The reentrant superconductivity is the peculiar phenomenon observed in paramagnetic metal UTe$_2$ in magnetic field parallel to the hard magnetisation axis. It is difficult to explain it in terms of field dependent intensity of magnetic fluctuations like it is done for explanation of the formally similar phenomena in the ferromagnetic uranium superconductors URhGe, UCoGe. Extremely large initial slope of the upper critical field temperature dependence suggests that the phenomenon has the quasi-two-dimensional nature. Indeed, according to the recent band structure calculations by Yuanji Xu et al, Phys.Rev. Lett. {\bf 123}, 217002 (2019) the Fermi surface of UTe$_2$ consists of two types slightly corrugated cylinders.The theory of reentrant superconductivity in UTe$_2$ based on its quasi-two-dimensional structure is presented here.
Reentrant superconductivity has been observed in the candidate spin-triplet superconductor UTe$_2$ as a function of the magnetic field applied along the hard axis. Resistivity measurements have shown, a broadened superconducting transition appears near the minimal $T_c$, highlighting the importance of superconducting fluctuations in this regime. We present a phenomenological study assuming a field-driven first-order transition between two superconducting states. We show that with quenched randomness, inhomogeneity-enhanced superconducting fluctuations near the transition could naturally accoun…
We report on theoretical studies on ferromagnetic superconductors, URhGe, and UCoGe and identifies the pairing state as a non-unitary spin-triplet one, analogous to superfluid $^3$He-A phase. A recently found superconductor UTe$_2$ with almost ferromagnet is analyzed by the same manner. Through investigating their peculiar upper critical field $H_{\rm c2}$ shapes, it is shown that the pairing symmetry realized in all three compounds can be tuned by their magnetization curves under applied fields. This leads to the reentrant $H_{\rm c2}$ in URhGe, an S-shaped in UCoGe and an L-shaped $H_{\rm c2…
The recent discovery of superconductivity in heavy Fermion compound UTe2, a candidate topological and triplet-paired superconductor, has aroused widespread interest. However, to date, there is no consensus on whether the stoichiometric sample of UTe2 is superconducting or not due to lack of reliable evidence to distinguish the difference between the nominal and real compositions of samples. Here, we are the first to clarify that the stoichiometric UT2 is non-superconducting at ambient pressure and under hydrostatic pressure up to 6 GPa, however we find that it can be compressed into supercondu…
It was theoretically predicted more than 20 years ago [A.G. Lebed and K. Yamaji, {\it Phys. Rev. Lett.} {\bf80}, 2697 (1998)] that a triplet quasi-two-dimensional (Q2D) superconductor could restore its superconducting state in parallel magnetic fields, which are higher than its upper critical magnetic field, $H > H_{c2}(0)$. It is very likely that recently such phenomenon has been experimentally discovered in the Q2D superconductor UTe$_2$ by Nicholas Butch, Sheng Ran and their colleagues and has been confirmed by Japanese-French team. We review our previous theoretical results, using such a g…
We report low-temperature muon spin relaxation/rotation (muSR) measurements on single crystals of the actinide superconductor UTe2. Below 5 K we observe a continuous slowing down of magnetic fluctuations that persists through the superconducting (SC) transition temperature (Tc = 1.6 K), but we find no evidence of long-range or local magnetic order down to 0.025 K. The temperature dependence of the dynamic relaxation rate down to 0.4 K agrees with the self-consistent renormalization theory of spin fluctuations for a three-dimensional weak itinerant ferromagnetic metal. Our muSR measurements als…
We present a study of reentrant behavior in a composite formed by a Hight-T$ _{c} $ superconductor, YBa$_2$Cu$_3$O$ _{7-δ}$ and Ammonium Terbium Oxalate, Tb(H$_2$O)(C$ _2$O$_4$)$_2$ $\cdot $NH$_4$. The composite has a transition temperature about 92 K, and it presents a reentrant behaviour resulting of the coexistence between superconductivity and magnetism. According to this study the values and shape of the critical magnetic fields were dramatically reduced in a similar form as in other known reentrant superconductors.
Magnetic field induced superconductivity is a fascinating quantum phenomenon, whose origin is yet to be fully understood. The recently discovered spin triplet superconductor, UTe2, exhibits two such superconducting phases, with the second one reentering in the magnetic field of 45 T and persisting up to 65 T. More surprisingly, in order to induce this superconducting phase, the magnetic field has to be applied in a special angle range, not along any high symmetry crystalline direction. Here we investigated the evolution of this high-field induced superconducting phase under pressure. Two super…
It was suggested by Rasolt and Tešanović that the Landau level quantization in isotropic superconductors could enhance superconductivity in a very strong magnetic field, above the upper critical field ($H_{c2}$). We derive a generalized Harper equation for superconducting systems, and show that a similar reentrant behavior appears in a lattice model, even though the Landau--level--structure is destroyed by the periodic potential in that case. Both the orbital and the Zeeman field--induced effects are taken into account.
