Elvezio Morenzoni

The temperature dependent measurements of the thermodynamic critical field and the specific heat for the pressure stabilized Ga-II phase of elemental gallium are presented. The discussion of these and other Ga phases data in the context of elemental and binary phonon-mediated superconductors allowed to establish simple scaling relations between BCS quantities such as $B_{\mathrm{c}}\left(0\right)/T_{\mathrm{c}}\sqrt{{\gamma }_{\mathrm{e}}}$ and the specific heat jump at $T_{\mathrm{c}}$ versus the coupling strength $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}$ [$\mathrm{\Delta }$ and $B_{\mathrm{c}}\left(0\right)$ are the zero-temperature values of the superconducting energy gap and the thermodynamic critical field, respectively, $T_{\mathrm{c}}$ is the transition temperature, and ${\gamma }_{\mathrm{e}}$ is the electronic specific heat]. The scaling relations can be analytically expressed by taking into account strong-coupling corrections to BCS theory. Such correlations can naturally explain the linear relation between $B_{\mathrm{c}}\left(0\right)$ and $T_{\mathrm{c}}$, which holds for conventional superconducting materials.

Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here, we use the muon spin rotation/relaxation ($\mu \mathrm{SR}$) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier $\mu \mathrm{SR}$ studies on powders and crystals, we show that while the superconducting gap is most probably anisotropic but nodeless along the crystallographic $c$ axis, it is nodal in the $ab$ plane, as indicated by the linear increase of the superfluid density at low temperature. We further show that the superconducting properties of FeSe display a less pronounced anisotropy than expected.

Using muon-spin rotation the pressure-induced superconductivity in the Bi-III phase of elemental bismuth (transition temperature $T_{\mathrm{c}}\simeq 7.05$ K) was investigated. A Ginzburg-Landau parameter $\kappa =\lambda /\xi =30\left(6\right)$ ($\lambda$ is the magnetic penetration depth, $\xi$ is the coherence length) was estimated, which turns out to be the highest among known single element superconductors. The temperature dependence of the superconducting energy gap $\left[\mathrm{\Delta }\right(T\left)\right]$ reconstructed from ${\lambda }^{-2}\left(T\right)$ deviates from the weakly coupled BCS prediction. The coupling strength $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}\simeq 4.34$ was estimated, thus implying that Bi-III stays within the strong-coupling regime. The density functional theory calculations suggest that superconductivity in Bi-III could be described within the Eliashberg approach with a characteristic phonon frequency ${\omega }_{\ln }\simeq 5.5$ meV. An alternative pairing mechanism to the electron-phonon coupling involves the possibility of Cooper pairing induced by Fermi-surface nesting.

We have observed the spatial distribution of magnetic flux in Nb, $\mathrm{Cu}/\mathrm{Nb}$, and $\mathrm{Cu}/\mathrm{Nb}/\mathrm{Co}$ thin films using muon-spin rotation. In an isolated 50-nm-thick Nb film, we find a weak flux expulsion (Meissner effect) which becomes significantly enhanced when adding an adjacent 40 nm layer of Cu. The added Cu layer exhibits a Meissner effect (due to induced superconducting pairs) and is at least as effective as the Nb to expel flux. These results are confirmed by theoretical calculations using the quasiclassical Green’s function formalism. An unexpected further significant enhancement of the flux expulsion is observed when adding a thin (2.4 nm) ferromagnetic Co layer to the bottom side of the Nb. This observed cooperation between superconductivity and ferromagnetism, by an unknown mechanism, forms a key ingredient for developing superconducting spintronics.

Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second order to first order for pressures exceeding the critical value $p_{\mathrm{c}}\simeq 2.4–2.5$ GPa. The magnetic ordering temperature ($T_{\mathrm{N}}$) and the value of the magnetic moment per Fe site ($m_{\mathrm{Fe}}$) increase continuously with increasing pressure, reaching $T_{\mathrm{N}}\simeq 50$ K and $m_{\mathrm{Fe}}\simeq 0.25{\mu }_{\mathrm{B}}$ at $p\simeq 2.6$ GPa, respectively. No pronounced features at both $T_{\mathrm{N}}\left(p\right)$ and $m_{\mathrm{Fe}}\left(p\right)$ are detected at $p\simeq p_{\mathrm{c}}$, thus suggesting that the stripe-type magnetic order in FeSe remains unchanged above and below the critical pressure $p_{\mathrm{c}}$. A phenomenological model for the $(p,T)$ phase diagram of FeSe reveals that these observations are consistent with a scenario where the nematic transitions of FeSe at low and high pressures are driven by different mechanisms.

Bulk FeSe is superconducting with a critical temperature $T_c\cong 8$ K and ${\mathrm{SrTiO}}_3$ is insulating in nature, yet high-temperature superconductivity has been reported at the interface between a single-layer FeSe and ${\mathrm{SrTiO}}_3$. Angle-resolved photoemission spectroscopy and scanning tunneling microscopy measurements observe a gap opening at the Fermi surface below $\approx 60$ K. Elucidating the microscopic properties and understanding the pairing mechanism of single-layer FeSe is of utmost importance as it is a basic building block of iron-based superconductors. Here, we use the low-energy muon spin rotation/relaxation technique to detect and quantify the supercarrier density and determine the gap symmetry in FeSe grown on ${\mathrm{SrTiO}}_3$ (100). Measurements in applied field show a temperature-dependent broadening of the field distribution below $\sim 60$ K, reflecting the superconducting transition and formation of a vortex state. Zero-field measurements rule out the presence of magnetism of static or fluctuating origin. From the inhomogeneous field distribution, we determine an effective sheet supercarrier density $n_s^{2\text{D}}\simeq 6\times {10}^{14}{\mathrm{cm}}^{-2}$ at $T\to 0$ K, which is a factor of 4 larger than expected from ARPES measurements of the excess electron count per Fe of 1 monolayer FeSe. The temperature dependence of the superfluid density $n_s\left(T\right)$ can be well described down to $\sim 10$ K by simple $s$-wave BCS, indicating a rather clean superconducting phase with a gap of 10.2(1.1) meV. The result is a clear indication of the gradual formation of a two-dimensional vortex lattice existing over the entire large FeSe/STO interface and provides unambiguous evidence for robust superconductivity below 60 K in ultrathin FeSe.

Bulk FeSe is superconducting with a critical temperature $T_c$ $\cong$ 8 K and SrTiO$_3$ is insulating in nature, yet high-temperature superconductivity has been reported at the interface between a single-layer FeSe and SrTiO$_3$. Angle resolved photoemission spectroscopy and scanning tunneling microscopy measurements observe a gap opening at the Fermi surface below $\approx$ 60 K. Elucidating the microscopic properties and understanding the pairing mechanism of single-layer FeSe is of utmost importance as it is a basic building block of iron-based superconductors. Here, we use the low-energy muon spin rotation/relaxation technique (LE-$\mu$SR) to detect and quantify the supercarrier density and determine the gap symmetry in FeSe grown on SrTiO$_3$ (100). Measurements in applied field show a temperature dependent broadening of the field distribution below $\sim$ 60 K, reflecting the superconducting transition and formation of a vortex state. Zero field measurements rule out the presence of magnetism of static or fluctuating origin. From the inhomogeneous field distribution, we determine an effective sheet supercarrier density $n_s^{2D} \simeq 6 \times 10^{14}$ cm$^{-2}$ at $T \rightarrow 0$ K, which is a factor of 4 larger than expected from ARPES measurements of the excess electron count per Fe of 1 monolayer (ML) FeSe. The temperature dependence of the superfluid density $n_s(T)$ can be well described down to $\sim$ 10 K by simple s-wave BCS, indicating a rather clean superconducting phase with a gap of 10.2(1.1) meV. The result is a clear indication of the gradual formation of a two dimensional vortex lattice existing over the entire large FeSe/STO interface and provides unambiguous evidence for robust superconductivity below 60 K in ultrathin FeSe.