Applied magnetic fields destabilize and eventually destroy superconductivity by breaking up the constituent paired electrons. In most cases, this occurs through the effect of orbital pair-breaking, a condition wherein magnetic flux cores overlap. A competing pair-breaking effect occurs at the Pauli limit, the typically higher magnetic field at which Zeeman splitting destabilizes spin anti-aligned Cooper pairs 1 . In uranium ditelluride (UTe 2 ) crystals that exhibit a low-field superconducting transition, however, superconductivity survives to fields that well exceed the Pauli limit, due to the occurrence of unconventional spin-triplet superconductivity 2,3 . When the magnetic field is applied along the crystallographic b axis, superconductivity survives to a remarkably large magnetic field value of 35 T, limited only by a first-order metamagnetic transition-a discontinuity in the magnetization-at H m . However, if the magnetic field is tilted between a range of angles 20 o -40 o from the crystallographic b-axis towards the c-axis 4,5 , superconductivity returns for fields greater than 40 T, persisting to approximately 70 T. The focus of this work is the relationship between this very high-field reentrant superconductivity (SC FP ) and the lowfield phases (SC 1 and SC 2 ); SC 1 is generally assumed to be the primary, or "parent," superconducting phase.

The properties of the lower-field superconductivities in UTe 2 have been extensively studied, but the symmetries of the superconducting order parameter(s) have yet to be unambiguously determined [6][7][8] . From specific heat capacity and optical Kerr effect measurements, it was inferred that superconductivity in the lowest-field phase, SC 1 , can be described by a chiral, time-reversal symmetry breaking, multicomponent order parameter 6 . More recent investigations call into question the existence of a two-component order parameter and whether the state intrinsically breaks time reversal symmetry [9][10][11] . Evidence for a low-field point node gap structure is robust [12][13][14] , but has recently been questioned 15 . Experimental evidence suggests that applied fields oriented along the b axis induce transitions between multiple superconducting phases 16 , though the pairing states of and sample-dependent boundaries between these phases remain unclear 17,18 .

The dominant feature in the high-field UTe 2 phase diagram when the field is nearly parallel to the b axis is the metamagnetic transition from either SC 2 into a field-polarized normal state at applied field H m . The curving H m . boundary line has a minimum of about 35 T when the field is perfectly oriented along b and increases smoothly as the field is rotated towards one of the other crystallographic axes. The most extraordinary aspect of this phase diagram is SC FP , a pocket of zero resistance emerging at field orientations 20 o -40 o between b and c. The lower boundary of SC FP follows H m , which at these angles occurs at approximately 40 T 4,5 .

Due to the unprecedentedly high fields required to stabilize the SC FP superconducting phase, determining its pairing symmetry presents an even greater challenge than those of SC 1 and SC 2 , and explorations have been limited despite plain fundamental interest 3,[19][20][21][22][23][24][25] . It is difficult to concretely establish the nature of the relationship between the lower field superconducting phases and SC FP as there are few relevant precedents. While other uranium-containing superconductors, such as URhGe 26 and UCoGe 1 , exhibit field stabilized reentrant superconductivity at specific angles, these phases occur in proximity to ferromagnetic quantum critical points, whereas UTe 2 does not magnetically order below 1.4 GPa 22 . Other proposed explanations for the intense field enhancement of SC FP include lowered dimensionality 20,21 , which can suppress the orbital limiting effects of magnetic fields, or internal exchange fields that counteract the applied external field 3,5,27,28 , leading the conduction electrons to experience smaller total magnetic fields than those applied. The commonality between these hypotheses is the assumption that high-field superconductivity represents an extension of a lower-field superconducting phase. The debate regarding SC FP thus centers upon which established mechanism fortifies low field superconductivity against the deleterious effects of extreme magnetic fields. The assumptions upon which these models are based are incompatible with a superconducting phase which emerges only at extremely high-fields, and such an observation would therefore require a new form of high-field superconductivity to explain.

In this work, we present the first evidence of "orphaned" high-field superconductivity (oSC FP ) without an accompanying low-field "parent" phase. This unusual configuration has been achieved in UTe 2 through the controlled introduction of disorder, which destabilizes SC 1 and SC 2 , while SC FP unexpectedly survives at high-fields. In addition to presenting the first example of exclusively high-field-stabilized superconductivity in a uranium-based system, these findings dramatically limit possible explanations for the stability of high-field superconductivity in UTe 2 and its relation to lower field superconductivity, demanding a new theoretical framework.

In the Orphan UTe 2 samples studied here, there is no evidence of SC 1 or SC 2 in any field orientation in the bc plane when the applied field is smaller than 35 T. Instead, the samples are paramagnetic metals which, like their low-field superconducting cousins, show evidence of Kondo lattice effects upon cooling from room temperature. Zero-field resistance measurements demonstrate Fermi-liquid T 2 dependence below 10 K (See Supplementary Information, Fig. S2) without evidence of a superconducting transition into the SC 1 phase down to 110 mK, well below its expected critical temperature, which usually ranges from 1.6 K to 2.1 K 2,3,5,9,29-32 . Disorder scattering, and thus approximate crystalline quality, is roughly estimated in metallic samples by dividing the resistivity at room temperature by the resistivity at 0 K (residual resistivity ratio: RRR = R 300K ðΩÞ R 0K ðΩÞ ), estimated in our case by extrapolating the T 2 fit 0-field data. Samples with a clear SC 1 transition show a great deal of variation in this regard, and can range from the typical 2 RRR = 18-40 all the way to a reported value of 1000 for exceptionally clean samples 29 . Little progress 27 has been made towards evaluating the relative sensitivities to disorder of the various superconducting phases, especially at high-fields.

