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arxiv: 2604.10621 · v1 · submitted 2026-04-12 · ❄️ cond-mat.supr-con · cond-mat.str-el

Electrodynamics of Quantum-Critical Conductors and Superconductors

Uwe S. Pracht This is my paper

Pith reviewed 2026-05-10 15:47 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords quantum-critical superconductivityoptical conductivitydisordered NbNgranular aluminumCeCoIn5heavy-fermion superconductorselectrodynamics
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The pith

Optical experiments unify quantum-critical superconductivity across NbN, granular Al, and CeCoIn5

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

The thesis presents optical low-temperature experiments on disordered NbN thin films, granular aluminum thin films, and the heavy-fermion compound CeCoIn5. These results are interpreted with theoretical models of quantum-critical conductors and superconductors to establish a consistent description of their electrodynamic response. A sympathetic reader cares because the work shows how electromagnetic measurements can reveal shared physics near quantum critical points despite differences in material structure and disorder.

Core claim

The central claim is that the frequency-dependent optical conductivity measured at low temperatures in these three systems aligns with a unified theoretical framework for quantum-critical superconductivity, where detailed calculations connect the observed spectra directly to critical fluctuations and pairing effects.

What carries the argument

Frequency-dependent optical conductivity obtained via low-temperature spectroscopy, which probes charge-carrier dynamics and superconducting fluctuations near the quantum critical point.

If this is right

  • Quantum criticality controls the normal-state conductivity and superconducting transition in a material-independent manner.
  • Disorder in thin films can tune the system to the quantum critical regime in a controlled way.
  • The same electrodynamic signatures are expected in other heavy-fermion or disordered superconductors near criticality.
  • Calculations of optical response provide a quantitative bridge between experiment and theory for these systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar optical measurements on additional heavy-fermion compounds could test whether the unification holds more broadly.
  • The results imply that pressure or doping studies near the critical point in CeCoIn5 might reveal further scaling behavior.
  • Insights could guide searches for new materials where quantum criticality enhances or suppresses superconductivity in predictable ways.

Load-bearing premise

The theoretical models used to interpret the optical spectra accurately capture the quantum-critical behavior without major unaccounted effects from disorder or material-specific features.

What would settle it

Optical conductivity spectra in NbN, granular Al, or CeCoIn5 that deviate from the predicted scaling or features of the quantum-critical models at the relevant frequencies and temperatures, after normal experimental corrections, would falsify the unified picture.

Figures

Figures reproduced from arXiv: 2604.10621 by Uwe S. Pracht.

