1. RF Nonlinearity in Thin-Film and Bulk Superconductors: A Mechanism for Cavity Q-Drop Behnood G. Ghamsari, Tamin Tai, Steven M. Anlage Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland

2. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 2 Quality Factor Mechanisms of Energy Loss: Ohmic Dissipation and Joule Heating Radiation Nonlinearities (Poynting Theorem)

3. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 3 Nonlinearity and Harmonic Generation In the absence of nonlinearity, the resonator comprises a single harmonic oscillator, despite the level of sophistication in its physical realization. Second Harmonic GenerationThird Harmonic Generation

4. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 4 Nonlinearity and Harmonic Generation When the nonlinear processes become significant? Second Harmonic Generation Third Harmonic Generation

5. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 5 Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors

6. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 6 Order Parameter Order parameter is a phenomenological measure of superconductivity as defined in the Ginsburg-Landau equation. Superconductivity may be destroyed through heating, applying strong magnetic field, or flowing high transport currents, which lead to the definition of T c, B c, and J c. Long before superconductivity quenches, order parameter begins to fluctuate, which gives rise to microwave nonlinearities.

7. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 7 Order Parameter Modulation Nonlinearity Order parameter modulation (OPM) predominantly generates odd harmonics. If dissipation is also significant, even harmonics can be generated as well. Third harmonic generation is the most prominent result of OPM:

8. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 8 For Niobium, which is an s-wave BSC superconductor, order parameter modulation won’t arise until T c, B c, and J c are approached. Therefore, this type of nonlinearity is significant in Niobium only near the quench point and is not a primary concern at normal operation conditions, unless defects induce localized nonlinear sites. For nodal superconductors, the order parameter modulation nonlinearity sustains, and even enhances, at low temperatures. JxJx J xy Order Parameter Modulation Filled Fermi Sea ss kxkx kyky Dahm and Scalapino, J. Appl. Phys. (81), 1997

9. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 9 It has been conjectured that MgB 2 may have a six-fold nodal structure. D. E. Oates, Y. D. Agassi, and B. H. Moeckly, Supercond. Sci. Technol. 23 034011, (2010). If this turns out to be correct, then MgB 2, which has been sought to be used as a coating to Nb, will show strong nonlinearity at low temperatures! Order Parameter Modulation Measurement under loop probe (a ~1mm diameter) Measurement under magnetic writer probe

10. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 10 Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors

11. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 11 Nonlinear Vortex Dynamics In the Meissner state, screening currents at the surface of the superconductor expel magnetic flux from the interior. If the applied field exceed H c1, vortices enter the superconductor. The repulsion between the screening current and the vortices, on one hand, and attraction between a vortex and it’s image at the surface, on the other hand, leads to an anharmonic oscillation of the vortices. A. Gurevich and G. Ciovati, Phys. Rev. B, 77, 104501(2008)

12. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 12 As the fundamental harmonic varies in time, the reluctance of the cavity also varies in time due to introduction and anhilation of vortices. Therefore, the magnetic flux becomes time-dependent. The rate of changes in the magnetic flux gives the electric voltage. Since the variation of the reluctance/flux are nonlinear with respect to the applied field, the voltage contains higher harmonics. Nonlinear Vortex Dynamics Magnetic Circuit Equivalent to an SRF Cavity

13. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 13 Nonlinear Vortex Dynamics Microwave Microscopy on Bulk Nb

14. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 14 Nonlinear Vortex Dynamics in Thin Films In thin films comparable to a penetration depth, vortex and anti-vortex pairs form. The number and distance between vortex-antivortex pairs is determined by the strength of the external magnetization m. Annihilation of vortex-antivortex pairs generates burst voltages rich of harmonics of the fundamental driving frequency.

15. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 15 Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors

16. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 16 Interband Josephson Coupling Liu, Mazin and Kortus (2002); Choi et al, (2002) Big gap,    7.2 meV Small gap,    2.1meV At T cσ  39K, the σ band goes superconducting and the normal π band becomes superconducting through the proximity effect. Since the superconductivity of the π band relies on the σ band, their order parameter phases are locked, and MgB 2 may be nearly treated as a single band superconductor for T cπ <T <T cσ. Below T cπ, the π band can become superconducting independently. Under certain circumstances, the phase of different bands may become unequal. [ Gurevich and Vinokur, PRL (90), 2003.] A Josephson coupling can establish between the bands, which is also referred to as the Leggett mode.

17. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 17 Interband Josephson Coupling Exposed to Air Minimal Exposure to Air

18. 5th International Workshop on Thin Films and New Ideas for Pushing the Limits of RF Superconductivity Thomas Jefferson National Accelerator Facility, Newport News, VA July 18-20, 2012 18 Conclusions Nonlinear processes can take power from the fundamental mode to generate harmonics, thereby, reducing the quality factor of the cavity. Modulation of superconducting order parameter, due to high field or currents, can generate strong odd harmonics. In nodal superconductors, order parameter modulation generates strong third order nonlinearity at low temperatures. Nonlinear vortex dynamics give rise to nonlinear RF response in thin films as well as bulk materials. Two-band superconductors such as MgB 2 are susiptible to interband Josephson transitions at low- temperatures. Our measurements on MgB 2 reveals enhanced nonlinearity at low temperatures, which are consistent with the order parameter modulation of a nodal superconductor as well as the interband Josephson nonlinearity of a multi-band superconductor. Our measurements on Nb nonlinearities (bulk and thin film) are consistent with vortex nonlinearity.