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## Quantum vortex liquid in iron-based superconductors FeSe_{1-x}S_{x} and FeSe_{1-x}Te_{x} with the electron nematic order

In a new paper published in Nature Communications, our colleague Matija Čulo in collaboration with scientists from England, Netherlands and Japan, reported a high-field magnetotransport study that provided compelling evidence for the existence of an exotic and a very rare quantum vortex liquid phase in superconductors FeSe_{1-x}S* _{x}* and FeSe

_{1-x}Te

*with the electron nematic order.*

_{x}**Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe**_{1-x}S_{x} and FeSe_{1-x}Te_{x}

_{1-x}S

*and FeSe*

_{x}_{1-x}Te

_{x}

M. Čulo, S. Licciardello, K. Ishida, K. Mukasa, J. Ayres, J. Buhot, Y.-T. Hsu, S. Imajo, M. W. Qiu, M. Saito, Y. Uezono, T. Otsuka, T. Watanabe, K. Kindo, T. Shibauchi, S. Kasahara, Y. Matsuda, N. E. Hussey.

Nature Communications **14**, 4150 (2023). DOI: 10.1038/s41467-023-39730-9

Quantum vortex liquid is an exotic state of type-II superconductors, in which the standard Abrikosov vortex lattice is melted even at extremelly low temperatures (*T*), due to strong quantum fluctuations of the superconducting order parameter. Such a state is theoretically very poorly understood, and experimentally has been confirmed only in a few materials. One of the key questions is the exact origin of these strong superconducting quantum fluctuations and the role played by nearby non-superconducting phases.

In a new study, our colleague Matija Čulo in collaboration with scientists from England, Netherlands and Japan, provides compelling evidence for the existence of such a rare and exotic quantum vortex liquid state in iron-based superconductors FeSe_{1-x}S* _{x}* and FeSe

_{1-x}Te

*, which are unique due to unconventional superconductivity that emerges from a pure eletron nematic state. Presence of the quantum vortex liquid was indicated by determining two critical magnetic fields (*

_{x}*H*): the so-called melting field

*H*, beyond which vortex lattice transforms into vortex liquid and upper critical field

_{m}*H*

_{c}_{2}, beyond which the vortex liquid transforms into normal (non-superconducting) state. The critical fields

*H*and

_{m}*H*

_{c}_{2}were extracted from the measurements of electrical resistance (

*R*) in high magnetic fields up to 60 T and at very low temperatures down to 0.3 K in a way illustrated in Figure 1a) for FeSe

_{1-x}S

*with*

_{x}*x*= 0.25 at

*T*= 0.3 K.

The same procedure was carried out for all measured temperatures and for all FeSe_{1-x}S* _{x}* and FeSe

_{1-x}Te

*samples, and such determined*

_{x}*H*(

_{m}*T*) and

*H*

_{c}_{2}(

*T*) were used for the construction of

*H*-

*T*phase diagrams in which the following phases can be discerned: vortex lattice/solid below

*H*(

_{m}*T*), vortex liquid between

*H*(

_{m}*T*) and

*H*

_{c}_{2}(

*T*) and normal (non-superconducting) state above

*H*

_{c}_{2}(

*T*). An example of such an

*H*-

*T*phase diagram is shown in Figure 1b) for FeSe

_{1-x}S

*with*

_{x}*x*= 0.25. As we can see, there is a large separation between

*H*(

_{m}*T*) and

*H*

_{c}_{2}(

*T*) lines, which implies that the vortex lattice is melted and transformed into the vortex liquid across a significant part of the phase diagram, due to strong thermal fluctuations of the superconducting order parameter. Moreover, large separation between

*H*(

_{m}*T*) and

*H*

_{c}_{2}(

*T*) persists even at

*T*→ 0, where thermal fluctuations become negligible so that only quantum fluctuations can be responsible for destroying the vortex lattice. Such behavior provides compelling evidence for the existence of a quantum vortex liquid in FeSe

_{1-x}S

*with*

_{x}*x*= 0.25.

Similar *H*-*T* phase diagrams were also obtained for the rest of FeSe_{1-x}S* _{x}* and FeSe

_{1-x}Te

*samples, indicating that the quantum vortex liquid regime is present for all S and Te compositions. How strong is the quantum vortex liquid can be determined from the ratio between the melting field and the upper critical field*

_{x}*H*(0)/

_{m}*H*

_{c}_{2}(0), estimated in the limit

*T*→ 0 in the phase diagrams like the one in Figure 1b). The further the ratio

*H*(0)/

_{m}*H*

_{c}_{2}(0) from 1, the stronger the quantum vortex liquid regime. The dependence of such obtained ratio

*H*(0)/

_{m}*H*

_{c}_{2}(0) on

*x*is shown in Figure 2 for both families FeSe

_{1-x}S

*and FeSe*

_{x}_{1-x}Te

*. As we can see, the quantum vortex liquid regime in FeSe*

_{x}_{1-x}S

*is the strongest outside of the nematic phase for*

_{x}*x*≈ 0.25, and in FeSe

_{1-x}Te

*inside the nematic phase for*

_{x}*x*≈ 0.30. Such behavior indicates that there is no simple correlation between superconducting quantum fluctuations, i.e. the quantum vortex liquid regime and the nearby (non-superconducting) nematic phase. On the other hand, Figure 2 clearly shows that there is a strong correlation between the quantum vortex liquid regime and the superconducting phase itself, since wherever the quantum vortex liquid is the strongest, the superconducting transition temperature

*T*is the smallest. Here it should be stressed that this is not a trivial conclusion, since such an expanded quantum vortex liquid regime is never observed in conventional superconductors, which have small values of

_{c}*T*. These results could therefore be the key for the understanding of this exotic and very rare state in unconventional superconductors.

_{c}