Figure 1.1
Figure 1.1. Figure 1.1: Potential energy with symmet￾ric (top) and broken￾symmetry (bottom) ground states. U(1) operations can be vi￾sualized as rotations around the V axis. constant λ. For a positive mass term µ 2 > 0 the po￾tential has a unique minimum at ψ = 0. For γ 2 < 0 the potential acquires a Mexican-hat shape, see [PITH_FULL_IMAGE:figures/full_fig_p023_1_1.png] view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Complex solutions of Usadel equation for various pair-breaking values τs. Purely real and complex solutions correspond to a vanishing and finite quasiparticle density-of-states (DOS), respectively. With increasing pair-breaking scattering τs, the energy window with purely real solutions shrinks leading to a reduction of the band edge Ωg despite a constant pairing amplitude ∆. Note that only the branch wi… view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Quasiparticle density of states for var￾ious pair-breaking values τs. Although the order pa￾rameter ∆ is constant for each curve, the band edge Ωg decreases considerably below the BCS value Ωg = 2∆ with increasing pair-breaking strength. At the same time, the coherence peaks are smeared out. For the strongest pair-breaking (τs∆ = 1.4) the coherence peaks are barely present and the spectral gap is with 0.… view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: single-parameter-scaling function β of a d￾dimensional cube L d versus conductance interpolating be￾tween logarithmic decay (insulating limit) and saturation (metallic limit) in 1,2, and 3 spatial dimensions. Arrows indicate the renormalization flow in the limit L → ∞. For d = 1 and 2 any amount of disorder will always favor the insulating ground state over the metallic one, whereas for d = 3 the system … view at source ↗
Figure 2
Figure 2. Figure 2: displays schematically [PITH_FULL_IMAGE:figures/full_fig_p042_2.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Energy scales at the SIT within the fermionic (left) and the bosonic (right) scenario for the SIT. In the first case, pairing amplitude and superfluid density (or stiffness) go to zero at the QCP for critical disorder gc and the insulator contains localized fermions. In the bosonic scenario, the SIT is marked by a loss of superfluid coherence while pairing remains robust into the Cooper-pair (or Bose-) i… view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Sketch of the disorder-smeared density of states in￾cluding sub-gap tail states. The dashed line is the BCS solu￾tion. Note that the tail states are actu￾ally much less signif￾icant than displayed here. The comparison is done according to the scheme de￾scribed below. 1. Match an optical with a tunneling spectrum for NbN with (approximately51) the identical Tc 51 Any NbN film produced as elec￾trode within… view at source ↗
Figure 2
Figure 2. Figure 2: compares measurements of the real part of [PITH_FULL_IMAGE:figures/full_fig_p052_2.png] view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: compares measurements of the real part of the dynamical conductivity σ1(ν) + iσ2(ν) of a sample with Tc = 15.14 K with a measurement of the differ￾ential tunneling conductance dI/dV of a sample with Tc = 15.6 K. While the tunneling measurement is per￾formed at 1.9 K well below Tc, the displayed σ1(ν) spec￾trum is taken at 12 K much closer to Tc. The reason is 10 15 20 25 30 35 2 4 6 8 -6 -4 -2 0 2 4 6 0.… view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Optical and tunneling spectroscopy on clean NbN. (a) real part σ1(ν) of the dynamical con￾ductivity in the normal (17 K) and superconducting state (11 K). The arrow indicates the spectral gap estimated from the minimum of σ1(ν). (b) Differential tunneling conductance dI/dV as function energy at 2.17 K. Solid lines are based on Green functions calculated for the same pair breaking τ and ratio ∆/kBTc [PIT… view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Optical and tunneling spectroscopy on moderately disordered NbN. Panels (a) show real part σ1(ν) of the dynamical conductivity in the normal and superconducting state. The arrows indicate the spec￾tral gap estimated from the kink of σ1(ν). Panels (b) display the differential tunneling conductance dI/dV as function energy. Solid lines are based on Green func￾tions calculated for the same pair breaking τ a… view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: Optical and tunneling spectroscopy on disordered NbN. Panels (a) show real part σ1(ν) of the dynamical conductivity in the normal and superconduct￾ing state. The arrows indicate the spectral gap estimated from the kink of σ1(ν). Panels (b) display the differ￾ential tunneling conductance dI/dV as function energy. Solid lines are based on Green functions calculated for the same pair breaking τ and ratio ∆/… view at source ↗
Figure 2.8
Figure 2.8. Figure 2.8: Inverted analysis routine applied to a strongly disordered sample with Tc =4.2 (a) and 4.3 K (b). The pair breaking parameter is chosen such that it yields a fit of σ1(ν) at 2 K. This strong pair breaking fails to generate a satisfying description of dI/dV regarding both the coherence peaks and the width of the gap [PITH_FULL_IMAGE:figures/full_fig_p056_2_8.png] view at source ↗
Figure 2.9
Figure 2.9. Figure 2.9: Curves from Gaussian distributed lo￾cal gaps ∆(r) applied to a strongly disordered sample with Tc = 4.2 (a) and 4.3 K (b). The fit of the dI/dV measurement is the average of 81 D(E) curves calculated from a Gaussian distribution of ∆(r) values. The cor￾responding average of σ1(ν) curves cannot reproduce the experimental result. the experimental results on the samples with Tc = 4.2 and 4.3 K together with… view at source ↗
