RF Nonlinearity in ThinFilm and Bulk Superconductors A
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
Quality Factor (Poynting Theorem) Mechanisms of Energy Loss: • Ohmic Dissipation and Joule Heating • Radiation • Nonlinearities 5 th 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
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 Generation 5 th 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 Third Harmonic Generation 3
Nonlinearity and Harmonic Generation When the nonlinear processes become significant? Second Harmonic Generation 5 th 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 Third Harmonic Generation 4
Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors 5 th 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
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 Tc, Bc, and Jc. Long before superconductivity quenches, order parameter begins to fluctuate, which gives rise to microwave nonlinearities. 5 th 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 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: 5 th 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 • For Niobium, which is an s-wave BSC superconductor, order parameter modulation won’t arise until Tc, Bc, and Jc 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. s ky Filled Fermi Sea Jxy kx Jx Dahm and Scalapino, J. Appl. Phys. (81), 1997 5 th 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
Order Parameter Modulation • It has been conjectured that Mg. B 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 Mg. B 2, which has been sought to be used as a coating to Nb, will show strong nonlinearity at low temperatures! Measurement under magnetic writer probe Measurement under loop probe (a ~1 mm diameter) 5 th 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
Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors 5 th 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
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 Hc 1, 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) 5 th 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 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. Magnetic Circuit Equivalent to an SRF Cavity 5 th 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
Nonlinear Vortex Dynamics Microwave Microscopy on Bulk Nb 5 th 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 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. 5 th 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
Mechanisms of Nonlinearity in Superconductors 1) Modulation of the Superconducting Order Parameter 2) Nonlinear Vortex Dynamics 3) Interband Josephson Coupling in Two-Band Superconductors 5 th 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
Interband Josephson Coupling • At Tcσ� 39 K, 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 Mg. B 2 may be nearly treated as a single band superconductor for Tcπ <T <Tcσ. • Below Tcπ, the π band can become superconducting independently. Big gap, • Under certain circumstances, the phase of different bands 7. 2 me. V Small gap, 2. 1 me. V 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. Liu, Mazin and Kortus (2002); Choi et al, (2002) 5 th 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 • Exposed to Air 5 th 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 Minimal Exposure to Air 17
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 Mg. B 2 are susiptible to interband Josephson transitions at lowtemperatures. • Our measurements on Mg. B 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. 5 th 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
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