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Inductances and attenuation constant for a thin-film superconducting coplanar waveguide resonator

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10.1063/1.4773070

### Abstract

The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness *d* obeying ( is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length . Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small . Exact results for arbitrary are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.

© 2013 American Institute of Physics

Received 22 October 2012
Accepted 06 December 2012
Published online 04 January 2013

Acknowledgments: I thank K. K. Berggren, D. T. Meyer, and T. P. Orlando for valuable correspondence. This research was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering and was performed at the Ames Laboratory, which is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358.

Article outline:

I. INTRODUCTION

II. INDUCTANCES FOR A THIN-FILM CPW ASSUMING NO FIELD PENETRATION

A. Geometric inductance for

B. Kinetic inductance for

C. Inductances for arbitrary relative to *a*

III. THIN-FILM CPW WITH NARROW SLITS

A. Exact solution for a film with one long slit

B. Exact solution for a CPW with two narrow slits

1. Geometric inductance

2. Kinetic inductance

3. Total inductance

IV. THIN-FILM CPW WITH WIDER SLOTS

A. General properties

B. Approximate solutions for a CPW

1. *p* vs

2. Geometric inductance

3. Kinetic inductance

4. Total inductance

5. Comparison of approximate and exact solutions for two narrow slits

V. ACCOUNTING FOR NORMAL-FLUID RESISTIVE LOSSES

VI. DISCUSSION

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2013-01-04

2014-04-17

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