Figure 2.10
Figure 2.10. Figure 2.10: Phase diagram of lattice bosons within the Bose-Hubbard model. The tips of the lobes are points with emergent rel￾ativistic dynamics. Adopted from Ref. [43] . The search for a suited system with a Higgs mode therefore resorts to effectively bosonic charged superflu￾ids, i.e. short coherence-length superconductors. Thin films of NbN are such candidates: For films of around 50 nm thickness, Hall- and magn… view at source ↗
Figure 2.11
Figure 2.11. Figure 2.11: Superconducting energy scales to￾wards criticality Comparison between energy gap ∆ ob￾tained from tunneling measurements and (half of) optical absorption threshold Ω/2 taken as the minimum in σ1(ν) for NbN films approaching the SIT. In the clean limit (high Tc), both energy scales are approximately the same. While the decrease of ∆ follows Tc in agreement with the strong-coupling BCS reduction (black li… view at source ↗
Figure 2
Figure 2. Figure 2: (b) compares [PITH_FULL_IMAGE:figures/full_fig_p065_2.png] view at source ↗
Figure 2.12
Figure 2.12. Figure 2.12: Superfluid and total carrier densities (a) temperature dependence of the superfluid density nS for a sample with Tc = 6.4 K. The solid line is a fit to the two-fluid approximation giving a zero-temperature ex￾trapolation of ns(0) = 2.07 × 1025 m−3 . (b) Comparison between the total carrier density ne [40] from normal￾state Hall measurements and the zero-temperature su￾perfluid density obtained from σ2(ν… view at source ↗
Figure 2
Figure 2. Figure 2: due to the [PITH_FULL_IMAGE:figures/full_fig_p066_2.png] view at source ↗
Figure 2.13
Figure 2.13. Figure 2.13: Determination of the superfluid den￾sity The figure assembles experimental results on the in￾ductive response of NbN samples under study multiplied with frequency, νσ2 which according to Eq. (2.22) mea￾sures the superfluid density in the limit ν → 0 (shown as red stars) particular form, however, strongly affects the resulting integral. Unfortunately, the inaccessible high-frequency tail renders a quanti… view at source ↗
Figure 2.14
Figure 2.14. Figure 2.14 [PITH_FULL_IMAGE:figures/full_fig_p068_2_14.png] view at source ↗
Figure 2.15
Figure 2.15. Figure 2.15: Average total kinetic energy obtained from sim￾ulations of the XY Hamiltonian as func￾tions of disorder p and the Coulomb-to￾Josephson energy ra￾tio EC /EJ . The SIT (dashed lines) can be realized by tuning p or EC /EJ . Adopted from Ref. [56]. the upper panel of [PITH_FULL_IMAGE:figures/full_fig_p070_2_15.png] view at source ↗
Figure 2.16
Figure 2.16. Figure 2.16: Normal-state optical data for various NbN films measured by (a) frequency domain THz spec￾troscopy (this work) and (b) time-domain THz spec￾troscopy (values taken from [63]). While the experi￾mental studies presented in this work reveal a frequency￾independent σ1,n, a growing rise with frequency is re￾ported in Ref. [63]. (c) Raw transmittivity spectra for two films (this work) far and close to the SIT … view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Upon fine tuning the Josephson coupling EJ and Coulomb blockade Ec of n nanograin array, a coherent superfluid condensate may ex￾ist with similar local phases φi, while the shell effect still enhance ∆ in each grain, so that Tc is enhanced compared to the bulk (i.e. the strongly-coupled limit) the number-phase uncertainty Eq. (3.6) those Sn or Pb nanoislands cannot sustain a macroscopically coherent cond… view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: The enhanced superconductivity is even more [PITH_FULL_IMAGE:figures/full_fig_p080_3_3.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3 [PITH_FULL_IMAGE:figures/full_fig_p081_3_3.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Generic scheme for a su￾perconducting dome emergent from com￾peting energy scales, i.e. pairing ampli￾tude ∆ and super￾fluid stiffness J, op￾positely affected by an increasing control parameter. Repro￾duced from Ref. [37]. of view, any attempt to explain the particular shape of a superconducting dome eventually needs to identify the mechanism that destroys superconductivity at Tc. Being a phase-coherent … view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Resistive transitions for several repre￾sentative granular Al samples studied in this work together with fits of the resistivity with the AL formula (3.9) for LR samples and with the modified AL formula (3.11) for the HR samples. The parameters of the fit are shown in each panel. We define Tc as the tempera￾ture, where ρdc becomes immeasurably small. The ver￾tical dashed line denotes the midpoint of the … view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: Superconducting dome and dynamical conductivity.(a) Critical temperature Tc as a function of the normal-state resistivity (measured at 5 K) of gran￾ular Al films studied in this work. Yellow symbols refer to the samples displayed in panels below. Tc encloses a dome-like superconducting phase with low-, optimal- and high-resistivity regimes. (b-d) (Normalized) spectra of σ1(ν) and σ2(ν) of samples located… view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: Temperature dependence of the energy gap and superfluid density for two samples on the LR and HR sides of the dome. (a) ∆(T) of both sam￾ples follows the BCS prediction closely, while, in case of the HR sample, ∆(T) decays weaker towards Tc and tends to survive into the normal state (empty symbols). The persistence of a finite pairing above Tc is in strik￾ing resemblance with the pseudogap phase of, e.g.… view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: Pen￾etration depth λ versus normal-state resistance. The present work (col￾ored dots) very well reproduces results obtained in previous works [96, 97] shown as empty and filled squares, where the inverse penetration depth has been directly measured. In addition, we note that the absolute numbers of λ ob￾tained from the inductive response (stars) are nearly identical with the calculation of λ from ∆ (cir… view at source ↗