The putative spin-triplet superconductor UTe2 has an Ising-like magnetic anisotropy, indicating the Cooper pair spins parallel to the easy-axis. However, the upper critical field for the hard-axis direction is much larger than that for the easy-axis, implying the strong suppression of the Pauli depairing effect even for the hard-axis direction. This observation is consistent with the recent NMR measurements which show the tiny decrease of the Knight shift below the transition temperature Tc for hard-axis magnetic fields. We clarify that these behaviors are naturally understood as a result of m…
By systematic investigations of the magnetic, transport and thermodynamic properties of single crystals of EuFe2(As1-xPx)2 we explore the complex interplay of superconductivity and Eu2+ magnetism. Below 30K, two magnetic transitions are observed for all P substituted crystals suggesting a revision of the phase diagram. In addition to the canted A-type antiferromagnetic order of Eu2+ at approximately 20K, a spin glass transition is discovered at lower temperatures. Most remarkably, the reentrant spin glass state of EuFe2(As1-xPx)2 coexists with superconductivity around x = 0.2.
A reentrant superconducting effect was observed in YBCO particles as a consequence of their size and microstructure. It rises from the coexistence between bulk superconductivity and surface ferromagnetism, where the enhanced magneto-electric coupling induced by broken spatial-inversion symmetry in layers near structural defects plays a very important role on surface ferromagnetism. The study assumes grain boundaries inside the particles act as additional surface regions that enhance the ferromagnetic properties. Magnetic and superconducting properties as a function of particle size were studie…
There is presented a phenomenological description of phase diagram of ferromagnet superconductor URhGe. In frame of the Landau phenomenological theory it was found that phase transition between anisotropic ferromagnetic and paramagnetic states under strong enough magnetic field perpendicular to direction of easy magnetization changes from the second to the first order type. It is shown that magnetic susceptibility corresponding to longitudinal magnetic fluctuations strongly increases in vicinity of the first order transition stimulating reentrance of superconducting state. The reentrant superc…
The spin-triplet state is most likely realized in uranium ferromagnetic superconductors, UGe2, URhGe, UCoGe. The microscopic coexistence of ferromagnetism and superconductivity means that the Cooper pair should be realized under the strong internal field due the ferromagnetism, leading to the spin-triplet state with equal spin pairing. The field-reinforced superconductivity, which is observed in all three materials when the ferromagnetic fluctuations are enhanced, is one of the strong evidences for the spin-triplet superconductivity. We present here the results of a newly discovered spin-tripl…
We report duration dependence of superconductivity in a 43 \% humidity atmosphere and $^{59}$Co nuclear quadrupole resonance (NQR) of polycrystalline samples of $bi$layer hydrated Na$_x$CoO$_2 \cdot y$H$_2$O. We found a reentrant behavior of superconductivity with respect to the time duration. We obtained the universal phase diagram where two superconducting phases and an in-between magnetic phase are classified by $^{59}$Co NQR frequency. Zero field $^{59}$Co nuclear spin-lattice relaxation rates $1/T_1$ indicated a magnetic critical slowing down at 5 K in the magnetic phase, excluding a char…
We study a bilayer consisting of an ordinary superconductor and a magnet with a spiral magnetic structure of the {\rm Ho} type. We use a self consistent solution of the Bogolioubov-de Gennes equations to evaluate the pair amplitude, the transition temperature, and the thermodynamic functions, namely, the free energy and entropy. We find that for a range of thicknesses of the magnetic layer the superconductivity is reentrant with {\it temperature} $T$: as one lowers $T$ the system turns superconducting, and when $T$ is further lowered it turns normal again. This behavior is reflected in the con…
We report evidence for a reentrant spin glass phase in electron-doped $\text{EuFe}_2\text{As}_2$ single crystals and first traces of the superconductivity re-entrance in optics. In the close-to-optimal doped $\text{Eu}(\text{Fe}_{0.91}\text{Ir}_{0.09})_2\text{As}_2$ and $\text{Eu}(\text{Fe}_{0.93}\text{Rh}_{0.07})_2\text{As}_2$ samples two magnetic transitions are observed below the superconducting critical temperature $T_c \approx 21$~K: the canted $A$-type antiferromagnetic order of the $\text{Eu}^{2+}$ ions sets in around $17\,\text{K}$; the spin glass behavior occurs another $2\,\text{K}$ …
Ferromagnet/Superconductor/Ferromagnet (F/S/F) trilayers, in which the establishing of a Fulde-Ferrell Larkin-Ovchinnikov (FFLO) like state leads to interference effects of the superconducting pairing wave function, form the core of the superconducting spin valve. The realization of strong critical temperature oscillations in such trilayers, as a function of the ferromagnetic layer thicknesses or, even more efficient, reentrant superconductivity, are the key condition to obtain a large spin valve effect, i.e. a large shift in the critical temperature. Both phenomena have been realized experime…
