Theoretical Study of Specific Heat and Density of States of MgB₂ Superconductor in Two Band Model

Anuj Nuwal, Shyam Lal Kakani

Department of Physics, Sangam University, Bhilwara, India.
Shastri Nagar, New Housing Board, Bhilwara, India.

DOI: 10.4236/wjcmp.2013.31006                

Abstract

MgB₂ with T_c ≈ 40 K, is a record-breaking compound among the s-p metals and alloys. It appears that this material is a rare example of the two band electronic structures, which are weakly connected with each other. Experimental results clearly reveal that boron sub-lattice conduction band is mainly responsible for superconductivity in this simple compound. Experiments such as tunneling spectroscopy, specific heat measurements, and high resolution spectroscopy show that there are two superconducting gaps. Considering a canonical two band BCS Hamiltonian containing a Fermi Surface of π- and σ-bands and following Green’s function technique and equation of motion method, we have shown that MgB₂ possess two superconducting gaps. It is also pointed out that the system admits a precursor phase of Cooper pair droplets that undergoes a phase locking transition at a critical temperature below the mean field solution. Study of specific heat and density of states is also presented. The agreement between theory and experimental results for specific heat is quite convincing. The paper is organized in five sections: Introduction, Model Hamiltonian, Physical properties, Numerical calculations, Discussion and conclusions.

 