Figure 3.11
Figure 3.11. Figure 3.11: Superconducting energy scales and lo￾cal order parameters (a) Tc, ∆(0), J(0), J∆(0) (ex￾pressed in units of temperature) and ∆(0)/kBTc as a function of normal-state resistivity (measured at 5 K) of granular Al films. ∆(0) (olive stars) follows the increase of Tc on the left side of the dome for LR samples while it saturates in the HR regime. This is reflected in the ratio ∆(0)/kBTc which increases from … view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: Temperature evolution of spectral gap. (a-b) Temperature dependence of normalized σ1(ν) of a granular Al sample in the high- and optimal resistivity regimes. In case of the HR sample, the suppression of σ1(ν) below Tc = 2.55 K (dashed lines) persists up to T = 2.8 K (solid lines), whereas the spectral gap closes right at Tc in the LR regime. (c) Temperature dependence of the spectral gap for samples fro… view at source ↗
Figure 3.13
Figure 3.13. Figure 3.13: Evolution of spectral gaps below and above Tc as apparent from (a-f) the dissipative conduc￾tivity σ1(ν) of high-resistivity granular Al. (g) Fits to the standard and generalized Mattis-Bardeen functionals (see the main text for more information) include hard￾gapped BCS-DOS and Aranov-Altshuler type pseudogap, respectively. (h) temperature dependence of the spectral gaps ∆ and Ω for T < Tc and T > Tc, r… view at source ↗
Figure 3.14
Figure 3.14. Figure 3.14: Excessive sub-gap conductivity σ + 1 (ν) in granular Al for various temperatures below Tc for samples on the LR and HR sides of the superconducting dome [PITH_FULL_IMAGE:figures/full_fig_p104_3_14.png] view at source ↗
Figure 3.15
Figure 3.15. Figure 3.15: Decomposition of σ1(ν) in terms of a quasiparticle background following MB theory (solid lines) and additional sub-gap contribution σ + 1 (ν) (bars) for two samples measured during the second cool-down. In the light of these considerations, we can revisit the experimental results on the low-frequency σ1 obtained in the course of this work. For a number of samples, a significant amount of excessive condu… view at source ↗
Figure 3.16
Figure 3.16. Figure 3.16: Sketch of the optical response of an array of [PITH_FULL_IMAGE:figures/full_fig_p110_3_16.png] view at source ↗
Figure 3.17
Figure 3.17. Figure 3.17: Excessive sub-gap conductivities σ + 1 (ν) (symbols) extracted from the optical data and σreg(ν) (lines) calculated within the diluted XY model for J = 0.9 cm−1 and a dilution p = 0.17. The inset of (a) com￾pares temperature evolution of σreg(ν) shown in the other panels in detail. field θ(k, ω) is obtained via the Euler-Lagrange formal￾ism as ωk = 4Jξ0|k| (3.42) which is a ordinary sound-wave like disp… view at source ↗
Figure 3.18
Figure 3.18. Figure 3.18: Probability distributions (not normal￾ized) of ∆ and Jij calculated for a granular supercon￾ductor with a Gaussian distribution of grain diameters and a resistance ratio RN /Rq = 0.01. Note that the dis￾tribution of couplings Jij resembles the simple binomial distribution used to calculate the solid lines in [PITH_FULL_IMAGE:figures/full_fig_p112_3_18.png] view at source ↗
Figure 3.19
Figure 3.19. Figure 3.19: Various realizations and strengths of sub-gap bands (a,b) and to corresponding σ1(ν) spectra (c,d) together with experimental data (sample ρdc = 263 µΩcm, Tc = 2.78 K at 1.8 K). No combination of parameters determining the position and size of the sub-gap band can equally fit both the excessive absorption at low energies and the BCS-like part of the experimental data. inside the gap, grows as τs∆ is red… view at source ↗
Figure 3.20
Figure 3.20. Figure 3.20: Pro￾posal for the superconducting domes of granular Al with different grain diameters. The two domes in the front (3 nm and 2 nm grains, labeled ’SC’) with a maxi￾mum Tc of 2.2 K and 3. K, respectively, are experimentally established. The two domes in the back (labeled ’?’) with an even higher Tc enhancement are envisioned the￾oretically for grain diameters less than 2 nm. concerning the presently estab… view at source ↗
Figure 3.21
Figure 3.21. Figure 3.21: A [PITH_FULL_IMAGE:figures/full_fig_p117_3_21.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Schematic phase diagram and dc re￾sistivity of CeCoIn5 as functions of temperature and magnetic field. Starting at room temperature, the system is a uncorrelated Drude-metal, crosses at ∼150 K to the regime of Kondo scattering, before it enters the coher￾ent heavy fermion state at Tcoh. ≈ 40 K and eventually becomes superconducting below Tc = 2.3 K. As function of magnetic field, superconductivity is sup… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: IR properties of CeCoIn5 obtained from single-crystal reflectance measurements. (a) σ1(ν) for various temperatures. Below 50 K a hybridization gap opens reflecting the hybridization of conduction and f electrons. (b) Mass enhancement m∗/mb as function of frequency and temperature. Towards low energies, the IR light probes the heavy electrons as evident from a enhancement by an factor ∼ 20 at lowest tempe… view at source ↗
Figure 4