Previous works on nodal d-wave superconductors have shown that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like modulated superconducting (SC) state can be realized with no magnetic field when quasiparticles acquire an additional linear term in the wavevector in their dispersion. In the present work, stability of such a novel modulated SC state in an artificial film against an applied magnetic field is studied. As a reflection of the presence of the two different FFLO states, one close to zero field and the other at the high field end, in a single field v.s. temperature phase diagram of thin fil…
We derive integral equation for superconducting gap, which takes into account the quantum nature of electron motion in a parallel magnetic field in a quasi-two-dimensional (Q2D) superconductor in the presence of a non-zero perpendicular field component. By comparison of our theoretical results with the recent experimental data obtained on the NbS$_2$, we show that the orbital effect against superconductivity partially destroys superconductivity in the so-called Ginzburg-Landau area of this Q2D conductor, as expected. Nevertheless, at relatively high magnetic fields, $H \simeq 15 \ T$, the orbi…
In the following paper we investigate the critical temperature $T_c$ behavior in the two-dimensional S/TI (S denotes superconductor and TI - topological insulator) junction with a proximity induced in-plane helical magnetization in the TI surface. The calculations of $T_c$ are performed using the general self-consistent approach based on the Usadel equations in Matsubara Green's functions technique. We show that the presence of the helical magnetization leads to the nonmonotonic behavior of the critical temperature as a function of the topological insulator layer thickness.
The discovery of superconductivity in the heavy-fermion paramagnet UTe$_2$ has attracted a lot of attention, particularly due to the reinforcement of superconductivity near pressure- and magnetic-field-induced magnetic quantum phase transitions. A challenge is now to characterize the effects of combined pressure and magnetic fields applied along variable directions in this strongly anisotropic paramagnet. Here, we present an investigation of the electrical resistivity of UTe$_2$ under pressure up to 3~GPa and pulsed magnetic fields up to 58~T along the hard magnetic crystallographic directions…
Time-reversal symmetry breaking (TRSB) in UTe2 was inferred from observations of a spontaneous Kerr response in the superconducting state after cooling in zero magnetic field, while a finite c-axis magnetic field training was further used to determine the nature of the non-unitary composite order-parameter of this material. Here we present an extensive study of the magnetic-field-trained Kerr effect, which unveils a unique critical state of pinned ferromagnetic vortices. We show that a remanent Kerr signal that appears following the removal of a training magnetic field, which reflects the resp…
Ferromagnet/Superconductor/Ferromagnet (F/S/F) trilayers constitute the core of a superconducting spin valve. The switching effect of the spin valve is based on interference phenomena occurring due to the proximity effect at the S/F interfaces. A remarkable effect is only expected if the core structure exhibits strong critical temperature oscillations, or most favorable, reentrant superconductivity, when the thickness of the ferromagnetic layer is increased. The core structure has to be grown on an antiferromagnetic oxide layer (or such layer to be placed on top) to pin by exchange bias the ma…
Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect and Bose-Einstein condensation of spin excitations. Superconductivity, on the other hand, is inherently antagonistic towards magnetic fields. Only in rare cases can these effects be mitigated over limited fields, leading to reentrant superconductivity. Here, we report the unprecedented coexistence of multiple high-field reentrant superconducting phases in the spin-triplet superconductor UTe2. Strikingly, we observe superconductivity in the highest magnetic field range identified for any reentrant…
We report the magnetoresistance in the novel spin-triplet superconductor UTe2 under pressure close to the critical pressure Pc, where the superconducting phase terminates, for field along the three a, b and c-axes in the orthorhombic structure. The superconducting phase for H // a-axis just below Pc shows a field-reentrant behavior due to the competition with the emergence of magnetic order at low fields. The upper critical field Hc2 for H // c-axis shows a quasi-vertical increase in the H-T phase diagram just below Pc, indicating that superconductivity is reinforced by the strong fluctuations…
