1. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators A.P. Zhuravel*, S. M. Anlage #, and A. V. Ustinov Physikalisches Institut, Universität Erlangen-Nürnberg, Erlangen, Germany * Institute for Low temperature Physics and Engineering, Kharkov, Ukraine # Physics Department, Center for Superconductivity Research, University of Maryland, USA Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

2. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Motivation / Goals To image rf currents in operating superconducting microwave circuits and devices To identify sources of microwave nonlinearities in superconductors To investigate how rf currents are redistributed by  m- and nm- scale defects To develop new methods to investigate microwave nonlinearities in superconductors A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

3. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, Conventional Laser Scanning Microscopy (LSM) patterned superconducting film V laser beam laser power ac modulated lock-in voltmeter  V(x,y) measured signal y x dc current dc current 2 – 300 K

4. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Microwave imaging LSM combiner f1f1 spectrum analyzer lock-in computer 77 – 95 K laser beam YBCO film LAO substrate ground plane isolatorssources f2f2 crystal detector P IN P OUT amplifier switch A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, LSM

5. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Erlangen LSM setup A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

6. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Imaging modes of LSM A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,  optical contrast  dc voltage contrast;  thermoelectric response imaging  linear microwave contrast  nonlinear (intermodulation distortion) microwave contrast

7. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Principle of the measurement A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, P out f f0f0 |S 21 (f 0 )| 2 laser OFF laser ON co-planar resonator f 0 ~ 5.2 GHz P in modulated laser resonator transmission  |S 12 | 2 ~ [J RF (x,y)] 2 Local heating produces a change in transmission coefficient proportional to the local value of J RF 2 J. C. Culbertson, et al. J.Appl.Phys. 84, 2768 (1998) A. P. Zhuravel, et al., Appl.Phys.Lett. 81, 4979 (2002)

8. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Intermodulation distortion LSM imaging f1f1 f2f2 device under test LSM induced changes in the amplitude of transmitted microwave signals note 100 kHz square wave laser power modulation (red arrows). LSM P OUT (f 1 ) 2f 2 – f 1 +IMD 3 2f 1 – f 2 -IMD 3 f0f0 D f=1 MHz laser 100 kHz P OUT (f 2 ) A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, spectrum analyser

9. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Device Under Test Meandering microstrip resonator (Agile Devices, USA) Capacitive coupling ( g = 200 m m) Patterned center line top view of the resonator topology YBCO film HTS strip: YBa 2 Cu 3 O 7- d T C = 92 K, D T C = 6 K Thickness = 1 m m, Width W = 250 m m Substrate: LaAlO 3 ( e r =24.2) 5x10x0.5 mm 3 Resonator at 77 K: loaded Q L ~2000, f 0 = 1.85 GHz A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

10. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Global microwave response slope=1 slope=3 P d =4 dBm Log-log plot of input power dependence of the fundamental RF signals (black diamonds) and two-tone the third order IMD (blue circles) measured at T = 83 K. A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, P OUT (f 1 ) P OUT (2f 1 -f 2 ) 1 mm RF IN RF OUT

11. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Spatially-resolved microwave photo-response - YBCO film - LAO substrate 1 mm 1x1 mm X Y X Y J RF 0 max Frequency Power [dBm] f1f1 f2f2 - 42 -14 - 43 2f 1 -f 2 2f 2 –f 1 - 43- 42 - 49 - 55 1x1 mm IMD PR J rf x y 1x1 mm 0 max (a) (b) (c) RF IN RF OUT X Y J RF X Y J IMD (a) Top view of the resonator topology along with overall and (b, c) detailed 1x1 mm 3-d LTLSM plots (bottom images) showing (b) J RF (x,y) and (c) IMD PR distribution. The upper part of (b) shows the two input tones at –14 dBm as well as the output tones. The upper part of (c) shows the signals entering the spectrum analyzer after the primary tones have suffered partial cancellation. A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

12. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Laser-induced signal generation model The power distribution induced by a focused modulated laser beam can be described as: temporalspatial x-y z t focused laser beam ( l LAS = 670 nm, P L = 1 mW) substrate HTS film d heat source x z The thermally induced changes of S 21 (f) in the probe are understood as LSM photo-response (PR) that can be expressed as: inductive PR + resistive PR + insertion loss PR where A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, ~ 21

13. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Modeling of the linear photo-response (PR) d |S 12 | 2 inductive PR X resistive PR R x100 total PR f f0f0 insertion loss PR IL x 100 laser OFF laser ON (a)Microwave transmittance |S 21 | 2 (f) of a resonator at Р IN =0 dBm at a fixed temperature T = 80.7 K (b)difference between the traces in (a) that is proportional to the total PR, along with the inductive, insertion loss (IL) and resistive components A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

14. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Partition of inductive and resistive components f 1 = 5.957 GHz PR (f 2 ) ± = reflective LSM image resistive component inductive component PR R (x,y) PR(f 2 ) and PR(f 1 ) are the LSM PR at equidistant frequencies f 2 (above) and f 1 (below) from f 0 f 2 = 5.977 GHz PR (f 1 ) 300x300 m m 2 RF photoresponse maps obtained at T = 78 K, P RF (f 1 ) = P RF (f 2 ) = 0 dBm, and laser power P L = 123 m W. Areas A and B are chosen for detailed spatial analysis of the resonator RF properties. 1 mm A B YBCO LAO = LSM PR minmax A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, PR R =|PR (f 2 )+PR (f 1 )| / 2 PR x =|PR (f 2 )-PR (f 1 )| / 2

15. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Simplified estimate of resistive photo-response FBFB LSM PR minmax F1F1 PR X >> PR R PR X << PR R 25 m m (a)resistive and inductive components of LSM photo-response (PR) (b)their ratio F2F2 PR X >> PR R PR X ~ PR R FAFA F1F1 FAFA FBFB F2F2 Resistive PRx400 Inductive PR A.P. Zhuravel, S. M. Anlage and A.V. Ustinov, (a) (b) inductive resistitive

16. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: In-plane rotated grain Grain Boundaries LAO YBCO Large Grain position 200x100  m reflectivity LSM image -10 dBm 0 dBm +10 dBm 2D and 3D maps of RF current distribution in a YBCO film on LAO substrate A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

17. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: Crack LAO YBCO reflectivity Position of a crack J RF (x,y) x y Evident spatial modulation of rf current density along the crack formed by localized vortices pinning on a twin-domain structure of the YBCO film 0 J RF MAX 50 m m A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

18. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: Standing wave 82.2 K 0 PR max 5.9 GHz standing wave of YBCO/LAO 1850 MHz resonators. A B C D E F G H Points A-H are the same for both figures. LSM PR data on the graph corresponds to the PR averaged in each cross section of the HTS strip along the path from A to H. Only a very small fraction of the structure contributes to the global RF response. RF currents are peaked at the edges, however, interior corners give at least three times higher densities. F B A F G ED C H Reflectivity LSM image A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

19. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: Power dependence of LSM PR Resistive, PR R (x,y) Inductive, PR X (x,y) 25 m m 10 m m 0 peak PR +12 dBm 0 dBm -12 dBm Power-dependent penetration of PR X is spatially aligned with the direction of twin-domain blocks (TDB), whereas the development of the resistive state is uncorrelated with the TDBs. Note the different spatial scale for the upper and bottom figures. A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

20. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: Power dependence of PR R (x,y) LAO YBCO 10 m m 0 dBm +6 dBm+4 dBm +2 dBm LAO 50x50 m m Images of resistive LSM PR penetrating into HTS film (area B) at the different input HF power indicated in the images. White dotted boxes show the YBCO/LAO patterned edge. Brighter regions correspond to larger amplitude of PR R (x,y). 3D plot of resistive LSM PR at +6 dBm LAO YBCO PR R (x,y) A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

21. Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators Results: Corners and grain boundaries ILT 0.5 mm Reflectivity LAO YBCO 100 m m IMD PR GBs Vortices X Y Intermodulation LTLSM image showing a spatial modulation of the photoresponse at P IN = 4 dBm. Two different mechanisms of the LSM PR are shown. First one is the increasing of PR produced by grain boundaries (GBs) while in the second the LSM PR is reduced due to spatial vibration of RF induced vortices at the corner leading to an opposing electric field produced by the moving vortices. A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

22. The laser scanning microscope (LSM) is a convenient tool for imaging RF currents in superconducting microwave devices Many irregularities can be identified in the RF current flow: grain boundaries, cracks, defects, vortices, phase slips, current peaks at device edges and corners (IMD generation) Linear RF photo-response LSM images show J RF 2 (x,y) Our partition method allows to separate inductive and resistive changes in the microwave impedance Nonlinearities are mapped by intermodulation distortion (IMD) imaging: IMD features ~ J RF 4 (x,y) are thus sharper than linear response IMD response strongly varies at defects and device corners Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators SUMMARY A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,

23. Appl.Phys.Lett. 81, 4979 (2002). IEEE Trans.Appl.Superc. 13, 340 (2003). Low Temp.Phys. 32, 592 (2006). Appl.Phys.Lett. 88, 212503 (2006). cond-mat/0609244 (2006). Steven Anlage Alexander Zhuravel Thanks to my collaborators We are now looking for new applications, collaborations and funding sources