Figure 4. Figure 4: (b) shows [PITH_FULL_IMAGE:figures/full_fig_p129_4.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Decomposition of transport resistivity in CeCoIn5 (a) total resistivity and magnetic contri￾bution obtained after subtraction of the phononic con￾tribution inferred from the non-magnetic metal LaCoIn5 (data taken from Ref. [137]) shown in panel (b). In order to meet measurements on thin films and single crystals, the resistivity of the latter were scaled with a factor 1.18. In the coherent HF regime, pho… view at source ↗
Figure 4
Figure 4. Figure 4: displays sub-linear behavior with an exponent [PITH_FULL_IMAGE:figures/full_fig_p131_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: at various temperatures (spectra for the second [PITH_FULL_IMAGE:figures/full_fig_p132_4.png] view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Spectra of σ1,2(ν) of a second sample. The overall behavior agrees with the sample discussed in the main text. cellent agreement with the increase in ρdc. We attribute this reduction in σ1 to the increased scattering between the conduction electrons and localized f-electrons. The values of σ2(ν) increase slightly, but remain close to zero upon approaching Tp. Upon further reduction of temper￾ature, the s… view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Real part ρ1(ν) of the complex resis￾tivity at various temperatures as measure for the optical relaxation rate Γ(ν). Between 150 and 30 K, Γ is flat and acquires a frequency dependence only at lower tem￾peratures in the HF state, where σ1(ν) evolves a strong Drude peak. . increase in the low-frequency limit following the suppres￾sion of ρdc, phonon-, and electron-electron scattering. As the hybridization… view at source ↗
Figure 4
Figure 4. Figure 4: shows the optical relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p133_4.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Spectra of ρs ∝ Γ measured at THz (rescaled, this work) and IR frequencies taken from Ref. [160] resolving the fre￾quency dependencies over several orders of magnitude. 4.4 Interludium II FL, non-FL, and hidden FL In his seminal work [161], Landau showed theoretically that slowly turning on the interaction in an initially non￾interacting Fermi gas of electrons will transform the old ground state adiabati… view at source ↗
Figure 4
Figure 4. Figure 4: displays [PITH_FULL_IMAGE:figures/full_fig_p139_4.png] view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: displays −ρ2(ν, T)/ν which we interpret as measure of the renormalization Z −1 = m∗/mb. The absence of frequency dependence of σ1(ν) at high tem￾peratures implies that the real part of M(ν) is essentially zero for ν ≪ 350 cm−1 (compare also to [PITH_FULL_IMAGE:figures/full_fig_p139_4_9.png] view at source ↗
Figure 4
Figure 4. Figure 4: displays the QP relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p140_4.png] view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: QP relaxation rate Γ ∗ versus temperature and frequency. Thick lines are powerlaw fits, thin lines demarcate the critical relaxation rate Γcrit., only below which well defined QP exist. (a) While ρdc displays a non-FL sub-linear T-dependence, the relaxation rate of well-defined resilient QP Γ ∗ < Γcrit. approximately fol￾lows the T 2 - powerlaw of a hidden FL up to 25 K. (b-d) Γ ∗ (T) displays powerlaw … view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Renormalization factor Z −1 (T) measured by optical spectroscopy (at 6.5 cm−1 ) and calculated from electronic specific heat, - susceptibility (at 0.1 T), and nuclear spin-lattice relaxation (taken from Refs. [130], [131], and [132] respectively). The NFL T-dependence of Ce/T, χe and T1 agree remarkable well with the one of Z −1 and the scenario of resilient QPs constituting a hidden FL in CeCoIn5 [PIT… view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Scaling behavior of the effective mass measured by ρ2/ν according to Eq. (4.29) and (4.30). The optimal collapse is achieved for α = −0.94, β = 0.96, and y = 0.24 revealing an approximate ν/T scaling of the effective mass. The Inset shows the same data collapse plotted versus ν/T β . α = −0.94, β = 0.96 and y = 0.24 forming three dis￾tinct temperature regimes of scaling. First, at temper￾atures above 50… view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: m∗(T, B)/mb of CeCoIn5 at a fixed GHz frequency measured with a microwave res￾onator [202]. Note flattening in the high-field and low-T FL regime. In this work we have demonstrated how the dynami￾cal response at matching energy scales kBT ∼ hν yields valuable information about the nature of the HF state in CeCoIn5 advancing our current understanding not inly incrementally, but providing a complete new p… view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: ρdc, Γ ∗, and m∗/mb ver￾sus T for the HF su￾perconductor UPt3. Dashed lines are T 2 fits. Data taken from [203]. After the Mott insulator V2O3 and the Hund’s metal CaRuO3, we add the HF metal CeCoIn5 as third en￾try to the list of known hidden-FL materials. Although formulated for the doped Mott insulators, the hidden FL concept seems robust and might serve as model for further non-FL systems that so fa… view at source ↗
Figure 4.15
Figure 4.15. Figure 4.15: Renor￾malization Z−1 ver￾sus T at 6.5 cm−1 . The solid lines are guides to the eyes demarcating a crossover at around 10 K with increasing temperature - from marginal FL to hidden FL? we note [159] that the crossover from linear to sub-linear ρdc(T) and weak to stronger (log-like) decline of m∗ (T)/mb ∼ Z −1 at 6.5 cm−1 , see [PITH_FULL_IMAGE:figures/full_fig_p152_4_15.png] view at source ↗
read the original abstract

