band hybrid Hamiltonian has been determined for a Fermi surface with varying fermions density and hybridization terms. It is from it that thermodynamic properties have been obtained by use of the Green’s function. Where the correlation function has been substituted in the second quantized Hamiltonian form and the energy gap derived. This enabled us to calculate the thermodynamic potential and energy density. These properties have helped not only in the understanding of multi-component type II superconductors, but more so in the development of high transition temperature superconductors needed for magnetic resonance imaging, high speed data transmission and energy transfers. In this research, inter-band interaction has been considered on a new dimension. Consequently a new Hamiltonian has been formulated and thermodynamic properties derived using the Green’s function. These properties show the possibility of attaining high transition temperature superconductivity. VL - 1 IS - 2 ER -
Information
Email: