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REVIEW 3 major objections 4 minor 27 references

Probing time-reversal symmetry breaking at microwave frequencies

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Pith's one-line read A degenerate microwave cavity can detect time-reversal symmetry breaking via the polar Kerr angle.

desk verdict The reciprocity-breaking cavity signature is a real and well-worked-out idea, but the paper's claimed relevance to spontaneous TRSB in UPt3 and Sr2RuO4 rests on an unexamined microscopic assumption. read the letter →

arxiv 2505.08898 v1 pith:5S6JQHIN submitted 2025-05-13 cond-mat.supr-con

T. Chouinard , D. M. Broun This is my paper · ORCID
classification cond-mat.supr-con
keywords time-reversalsymmetrybreakingpolarKerreffectmicrowavecavityresonatorTE111modereciprocitysurfaceimpedanceunconventionalsuperconductorsSagnacinterferometer
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes a microwave-frequency route to detecting time-reversal symmetry breaking (TRSB) in materials. The central claim is that TRSB always appears as a difference in surface reactance between left- and right-circularly polarized microwaves, so the polar Kerr angle can be read from a degenerate TE111 cavity mode. The paper's key additional move is that interrogating the resonator with circular polarization makes true TRSB show up as broken reciprocity between forward and reverse transmission, a signature that cannot be faked by linear birefringence or shape distortions. For a sample covering the cavity end wall, the projected single-sweep sensitivity is comparable to that of the near-infrared zero-loop-area Sagnac interferometer, around 100 nanoradians for a normal-metal resonator and a few nanoradians at $Q=10^{6}$.

What carries the argument

The machinery is the two-mode TE111 cylindrical cavity treated as a spin-$\tfrac12$ system in a magnetic field. All perturbations are parameterized by a vector $\boldsymbol{\Omega} = (\omega_{xy}, \omega_{\tau}, \omega_{x^2-y^2})$ of Pauli-matrix coefficients: quadrupolar shape distortions occupy $\sigma_x$ and $\sigma_z$, while the TRSB term is $\omega_\tau\sigma_y$, the only antisymmetric perturbation. Circularly polarized interrogation is set by quarter-wave tubes at each port, and the projection-operator calculation shows that reciprocity holds if and only if the resonator eigenmode projectors are symmetric; the $\sigma_y$ term violates this, so forward and reverse transmission differ by a factor that isolates $\omega_\tau/|\boldsymbol{\Omega}|$ even when TRSB is much weaker than the cavity bandwidth. The central identity is $\theta_K = 2\omega_\tau/(\Gamma Z_0)$.

What would settle it

Place a time-reversal-invariant but linearly birefringent sample, or a resonator with a deliberate quadrupolar shape distortion and zero magnetic field, in the TE111 cavity and interrogate with circularly polarized microwaves: the model predicts forward and reverse transmission remain identical; any observed reciprocity breaking in that control would refute the identification of $\omega_\tau$ with TRSB.

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Extended reading notes

Core claim

The paper's central discovery is that the polar Kerr angle of a TRSB material can be written, at microwave frequencies and for local electrodynamics, as $\theta_K = (X_s^+ - X_s^-)/Z_0$, where $X_s^{\pm}$ are the surface reactances seen by right- and left-circularly polarized waves. In a doubly degenerate TE111 cylindrical cavity, the TRSB term is the $\omega_\tau\sigma_y$ perturbation of the two-mode Hamiltonian; it splits the degenerate modes and, when the resonator is driven by circularly polarized microwaves, makes the forward and reverse transmission amplitudes unequal. The asymmetry is the definitive signature of TRSB, because $\omega_\tau$ is the only antisymmetric term in the perturbation, and the size of the splitting measures the Kerr angle through $\theta_K = 2\omega_\tau/(\Gamma Z_0)$.

Load-bearing premise

The load-bearing premise is that the sample's microwave response is local, so the surface reactance at the cavity's wavevector is the same function of conductivity that defines the polar Kerr angle; if nonlocal response matters in materials such as UPt3 and Sr2RuO4, that mapping is no longer clean.

Editorial extensions

If this is right

  • A degenerate microwave resonator can detect TRSB at photon energies comparable to superconducting gaps, where the optical Sagnac method does not operate.
  • The nonreciprocity test distinguishes true Faraday and circular-birefringence signals from linear birefringence and from spurious frequency splitting caused by resonator shape distortions.
  • In the weak-TRSB limit, deliberately detuning the two modes by about half a bandwidth turns the detection into a first-order ratiometric asymmetry $1 + 4\omega_\tau/|\boldsymbol{\Omega}|$, so weak signals remain measurable.
  • For a sample that covers one end wall, single-sweep Kerr-angle sensitivity is $\delta\theta_K \approx (\pi/Q)\,\delta A/A$: about 100 nrad at $Q=3\times10^{4}$ and 3 nrad at $Q=10^{6}$.
  • Measuring the field dependence of $\theta_K$ in the semiclassical conductor gives a contactless way to extract plasma frequency, cyclotron frequency, and transport scattering rate, hence carrier density and Hall angle.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The two-mode reciprocity argument is not specific to TE111: any doubly degenerate microwave or optical resonator mode could carry the same signature, so the method might transfer to dielectric whispering-gallery resonators or other high-Q geometries.
  • The local-electrodynamics assumption could be tested directly by building resonators at different mode frequencies and checking that the inferred Kerr angle does not drift; wavevector-dependent response would show up as a systematic frequency dependence.
  • If the predicted nanoradian sensitivity is realized, microwave Kerr measurements could be combined with muon-spin-rotation and infrared Kerr results on the same crystals to separate intrinsic TRSB from disorder-induced effects, since the three techniques probe different length and time scales.
  • A direct calibration experiment on a magnetic insulator with a known Kerr angle, such as yttrium iron garnet in a known field, would turn the sensitivity estimate into an absolute measurement.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a microwave-frequency method to detect time-reversal symmetry breaking (TRSB) through a difference in surface reactance for left- and right-circularly polarized fields. The authors derive the relation θ_K ≈ (X_+ − X_−)/Z0 from the Argyres formula (Sec. II), illustrate the effect with a semiclassical conductor in a magnetic field (Sec. III), and propose a doubly degenerate TE111 cylindrical cavity as the detector. They develop a two-mode perturbation formalism (Eqs. 21–27) in which TRSB appears as a σ_y term ω_τ, and show that interrogating the resonator with circularly polarized microwaves leads to a forward–reverse transmission asymmetry that uniquely signals reciprocity breaking (Secs. IV–V). Sensitivity estimates (Sec. VI) claim single-sweep Kerr-angle resolutions of ~100 nrad for a normal-metal resonator and ~3 nrad for a high-Q resonator in the large-sample limit. The paper is positioned as a complement to zero-loop-area Sagnac interferometry for unconventional superconductors such as UPt3 and Sr2RuO4.

Significance. If the proposed method works as described, it would provide a new, contactless probe of TRSB at microwave frequencies, where photon energies match the gap scales of low-Tc superconductors. The reciprocity-breaking test (Eq. 49) is a valuable contribution because it separates true Faraday effects from linear birefringence. The central derivation is transparent, internally consistent, and free of fitted parameters; the two-mode Hamiltonian treatment is elegant, and the sensitivity analysis is clearly laid out. The main caveats are that the only quantitative example is an applied-field normal conductor, and the numerical sensitivity estimates contain an arithmetic error. With those issues addressed, the technique could be a useful complement to optical Kerr measurements.

major comments (3)
  1. [Abstract and Sec. VII] The paper asserts without derivation that spontaneous TRSB in superconductors such as UPt3 and Sr2RuO4 will generically produce a measurable surface-reactance difference at microwave frequencies, but the only quantitative model is a semiclassical conductor in an applied magnetic field (Sec. III). For a superconductor in the Meissner state at T << Tc and frequencies below the gap, the response is dominated by the condensate; the antisymmetric (Hall-like) part of the conductivity is not fixed by the Drude/cyclotron model and may be suppressed as ω→0 or controlled by multiband and impurity effects. Please provide a microscopic estimate of X_+ − X_− (or of θ_K at ~16 GHz) for at least one target material, or explicitly state that the experiment is a null-test probe with unknown signal magnitude.
  2. [Sec. VI] The numerical sensitivity estimates are inconsistent with the stated cavity parameters. Using Eq. 68 with f0 = 16 GHz (λ = 1.875 cm), a = 0.625 cm, d = 1.8 cm, Veff ≈ 0.98πa²d, Asample = 2 mm², and δA/A = 10⁻³, one obtains δθ_K ≈ 24 μrad for Q = 3×10⁴ and ≈ 0.7 μrad for Q = 10⁶, not 10 μrad and 300 nrad as stated. Please re-check the arithmetic and also verify the claim that 4Veff/(Asample λ) ≈ 1 in the end-wall limit; for the TE111 geometry this factor is closer to 4d/λ ≈ 4 for the quoted dimensions.
  3. [Sec. II, Eq. (3)] The derivation of θ_K = (X_+ − X_−)/Z0 assumes local electrodynamics (Eq. 3). For clean unconventional superconductors, nonlocal (Pippard) effects may be important at microwave frequencies and could modify the quantitative relation between the measured cavity splitting and the polar Kerr angle. Please add a discussion of the validity of the local approximation for UPt3 and Sr2RuO4, and indicate how nonlocal corrections would affect the calibration of the method.
minor comments (4)
  1. [Eq. (20)] The last line contains a typo: '∆(1/λ+)−∆(1/λ+)' should read '∆(1/λ+)−∆(1/λ−)'.
  2. [Abstract] The phrase 'larger than the spot size (i.e., larger than the diameter of the microwave cavity)' is confusing because a cavity is not a spot; consider rephrasing to 'larger than the microwave mode cross-section'.
  3. [Sec. VI] The justification for the factor 4Veff/(Asample λ) ≈ 1 in the large-sample limit should be stated more carefully; the Fabry–Pérot analogy with a λ/2 separation appears to give 2d/λ, not 1/2, for the factor 2Veff/(Asample λ).
  4. [Sec. III, Eqs. (12)–(13)] There is a factor-of-√2 inconsistency between the weak-field low-frequency limit in Eq. (12) and the stated low-frequency limit in Eq. (13); a direct expansion of Eq. (11) for ω << Γtr gives θ_K ≈ (ωc/ωp)√(ω/(2Γtr)), so Eq. (13) appears to be missing a factor of 1/√2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Kerr-angle-to-cavity-splitting relation follows from standard electrodynamics and cavity perturbation, with no fitted parameter masquerading as a prediction.

full rationale

The derivation chain starts from the Argyres expression for the polar Kerr angle (Eq. 1) and the assumption of a local, skew-symmetric conductivity tensor (Eq. 2). Eq. (4) converts the Kerr angle into a surface-reactance difference using the local impedance relation n = Z0/Zs; this is a mathematical reduction of the input tensor structure, not an input in disguise. The semiclassical conductor example (Sec. III) is a concrete model whose cyclotron-frequency input independently produces a nonzero X_+ - X_-; it is used as a prototypical illustration, not as the source of the later detector equations. The cavity analysis uses standard perturbation theory (Eqs. 15-18) to relate the mode splitting to the reactance difference, and the two-level Hamiltonian parameter omega_tau is defined as the coefficient of the TRSB sigma_y perturbation (Eq. 25). Eq. (27) is then the identity splitting = 2 omega_tau combined with Eq. (19); it does not assume the Kerr angle it claims to predict. The reciprocity-breaking test (Eqs. 46-49) follows from the projection algebra of the Pauli-matrix Hamiltonian and is internally consistent. The sensitivity estimate (Eqs. 61-69) does use delta A/A = 1e-3 from prior work (Ref. 23), but this is an explicitly stated experimental resolution benchmark, not a value fitted to the target claim, and the resulting resolution scaling with Q and sample area is derived, not assumed. The absence of a microscopic estimate of X_+ - X_- for UPt3 or Sr2RuO4 is a scope or motivation gap, not circularity: the paper advertises a calibrated probe whose target signal is taken as an external physical premise. No self-citation carries the load of the derivation, and no equation reduces to a fitted value by construction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; the method uses known electromagnetic response properties and standard cavity modes. The free parameters are limited to empirical measurement benchmarks and geometric approximations used in the sensitivity estimate.

free parameters (2)
  • delta_A/A amplitude resolution = 10^-3
    Empirical fractional amplitude resolution from prior microwave spectroscopy (Ref 23), used in Section VI to estimate sensitivity. It is an external benchmark, not fitted to the paper's own data.
  • 4*Veff/(Asample*lambda) geometric factor = approx 1
    Claimed to be approximately 1 for a sample forming one end wall, on general grounds. Direct evaluation for the TE111 cavity parameters in the paper gives a factor closer to 2 to 4, affecting the numeric sensitivity estimate.
assumptions (5)
  • domain assumption The electrodynamic response of a TRSB material contains skew-symmetric off-diagonal terms (Eq. 2).
    This is the generic symmetry statement that motivates the model. For a specific superconducting state the magnitude and sign must be computed microscopically, which the paper does not do.
  • domain assumption Local electrodynamic limit for the surface impedance (Eq. 3).
    Underpins the relation n = Z0/Zs and hence the Kerr angle to reactance difference. May fail in nonlocal regimes, though typical penetration depths in the target materials support locality.
  • standard math Argyres formula for the polar Kerr angle (Eq. 1).
    Standard result from the magneto-optics literature, cited as Ref 19.
  • domain assumption Cavity perturbation formula delta_omega = -Gamma*Xs (Eq. 15).
    Standard cavity perturbation theory, cited as Refs 20 and 21. Requires small sample or weak perturbation, and uniform field over the sample surface.
  • domain assumption Two-level truncation of the TE111 mode pair (Eq. 22).
    Assumes only the doubly degenerate mode pair is relevant and all other modes are distant, so the system Hilbert space is two-dimensional.

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Pith. "Pith review of Probing time-reversal symmetry breaking at microwave frequencies." pith.science (2026). https://pith.science/paper/5S6JQHIN

@misc{pith2026250508898,
  author       = {Pith},
  title        = {Pith review of: Probing time-reversal symmetry breaking at microwave frequencies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5S6JQHIN}},
  note         = {Machine review of arXiv:2505.08898}
}
abstract

Motivated by experiments carried out in the near infrared using zero-loop-area Sagnac interferometers, we explore electromagnetic signatures of time-reversal symmetry breaking (TRSB) at microwave frequencies, using as a prototypical example a semiclassical conductor in a magnetic field. TRSB is generically accompanied by a skew-symmetric term in the electrodynamic response tensors (permittivity, conductivity, surface impedance), imparting a nonreciprocal phase shift to left- and right-circularly polarized electromagnetic waves reflected from the surface of such a material. We show that TRSB manifests as a difference in the surface reactance experienced by circularly polarized waves, and can be detected using a doubly degenerate resonator mode, such as the TE$_{111}$ mode of a cylindrical cavity. In addition to the frequency splitting induced by TRSB we show that, when interrogated by circularly polarized microwaves, the forward and reverse transmission responses of such a resonator break reciprocity, providing a crucial signature that distinguishes true Faraday effects (i.e., circular birefringence) from non-TRSB effects such as linear birefringence. In the limit that the sample is larger than the spot size (i.e., larger than the diameter of the microwave cavity) we show that the TRSB resonator has sensitivity to polar Kerr angle comparable to that of the zero-loop-area Sagnac, and should provide complementary insights into unconventional superconductors such as UPt$_3$ and Sr$_2$RuO$_4$ that have been observed to spontaneously break time-reversal symmetry.

Figures

Figures reproduced from arXiv: 2505.08898 by the authors.

Figure 1
Figure 1. FIG. 1. Field dependence of the polar Kerr angle in a semi-classical conductor, for di [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Electric and magnetic fields of the doubly degenerate TE [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The four types of perturbation to the TE [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic of the TRSB resonator system showing how in the forward direction: microwaves are launched from the left-hand coaxial [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Forward and reverse transmission amplitudes, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Forward and reverse transmission amplitudes, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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Reference graph

Works this paper leans on

27 extracted references · 25 canonical work pages

  1. [1]

    J. F. Annett, N. Goldenfeld, and A. J. Leggett, Constraints on the pairing state of the cuprate superconductors, Journal of Low Temperature Physics105, 473 (1996)

    work page 1996

  2. [2]

    0ω xy ωxy 0 # ,(23) ωx2−y2σz =

    The phase shift of each mode is 2πtimes the fractional change in wavelength (e.g.,∆ϕ + =2π∆λ +/λ), and can therefore be directly related back to the nonreciprocal phase shift,ϕ nr = ∆ϕ+−∆ϕ− =2θ K. While all the information about Kerr angle is contained in the relative frequency shift∆ω +−∆ω−, in practice it is not possible to simply measure the frequency ...

    work page

  3. [3]

    Kidwingira, J

    F. Kidwingira, J. D. Strand, D. J. V . Harlingen, and Y . Maeno, Dynamical superconducting order parameter do- mains in Sr2RuO4, Science314, 1267 (2006)

    work page 2006

  4. [4]

    (A.3) Each term of thezintegral contributes a factor ofd/2

    Working with the fields in complex form, the azimuthal dependence immedi- ately cancels out when forming|H| 2, leading to Veff =4π Z d 0 dz Z a 0 rdr " cos2(kzz) J′2 1 (krr)+ 1 (krr)2 J2 1(krr) ! +sin 2(kzz) kr kz J2 1(krr) # . (A.3) Each term of thezintegral contributes a factor ofd/2. To carry out therintegral we make the substitution x=k rr=1.8412r/a: ...

    work page

  5. [5]

    G. M. Luke, A. Keren, L. P. Le, W. D. Wu, Y . J. Uemura, D. A. Bonn, L. Taillefer, and J. D. Garrett, Muon spin relaxation in UPt3, Physical Review Letters71, 1466 (1993)

    work page 1993

  6. [6]

    G. M. Luke, Y . Fudamoto, K. M. Kojima, M. I. Larkin, J. Merrin, B. Nachumi, Y . J. Uemura, Y . Maeno, Z. Q. Mao, Y . Mori, H. Nakamura, and M. Sigrist, Time-reversal symmetry-breaking superconductivity in Sr2RuO4, Nature394, 558 (1998)

    work page 1998

  7. [7]

    Joynt and L

    R. Joynt and L. Taillefer, The superconducting phases of UPt3, Reviews of Modern Physics74, 235 (2002)

    work page 2002

  8. [8]

    J. Xia, Y . Maeno, P. T. Beyersdorf, M. Fejer, and A. Kapitulnik, High resolution polar Kerr effect measurements of Sr 2RuO4: evidence for broken time-reversal symmetry in the supercon- ducting state, Physical Review Letters97, 167002 (2006)

    work page 2006

Show all 27 references
  1. [9]

    J. D. Strand, D. J. Bahr, D. J. V . Harlingen, J. P. Davis, W. J. Gannon, and W. P. Halperin, The transition between real and complex superconducting order parameter phases in UPt3, Sci- ence328, 1368 (2010)

    2010

  2. [10]

    J. A. Sauls, The order parameter for the superconducting phases of UPt3, Advances In Physics43, 113 (1994)

    1994

  3. [11]

    A. P. Mackenzie, T. Scaffidi, C. W. Hicks, and Y . Maeno, Even odder after twenty-three years: the superconducting or- der parameter puzzle of Sr2RuO4, npj Quantum Materials2, 40 (2017)

    2017

  4. [12]

    J. D. Strand, D. J. V . Harlingen, J. B. Kycia, and W. P. Halperin, Evidence for complex superconducting order parameter sym- metry in the low-temperature phase of UPt 3 from Josephson interferometry, Physical Review Letters103, 197002 (2009)

    2009

  5. [13]

    Although states in the latter class are not chiral, they exhibit local currents in the presence of impurities or step edges

    ord xy±is ′ [14], wheres ′ denotes theA 1g symmetry cos(kx)+cos(k y) extendeds-wave state. Although states in the latter class are not chiral, they exhibit local currents in the presence of impurities or step edges. In the case of UPt 3 many experiments are well described by t...