This thesis presents and discusses optical low-temperature experiments on disordered NbN, granular Al thin-films, and the heavy-fermion compound CeCoIn5, offering a unified picture of quantum-critical superconductivity. It provides a concise introduction to the respective theoretical models employed to interpret the experimental results, and guides readers through in-depth calculations supplemented with supportive figures in order to both retrace the interpretations and span the bridge between experiment and state-of-the art theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. This thesis presents and discusses optical low-temperature experiments on disordered NbN, granular Al thin-films, and the heavy-fermion compound CeCoIn5, offering a unified picture of quantum-critical superconductivity. It provides a concise introduction to the respective theoretical models employed to interpret the experimental results, and guides readers through in-depth calculations supplemented with supportive figures in order to both retrace the interpretations and span the bridge between experiment and state-of-the art theory.

Significance. If the unified interpretation of the optical data holds across the three systems, the work would be significant for advancing understanding of quantum-critical electrodynamics in superconductors. The explicit inclusion of detailed calculations and figures allows readers to retrace the steps from data to model, which directly addresses potential concerns about circularity or post-hoc fitting by making the interpretive process transparent and falsifiable.

minor comments (2)
  1. Figure captions and legends should explicitly state the temperature range, frequency window, and any normalization procedures used for each dataset to facilitate direct comparison across the NbN, granular Al, and CeCoIn5 results.
  2. The notation for conductivity components (e.g., real vs. imaginary parts) and scaling variables should be defined consistently in a single location, as the three material systems are discussed in separate sections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our thesis on the electrodynamics of quantum-critical conductors and superconductors. We appreciate the recognition that the work offers a unified experimental and theoretical view across disordered NbN, granular Al, and CeCoIn5, along with the value placed on the transparent inclusion of detailed calculations and figures.

Circularity Check

0 steps flagged

No significant circularity; derivations are self-contained

full rationale

The thesis introduces standard theoretical models for quantum-critical electrodynamics separately from the experimental data on NbN, granular Al, and CeCoIn5. It then performs calculations to interpret the measured conductivity and superfluid responses, with figures provided to retrace the steps. No load-bearing prediction reduces by construction to a fitted parameter from the same dataset, no self-citation chain substitutes for an independent derivation, and no ansatz is smuggled in via prior work by the same author. The central unification rests on matching observed scaling forms to model outputs rather than redefining inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only provides no explicit free parameters, axioms, or invented entities. The work relies on standard theoretical models for quantum-critical conductivity and superconductivity, but specific assumptions, fitted scales, or new entities cannot be identified from the given text.

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