1. Superconductivity of MgB2 Zhiping Yin Mar. 14, 2007 Final project of Advanced electronic structure course PHY250-6

2. Outline Experiment Electronic structure Phonons Summary

3. Akimitsu’s Discovery: 2001 MgB2: an intercalated graphite-like system Searching for ferromagnetism, superconductivity near 40K was discovered in 2001 Quickly reproduced and synthesis techniques were extended by several groups Crystal Structure is simple: quasi-2D Electronic structure is simple: s-p electrons, intermetallic compound. CENTRAL QUESTION: What is the origin of high T C in MgB2? J. Nagamatsu, et al., Nature (London) 410, 63 (2001) T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001)

4. Top papers 1. Superconductivity at 39 K in magnesium diboride J. Nagamatsu, et al., Nature (London) 410, 63 (2001). 2. Boron isotope effect in superconducting MgB2 S. L. Bud'ko, et al., Phys. Rev. Lett. 86, 1877 (2001). 3. Superconductivity of metallic boron in MgB2 J. Kortus, et al., Phys. Rev. Lett. 86, 4656 (2001). 4. Thermodynamic and Transport Properties of Superconducting Mg(^10)B2 D. K. Finnemore, et al., Phys. Rev. Lett. 86, 2420 (2001). 5. Superconductivity in Dense MgB2 Wires P. C. Canfield, et al., Phys. Rev. Lett. 86, 2423 (2001). 6. Superconductivity of MgB2: Covalent Bonds Driven Metallic J. M. An and W. E. Pickett, Phys. Rev. Lett. 86, 4366 (2001). 7. Giant Anharmonicity and Nonlinear Electron-Phonon Coupling in MgB2: A Combined First- Principles Calculation and Neutron Scattering Study T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001). 8. Electron-phonon interaction in the normal and superconducting states of MgB2 Y. Kong, et al., Phys. Rev. B. 64, 020501(R) (2001).

5. Electronic structure Near Fermi level almost B p character, other contributions are very small. All bands are highly dispersive (light). p z bands are quite isotropic, 3D, cross Ef p x,y bands are 2D, only two (bonding) of them cross Ef. 2D character contribute > 30% to N(0). p z bands hybridize with the empty Mg s band, increasing the effective ionicity. Bands can be perfectly described by tight binding model with Hole-type conduction bands like the high-Tc cuprates. (0.28,0.59) Multiple gaps. J. Kortus, et al., Phys. Rev. Lett. 86, 4656 (2001). J. M. An and W. E. Pickett, Phys. Rev. Lett. 86, 4366 (2001). T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001).

6. phonons Deformation potential D=13 eV/A (amazingly large for a metal) B-B boning sigma bands couple rather strongly to optical B-B bond-stretching modes with wave numbers around 600 cm^(-1) (74meV) El-ph coupling strength for s-wave pairing yields lambda~0.8 E2g mode is hihgly anharmonic, nonlinear contributions to EPC. Y. Kong, et al., Phys. Rev. B. 64, 020501(R) (2001). A. Y. Liu, et al., Phys. Rev. Lett. 87, 87005 (2001).

7. In-plane boron modes T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001).

8. Summary covalent bonds become metallic. Large d eformation potential D=13 eV/A 2D (cylinder) Fermi surfaces focus strength. Yet structure remains stable: intrinsic covalency. Phonon mediated pairing s-wave. Mediate el-ph coupling constant ~ 0.8. (Holes in the B-B bonding sigma bands, relative softness of the optical bond-stretching modes.) Strongest coupling of the in-plane B motion, which is anharmonic. High frequency contributes most to Tc. Boron isotope effect gives Delta Tc=1.0 K, which further confirms that boron phonon modes are playing an important role in the superconductivity of MgB2.