Keywords

Green’s Function; p and d Holes; Specific Heat; Density of States

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, “Superconductivity at 39 K in Magnesium Diboride,” Nature, Vol. 410, No. 6824, 2001, pp. 63-64. doi:10.1038/35065039
[2]	C. Buzea and T. Yamashita, “Review of the superconducting properties of MgB2,” Superconductor Science and Technology, Vol. 14, No. 11. 2001, p. R115.
[3]	S. L. Kakani, S. Kakani, “Superconductivity,” Anshan, Ltd., Kent, 2009.
[4]	A. Y. Liu, I. I. Mazin and J. Kortus, “Beyond Eliashberg Superconductivity in MgB2: Anharmonicity, Two-Phonon Scattering, and Multiple Gaps,” Physical Review Letters, Vol. 87, No. 8, 2001, pp. 087005-087009. doi:10.1103/PhysRevLett.87.087005
[5]	J. M. An and W. E. Pickett, “Superconductivity of MgB2: Covalent Bonds Driven Metallic,” Physical Review Letters, Vol. 86, No. 19, 2001, pp. 4366-4369. doi:10.1103/PhysRevLett.86.4366
[6]	K. D. Belaschenko, M. von Schilfgaarde and A. V. Antropov, “Coexistence of Covalent and Metallic Bonding in the Boron Intercalation Superconductor MgB2,” Physical Review B, Vol. 64, No. 9, 2001, pp. 092503-092507. doi:10.1103/PhysRevB.64.092503
[7]	D. A. Papaconstantopoulos and M. J. Mehl, “Precise TightBinding Description of the Band Structure of MgB2,” Physical Review B, Vol. 64, No. 17, 2001, pp. 2510-2514
[8]	I. I. Mazin and V. P. Antropo, “Electronic Structure, Electron-Phonon Coupling, and Multiband Effects in MgB2,” Physica C: Superconductivity, Vol. 385, No. 1-2, 2003, pp. 49-65. doi:10.1016/S0921-4534(02)02299-2
[9]	F. Bouqut, Y. Wang, R. A. Fisher, D. G. Hinks, J. D. Jorgensen, A. Junod and N. E. Phillips, “Phenomenological Two-Gap Model for the Specific Heat of MgB2,” Europhysics Letters, Vol. 56, No. 6, 2001, p. 856. doi:10.1209/epl/i2001-00598-7
[10]	F. Bouquet, R. A. Fisher, N. E. Phillips, D. G. Hinks and D. Jorgensen, “Specific Heat of Mg11B2: Evidence for a Second Energy Gap,” Physical Review Letters, Vol. 87, No. 4, 2001, pp. 047001-047005. doi:10.1103/PhysRevLett.87.047001
[11]	Y. Wang, T. Plackowski and A. Junod, “Specific Heat in the Superconducting and Normal State (2-300 K, 0-16 T), and Magnetic Susceptibility of the 38 K Superconductor MgB2: Evidence for a Multicomponent Gap,” Physica C: Superconductivity, Vol. 355, No. 3-4, 2001, pp. 179-193. doi:10.1016/S0921-4534(01)00617-7
[12]	G. A. Ummarino, R. S. Gonnelli, S. Massidda and A. Bianconi, “Electron-Phonon Coupling and Two-Band Superconductivity of Aland C-Doped MgB2,” 2010.
[13]	S. L. Bud’ko, G. Lapertot, C. Petrovic, C. E. Cunningham, N. Anderson and P. C. Canfield, “Boron Isotope Effect in Superconducting MgB2,” Physical Review Letters, Vol. 86, No. 9, 2001, pp. 1877-1880. doi:10.1103/PhysRevLett.86.1877
[14]	H. Shul, B. T. Matthias and L. R. Walker, “Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands,” Physical Review Letters, Vol. 3, No. 12, 1959, pp. 552-554. doi:10.1103/PhysRevLett.3.552
[15]	V. A. Moskalenko, M. E. Palistrant and V. M. Vakalyuk, “High-Temperature Superconductivity and the Characteristics of the Electronic Energy Spectrum,” Soviet Physics Uspekhi, Vol. 34, No. 8, 1991, p. 717. doi:10.1070/PU1991v034n08ABEH002466
[16]	N. Kristoffel, P. Konsin and T. Ord, “Two-Band Model for High-Temperature Superconductivity,” Rivista Del Nuovo Cimento, Vol. 17, No. 9, 1994, pp. 1-41. doi:10.1007/BF02724515
[17]	N. Kristoffel and P. Rubin, “Pseudogap and Superconductivity Gaps in a Two Band Model with Doping Determined Components,” Solid State Communications, Vol. 122, No. 5, 2002, pp. 265-268.
[18]	B. K. Chakraverty, “Superconductivity in Two Band Model,” Physical Review B, Vol. 48, No. 6, 1993, pp. 4047-4053. doi:10.1103/PhysRevB.48.4047
[19]	R. Lal, Ajay, R. L. Hota and S. K. Joshi, “Model for c-Axis Resistivity of Cuprate Superconductors,” Physical Review B, Vol. 57, No. 10, 1998, pp. 6126-6136. doi:10.1103/PhysRevB.57.6126
[20]	A. Pratap, Ajay and A. S. Tripathi, “Effect of Interlayer Interactions in High-Tc Cuprate Supercoductors,” Journal of Superconductivity, Vol. 9, No. 6, 1996, pp. 595-597. doi:10.1007/BF00728239
[21]	S. Khandka and P. Singh, “Effect of Interlayer Interaction on Tc with Number of Layers in High Tc Cuprate Superconductors,” Physica Status Solidi B, Vol. 244, No. 2, 2007, pp. 699-708. doi:10.1002/pssb.200542285
[22]	S. Das and N. C. Das, “ Erratum: Theory of Hole Superconductivity,” Physical Review B, Vol. 46, No. 10, 1992, pp. 6451-6457. doi:10.1103/PhysRevB.46.6451
[23]	S. L. Kakani and U. N. Upadhyaya, “Cooperative Phenomena in Ternary Superconductors,” Journal of Low Temperature Physics, Vol. 53, No. 1-2, 1983, pp. 221-253. doi:10.1007/BF00685781
[24]	S. L. Kakani and U. N. Upadhyaya, “Superconducting and Magnetic Order Parameters in the Coexistence Region of Ternary Superconductors,” Physica Status Solidi B, Vol. 125, No. 2, 1984, pp. 861-867. doi:10.1002/pssb.2221250249
[25]	S. L. Kakani and U. N. Upadhyaya, “Frequency Dependent Susceptibility of Rare Earth Ternary Superconductors,” Physica Status Solidi B, Vol. 136, No. 1, 1986, pp. 115-121. doi:10.1002/pssb.2221360113
[26]	S. L. Kakani and U. N. Upadhyaya, “Coexistence of Superconductivity and Ferromagnetism in Rare Earth Ternary Systems,” Physica Status Solidi A, Vol. 99, No. 1, 1987, pp. 15-36. doi:10.1002/pssa.2210990104
[27]	S. L. Kakani and U. N. Upadhyaya, “Magnetic Superconductors: A Review,” Journal of Low Temperature Physics, Vol. 70, No. 1-2, 1988, pp. 5-82. doi:10.1007/BF00683246
[28]	A. L. Fetter and J. D. Walecka, “Quantum Theory of Many Particle Physics,” McGraw-Hill, New York, 1971.
[29]	C. Buzea and T. Yamashita, “Review of the Superconducting Properties of MgB2,” Superconductor Science and Technology, Vol. 14, No. 11, 2001, p. R115. doi:10.1088/0953-2048/14/11/201
[30]	C. Walti, E. Felder, C. Degen, G. Wigger, R. Monnier, B. Delley and H. R. Ott, “Strong Electron-Phonon Coupling in Superconducting MgB2: A Specific Heat Study,” Physical Review B, Vol. 64, No. 17, 2001, pp. 172515172519. doi:10.1103/PhysRevB.64.172515
[31]	N. E. Phillips and R. A. Fisher, “Superconducting-State Energy Gap Parameters from Specific Heat Measurements,” Journal of Thermal Analysis and Calorimetry, Vol. 81, No. 3, 2005, pp. 631-635. doi:10.1007/s10973-005-0835-y
[32]	S. L. Kakani, “Superconductivity: Current Topics: Chapters 2 and 3,” Bookman Associate, Jaipur, 1999.
[33]	S. Kakani and S. L. Kakani, “Theoretical Study of Specific Heat, Density of States and Free Energy of Itinerant Ferromagnetic Superconductor URhGe,” Journal of Superconductivity and Novel Magnetism, Vol. 22, No. 7, 2009, pp. 677-685. doi:10.1007/s10948-009-0465-x
[34]	A. Kashyap, S. C. Tiwari, A. Surana, R. K. Paliwal and S. L. Kakani, “Theoretical Study of Specific Heat, Density of States, Free Energy,and Critical Field of High Temperature Cuprate Superconductors Based on Intra and Interlayer Interactions,” Journal of Superconductivity and Novel Magnetism, Vol. 21, No. 2, 2008, pp. 129-143. doi:10.1007/s10948-008-0308-1
[35]	A. Nuwal, R. K. Paliwal, S. L. Kakani and M. L. Kalara, “Theoretical study of Photoinduced Superconductors in a Two Band Model,” Physica C: Superconductivity, Vol. 471, No. 9-10, 2011, pp. 318-331. doi:10.1016/j.physc.2011.03.004
[36]	G. Alecu, “Reports in Physics,” Romanian Reports in Physics, Vol. 56, No. 3, 2004, pp. 404-412.