  6. [14]

    E. R. Schemm, W. J. Gannon, C. M. Wishne, W. P. Halperin, and A. Kapitulnik, Observation of broken time-reversal sym- metry in the heavy-fermion superconductor UPt3, Science345, 190 (2014)

    2014

  7. [15]

    Kapitulnik, J

    A. Kapitulnik, J. Xia, E. Schemm, and A. Palevski, Polar Kerr effect as probe for time-reversal symmetry breaking in uncon- ventional superconductors, New Journal Of Physics11, 055060 (2009)

    2009

  8. [16]

    S. A. Kivelson, A. C. Yuan, B. Ramshaw, and R. Thomale, A proposal for reconciling diverse experiments on the supercon- ducting state in Sr2RuO4, npj Quantum Materials5, 43 (2020)

    2020

  9. [17]

    A. T. Rømer, T. A. Maier, A. Kreisel, I. Eremin, P. J. Hirschfeld, and B. M. Andersen, Pairing in the two-dimensional Hubbard model from weak to strong coupling, Phys. Rev. Res.2, 013108 (2020)

    2020

  10. [18]

    that detects TRSB via the nonreciprocal phase shift,ϕ nr, between LCP and RCP light reflected from the sample. Their experiments resolveϕ nr with a precision of tens of nanoradi- ans, using state-of-the-art optical techniques to cancel out al- most all common-mode phase shifts...

    2025 arXiv

  11. [19]

    A. T. Rømer, P. J. Hirschfeld, and B. M. Andersen, Super- conducting state of Sr 2RuO4 in the presence of longer-range Coulomb interactions, Phys. Rev. B104, 064507 (2021)

    2021

  12. [20]

    B. M. Andersen, A. Kreisel, and P. J. Hirschfeld, Spontaneous time-reversal symmetry breaking by disorder in superconduc- tors, Frontiers in Physics12, 1353425 (2024)

    2024

  13. [21]

    J. Xia, E. Schemm, G. Deutscher, S. A. Kivelson, D. A. Bonn, W. N. Hardy, R.-X. Liang, W. Siemons, G. Koster, M. Fejer, and A. Kapitulnik, Polar Kerr-effect measurements of the high- temperature YBa 2Cu3O6+x superconductor: evidence for bro- ken symmetry near the pseudogap tem...

    2008

  14. [22]

    J. Xia, P. T. Beyersdorf, M. Fejer, and A. Kapitulnik, Modified Sagnac interferometer for high-sensitivity magneto-optic mea- surements at cryogenic temperatures, Applied Physics Letters 12 89, 062508 (2006)

    2006

  15. [23]

    P. N. Argyres, Theory of the Faraday and Kerr effects in ferro- magnetics, Physical Review97, 334 (1955)

    1955

  16. [24]

    R. J. Ormeno, D. C. Morgan, D. M. Broun, S. F. Lee, and J. R. Waldram, Sapphire resonator for the measurement of surface impedance of high-temperature superconducting thin films, Re- view of Scientific Instruments68, 2121 (1997)

    1997

  17. [25]

    W. A. Huttema, B. Morgan, P. J. Turner, W. N. Hardy, X. Zhou, D. A. Bonn, R. Liang, and D. M. Broun, Apparatus for high- resolution microwave spectroscopy in strong magnetic fields, Review Of Scientific Instruments77, 023901 (2006)

    2006

  18. [26]

    This can be modelled via the addition of a complex amplitude ˜D21

    In addition to the resonant coupling channels it is sometimes also necessary to consider direct coupling between input and output ports. This can be modelled via the addition of a complex amplitude ˜D21

  19. [27]

    C. J. S. Truncik, W. A. Huttema, P. J. Turner, S. ¨Ozcan, N. C. Murphy, P. R. Carri`ere, E. Thewalt, K. J. Morse, A. J. Koenig, J. L. Sarrao, and D. M. Broun, Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn 5 revealed by preci- sion microwave spectrosco...

    2013

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