UTe$_2$ has recently been found to be a likely spin-triplet superconductor that exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe$_2$ is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of superconductivity. In particular, we show that DFT+$U$ calculations generically reveal a topological band that originates from a band inversion associated with $5f$ electrons residing on these rung sublattice …
Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature $T_c$. Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin $S=0$, although they can also form parallel spin-triplet Cooper pairs with $S=1$ and an odd parity wavefunction. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation. Because spin-triplet pairing is usually mediated by ferromagnetic (FM…
Superconductivity (S) and ferromagnetism (F) are probed through transport and magnetization measurements in nanometer scale HoNi$_5$-NbN (F-S) bilayers and HoNi$_5$-NbN-HoNi$_5$ (F-S-F) trilayers. The choice of materials has been made on the basis of their comparable ordering temperatures and strong magnetic anisotropy in HoNi$_5$. We observe the normal state reentrant behavior in resistance vs. temperature plots of the F-S-F structures just below the superconducting transition in the limited range of HoNi$_5$ layer thickness d$_{HN}$ (20 nm $<$ d$_{HN}$ $<$ 80 nm) when d$_{NbN}$ is fixed at $…
We theoretically study superconductivity in UTe$_2$, which is a recently-discovered strong candidate for an odd-parity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA$+U$ method and show the insulator-metal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of $U$, we clarify topological properties of possible superconductin…
We investigate the spin dynamics in the superconducting phase of UTe$_{2}$ by triple-axis inelastic neutron scattering on a single crystal sample. At the wave-vector $\bf{k_1}$=(0, 0.57, 0), where the normal state antiferromagnetic correlations are peaked, a modification of the excitation spectrum is evidenced, on crossing the superconducting transition, with a reduction of the relaxation rate together with the development of an inelastic peak at $Ω$ $\approx$ 1 meV. The low dimensional nature and the the $a$-axis polarization of the fluctuations, that characterise the normal state, are essent…
The interplay between superconductivity and Eu$^{2+}$ magnetic ordering in Eu(Fe$_{1-x}$Ir$_{x}$)$_{2}$As$_{2}$ is studied by means of electrical transport and magnetic measurements. For the critically doped sample Eu(Fe$_{0.86}$Ir$_{0.14}$)$_{2}$As$_{2}$, we witnessed two distinct transitions : a superconducting transition below 22.6 K which is followed by a resistivity reentrance caused by the ordering of the Eu$^{2+}$ moments. Further, the low field magnetization measurements show a prominent diamagnetic signal due to superconductivity which is remarkable in presence of a large moment magne…
We studied the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like state establishing due to the proximity effect in superconducting Nb/Cu41Ni59 bilayers. Using a special wedge-type deposition technique, series of 20-35 samples could be fabricated by magnetron sputtering during one run. The layer thickness of only a few nanometers, the composition of the alloy, and the quality of interfaces were controlled by Rutherford backscattering spectrometry, high resolution transmission electron microscopy, and Auger spectroscopy. The magnetic properties of the ferromagnetic alloy layer were characterized with…
The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after the discovery of superconductivity it has been expected to be close to a ferromagnetic instability showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. The competition between different types of magnetic interactions and the duality between the local and itinerant character…
Spin-flip scattering from magnetic impurities has a strong pair-breaking effect in $s$-wave superconductors where increasing the concentration of impurities rapidly destroys superconductivity. For small Kondo temperature $T_K$ the destruction of superconductivity is preceded by the reentrant superconductivity at finite temperature range $T_{c2} < T < T_{c1}$, while the normal phase reappears at $T<T_{c2} \sim T_K$. Here we explore the superconducting phase in a periodic system modeled as the Anderson lattice with additional attractive on-site (Hubbard) interaction $g$ acting on the conduction …
Superconductivity induced by a magnetic field near metamagnetism is a striking manifestation of magnetically-mediated superconducting pairing. After being observed in itinerant ferromagnets, this phenomenon was recently reported in the orthorhombic paramagnet UTe$_2$. Under a magnetic field applied along the hard magnetization axis b, superconductivity is reinforced on approaching metamagnetism at $μ_0H_m$ = 35 T, but it abruptly disappears beyond $H_m$. On the contrary, field-induced superconductivity was reported beyond $μ_0H_m$ = 40-50 T in a magnetic field tilted by $\simeq25-30°$ from b i…
Newly-discovered superconductor UTe$_2$ is a strong contender for a topological spin-triplet state wherein a multi-component order parameter arises from two nearly-degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe$_2$ at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the tw…
