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Now, we will first focus on the features that are visible outside the superconducting gap range. In Fig. 8.7a, the superconducting spectrum of Fig. 8.6 is shown as a normal-

8.4 Spectroscopic Results ized spectrum. The normalization was performed according to the measured normally conducting spectrum (shown as green line in Fig. 8.6) by

dI/dU_norm(U ) = dI/dUsc(U ) dI/dUnc(pU2− ∆2/e2

. (8.3)

A peak is visible around ±4.46 mV (black line) and a hump at ±6.5 mV (green line). Sec. 6.3 showed what the differential conductance of an unconventional superconduc- tor looks like in the case of the spin-fermion approach (see Fig. 6.11). In Fig. 8.8, the theoretically calculated dI/dU and dI/dU spectra are compared to each other in the cases of weak and strong inelastic contributions. This calculation was done by P. Hlo- bil and J. Schmalian. In the case of negligible small inelastic contributions, a peak-like feature arising from a resonance mode would be visible at an energy ∆ + ωres. The

energy of the resonance mode is coupled to the superconducting gap size and is usu- ally in the range of ωres≈ 1.3∆. Since we have at least three different superconducting

energy gaps in our experimental data, the situation becomes complicated. One might think that we should see a separate resonance mode for every different superconduct- ing gap. However, according to discussions with J. Schmalian, P. Hlobil and M. Klug, the most striking one should be the one coming from the gap with the largest spec- tral weight. This would be ∆2 in our case. The position of 1.3 · ∆2 + ∆2 =2.76 mV

would almost coincide with the position of ∆3 ≈ 2.45 mV. We do not question the peak

around 2.45 mV to be a superconducting gap feature, since it turned out to be of largest intensity among the other gaps in previous measurements (see. Fig. 8.5). Therefore, a possible resonance feature at this position would be overshadowed by the quasiparti- cle coherence peak of ∆3 and no statement can be made about this resonance mode.

Another possibility for the occurrence of a resonance mode could be a weighed reso- nance mode, which occurs around an energy that corresponds, e.g., to the mean value of the two clearest gaps (∆2, ∆3). The position would be given by

∆avg(2,3) ≈ 1.3 ·

∆2 + ∆3

2 +

∆2+ ∆3

2 ≈ 4.2 mV. (8.4)

In Fig. 8.7a/b, a feature around this energy can be seen and it is marked by the black dashed line. Since it appears as a peak-like feature in the first derivative of the tun- neling current (Fig. 8.7a), it would indicate rather weak inelastic contributions to this system, even though this does not fit to the observed V-shaped tunneling conductance in the normal state. As a third possibility, we consider only the largest superconducting energy gap ∆3 and its resonance mode ωres,3. In the superconducting dI/dU spectrum,

the corresponding feature would occur at

ωres,3+ ∆3 = 1.3 · ∆3+ ∆3 = 5.64 mV. (8.5)

This position is marked by an orange dashed line in Fig. 8.7a/b. At this energy, a downward-pointing step-like feature is visible. In the case of slightly larger energies, the normalized differential conductance falls below unity and therefore below the cor- responding normally conducting differential conductance. This can be observed in

8 FeSe

Fig. 8.6 as well. The occurrence of the humpl-like features would imply significant in- elastic contributions in the system (cf. Fig. 8.8) and would fit to the observed V-shaped background in the normally conducting differential conductance (see green spectrum in Fig 8.6). Furthermore, the resonance mode observed by neutron scattering was lo- cated at an energy of 4 meV [289]. This resonance mode would appear at an energy shifted by the superconducting energy gap in a tunneling spectrum. The energy of 4 meV is closest to the energy of the resonance mode at ωres,3 ≈ 3.2 mV. The latter cor-

responds to the resonance mode of our largest superconducting gap ∆3 and would

therefore fit. The energy position of the resonance mode located around 4 meV, shifted by ∆3, is marked by a green dashed line in Fig. 8.7a/b. It is still in the region of the

hump-like feature just explained.

