Characterization of harmonic modes and parasitic resonances in multi-mode superconducting coplanar resonators

Planar superconducting microwave transmission line resonators can be operated at multiple harmonic resonance frequencies. This allows covering wide spectral regimes with high sensitivity, as it is desired e.g. for cryogenic microwave spectroscopy. A common complication of such experiments is the presence of undesired 'spurious' additional resonances, which are due to standing waves within the resonator substrate or housing box. Identifying the nature of individual resonances ('designed' vs. 'spurious') can become challenging for higher frequencies or if elements with unknown material properties are included, as is common for microwave spectroscopy. Here we discuss various experimental strategies to distinguish designed and spurious modes in coplanar superconducting resonators that are operated in a broad frequency range up to 20 GHz. These strategies include tracking resonance evolution as a function of temperature, magnetic field, and microwave power. We also demonstrate that local modification of the resonator, by applying minute amounts of dielectric or ESR-active materials, lead to characteristic signatures in the various resonance modes, depending on the local strength of the electric or magnetic microwave fields

Tuning Charge Order in (TMTTF)₂<i>X</i> by Partial Anion Substitution

In the quasi-one-dimensional (TMTTF)2X compounds with effectively quarter-filled bands, electronic charge order is stabilized from the delicate interplay of Coulomb repulsion and electronic bandwidth. The correlation strength is commonly tuned by physical pressure or chemical substitution with stoichiometric ratios of anions and cations. Here, we investigate the charge-ordered state through partial substitution of the anions in (TMTTF)2[AsF6]1−x[SbF6]x with x≈0.3, determined from the intensity of infrared vibrations, which is sufficient to suppress the spin-Peierls state. Our dc transport experiments reveal a transition temperature TCO = 120 K and charge gap ΔCO=430 K between the values of the two parent compounds (TMTTF)2AsF6 and (TMTTF)2SbF6. Upon plotting the two parameters for different (TMTTF)2X, we find a universal relationship between TCO and ΔCO yielding that the energy gap vanishes for transition temperatures TCO≤60 K. While these quantities indicate that the macroscopic correlation strength is continuously tuned, our vibrational spectroscopy results probing the local charge disproportionation suggest that 2δ is modulated on a microscopic level

Tuning Charge Order in (TMTTF)2X by Partial Anion Substitution

In the quasi-one-dimensional (TMTTF)2X compounds with effectively quarter-filled bands, electronic charge order is stabilized from the delicate interplay of Coulomb repulsion and electronic bandwidth. The correlation strength is commonly tuned by physical pressure or chemical substitution with stoichiometric ratios of anions and cations. Here, we investigate the charge-ordered state through partial substitution of the anions in (TMTTF)2[AsF6]1&minus;x[SbF6]x with x&asymp;0.3, determined from the intensity of infrared vibrations, which is sufficient to suppress the spin-Peierls state. Our dc transport experiments reveal a transition temperature TCO = 120 K and charge gap &Delta;CO=430 K between the values of the two parent compounds (TMTTF)2AsF6 and (TMTTF)2SbF6. Upon plotting the two parameters for different (TMTTF)2X, we find a universal relationship between TCO and &Delta;CO yielding that the energy gap vanishes for transition temperatures TCO&le;60 K. While these quantities indicate that the macroscopic correlation strength is continuously tuned, our vibrational spectroscopy results probing the local charge disproportionation suggest that 2&delta; is modulated on a microscopic level

Structural and Electronic Properties of (TMTTF)2X Salts with Tetrahedral Anions

Comprehensive measurements of the pressure- and temperature-dependent dc-transport are combined with dielectric spectroscopy and structural considerations in order to elucidate the charge and anion orderings in the quasi-one-dimensional charge-transfer salts (TMTTF) 2 X with non-centrosymmetric anions X = BF 4 , ClO 4 and ReO 4 . Upon applying hydrostatic pressure, the charge-order transition is suppressed in all three compounds, whereas the influence on the anion order clearly depends on the particular compound. A review of the structural properties paves the way for understanding the effect of the anions in their methyl cavities on the ordering. By determining the complex dielectric constant ϵ ^ ( ω , T ) in different directions we obtain valuable information on the contribution of the anions to the dielectric properties. For (TMTTF) 2 ClO 4 and (TMTTF) 2 ReO 4 , ϵ b ′ exhibits an activated behavior of the relaxation time with activation energies similar to the gap measured in transport, indicating that the relaxation dynamics are determined by free charge carriers