Figure 8.8:The upper panel shows the calcu- lated supeconducting differential conductance σ which was normalized according to Eq. 8.3. The calculation was performed by P. Hlobil and J. Schmalian for inelastic contributions varying in size. The resonance feature occurs between 2∆ and 3∆ and appears as a shoulder in the case of weak inelastic contributions and as a dip in the case of strong inelastic contributions. The lower panel shows the corresponding cal- culated derivative (=db

2_I/dU2_{). At the posi-} tive energy range, strong inelastic contributions lead to a peak reaching a positive intensity at ∆ + ωres. Taken from Ref. [11].

strong inelastic contr. pure elastic 0 Δ Δ+ωres 0 1 Δ 2Δ 3Δ a - 6 - 4 - 2 0 2 4 6 Δ Δ+ωres

strong inelastic contr.

pure elastic

In Fig. 8.7c, the symmetrized superconducting dI/dU spectrum is shown, which was obtained from another measurement on a different FeSe sample and with a differ- ent W-tip. The temperature during the measurements shown in Fig. 8.7a and c are comparable, whereas the tunneling current was significantly larger in the case of the spectrum shown in Fig. 8.7c (I=21.8 nA). The dashed lines mark the same position as in Fig. 8.7a and b. Again, a hump-like feature is visible around ±4.2 mV followed by a step pointing downwards at around 5.6 mV. In Fig. 8.7d, the to c corresponding antisymmetrized dI/dU spectrum corresponding to c is shown. The red dashed line marks another feature which is clearly visible around ±8 mV. It appears as a dip at −8 mV and as a peak at +8 mV. According to the experimental data, the largest gap ∆3 is at ≈ 2.45 mV. The values for the energy positions of two and three times of this

gap size are marked in Fig. 8.7c. In this energy range, the resonance feature of ∆3

8.4 Spectroscopic Results is expected1_{. The observed feature is located at a slightly larger energy than 3 · ∆}

3.

Assuming an electronic temperature of 100 mK and taking into account a modula- tion voltage of U∆ = 200 µV, the energy resolution of the spectra in Fig. 8.7b and d

isp(1.22U∆)2+ (5.4kBT )2 ≈250 µeV. This high energy resolution can probably not ex-

plain an energy deviation of more than 500 µeV to the position of 3∆3. On the other

hand, one could argue that the energy range for the existence of the resonance might not end abruptly. In this case, we might be still be allowed to talk about a resonance feature that would be strongly overshadowed by inelastic contributions in the present case. On the other hand, the deviation to the position of the resonance feature accord- ing to the recent INS data [289] (ωres,INS+ ∆3 ≈ 6.45 mV assuming an energy shift of ∆3)

is off about 1 meV and therefore not negligible small. However, the energy resolution of the INS setup is 1 meV [289]. Therefore, it could be indeed possible that the feature around 8 meV yet corresponds to the resonance mode measured by Wang et al. [289]. Nevertheless, only one resonance mode can occur from the opening of ∆3 in the su-

perconducting state. Therefore, one has to decide whether the feature around 5.6 mV (orange line in Fig. 8.7) or the one around 8 meV corresponds to the resonance mode of ∆3. According to a neutron scattering measurement [308] and an57Fe nuclear inelastic

scattering experiment [309], a transversal acoustic phonon exists at 5.6 meV [309]. In a corresponding superconducting tunneling spectrum, this phonon mode would appear at an energy shifted by the superconducting gap energy ∆. Adding ∆3to the energy of

this phonon mode, we would end up at an energy of 8 mV for the position of the mode in a superconduting tunneling spectrum. The phonon, being an inelastic excitation, would appear as a dip for the negative energy range and as a peak for the positive voltage range. This appearance can be observed for our mode at ±8 mV. Therefore, a possible final conclusion could be the following: The feature around 5.64 mV (orange line in Fig. 8.7) corresponds to the resonance mode of ∆3 which is overshadowed by

inelastic contributions. The feature around 8 mV corresponds to a Van Hove singular- ity of a transversal acoustic mode. The clearer occurrence of this feature in the case of Fig. 8.7d is most likely due to the larger tunneling current used in this case and therefore a larger probability of the creation of inelastic excitations.