UTe 2 crystals with no SC 1 transition usually have a RRR ≲ 5, which implies a high degree of disorder 33,34 . While the value reported herein for Orphan UTe 2 , RRR ≈ 7, is slightly out of this range, it still indicates that these samples are likewise quite disordered. To better understand the relative fragility of the low and high-field superconducting phases, we compare the extraordinarily robust oSC FP phase diagram of Orphan UTe 2 with two additional crystals. For both additional crystals, T cSC 1 ≈ 1.85 K, which indicates very good quality. However, the large variation of RRR values for "Low-R" (RRR = 8) and "High-R" (RRR = 64), crystals of low-field superconducting UTe 2 is atypical for any two superconductors with the same chemical formula and T c value. This intimates that the scattering mechanisms that determine RRR in these samples are not identical to the determinants of T c .

As shown in Fig. 1 and Fig. 2, the metamagnetic transition, H m , occurs just below 35 T along the b axis in the Orphan UTe 2 . This value is slightly lower than previous observations of H m reported from lowfield-superconducting samples of UTe 2 3,5,18,35-37 , and lower than the metamagnetic transitions recorded for both Low-R and High-R UTe 2 (Fig. 2b). Nevertheless, the field value of this transition still corresponds to the temperature value of a maximum in the magnetic susceptibility with field along b, T χ max ≈ 35 K, previously reported for both nonsuperconducting 38 and superconducting 4 UTe 2 . A similar feature is known in heavy fermion paramagnets with metamagnetic transitions, implying in those cases that H m and T χ max are related by a single energy scale 39 . The agreement between the energy scales associated with T χ max and H m is also important in UTe 2 13,35,36 and reflects the Kondo hybridization energy scale, as further observed in scanning tunneling microscopy 13 and magnetic excitations in inelastic neutron scattering experiments 40 . These results show that the heavy fermion state in UTe 2 is a robust characteristic.

We now consider the field-induced orphan superconducting phase that occurs at fields greater than H m in the field polarized state. This oSC FP phase, with boundaries defined here as 50% of the observed transition, emerges close to a 29 o offset from b to c and extends to 42 o (Fig. 1a). The narrower angular range of the oSC FP is striking when compared to typical SC FP, which extends from 25 o to 42 o in crystals with higher RRR (Fig. 2b, see Fig. S4 in Supplementary Information for comparison with published data 3,35,36,41 ). Likewise, the field range oSC FP is reduced, with an upper bound of 52 T. Previous reports have extrapolated the maximum field of SC FP to above 65 T in samples with T cSC 1 ≈1:6 K 3,5,25 . Nevertheless, in terms of magnetoresistance (Fig. 1), the transitions into the FP and SC FP states are qualitatively similar to those in other samples. Note two important features: relatively wide transitions as a function of field and a limited range of zero resistance, both as measured at 0.5 K. The zero-resistance state is centered at 36 o , which is far from the crystallographic (0 1 1) direction, situated at 23.7 o , suggesting that there is not a direct relationship between the two, which has been previously hypothesized 4 .

The temperature dependence of oSC FP gives further information about the unprecedented robustness of the superconductivity at these high-fields. The zero resistance state persists to just above 0.5 K (Fig. 3a), and a superconducting envelope persists to almost 0.9 K. All resistive signatures of superconductivity are suppressed by 1 K. This temperature differs dramatically from the value of 1.5 K reported before in samples exhibiting low field superconductivity 3 , and even more so from the high T cSC 1 High-R sample (Fig. 3b). As shown in Fig. 3b, the critical temperature of a more-typical SC FP phase is only slightly higher than that of the low field SC 1 phase. Previously, the similar T c 's reported for SC 1 and SC FP led to the inference that the two phases must involve similar pairing energies 3 , or even that SC FP represents true reentrance of SC 1 42 . These observations led to the expectation that crystallographic disorder should affect T c of both low-field and high-field superconductivity similarly. The observation of oSC FP is at odds with this expectation, further suggesting that the scattering mechanism that dictates the values of RRR is not directly analogous to the strength of the superconducting pair-breaking that sets T c .

Relevant theoretical attempts to describe high field superconductivity generally require the presence of zero-field superconductivity 2,3,5,[19][20][21]43 , an assumption which has been reinforced by experimental evidence that high-field superconductivity is typically affected more strongly by temperature and disorder than low field superconductivity 26,44 . It is therefore surprising to see the presumptive fragile phase without its presupposedly more robust neighbor in Orphan UTe 2 , and it will be instructive to review these mechanisms in light of the recontextualization demanded by the orphan SC FP phase. The magnetic field dependence of the superconductivity due to these theoretical mechanisms is illustrated in Fig. 4.

Recently, the Jaccarino-Peter mechanism has been proposed as a likely candidate for the stabilization of SC FP in UTe 2 25 . This mechanism is believed to be relevant to reentrant superconductivity in organic superconductors and several chevrel phases [45][46][47] . It involves an internal exchange field generated by the short-range magnetic fluctuations of localized moments, which opposes the applied magnetic field and reduces the total field 48 , allowing superconductivity to persist to higher external fields than it otherwise should (Fig. 4). This exchange field can lead to reetrance, as in the Chevrel phase Eu 0.75 Sn 0.25 Mo 6 S 7.2 Se 0.8 , in which zero-field superconductivity appears below 3.9 K and is suppressed by 1 T 45 . Above 4 T, the external field begins to adequately compensate for the internal exchange field, and superconductivity returns, persisting to approximately 22 T 45 . A similar mechanism is argued to be relevant to field-stabilized superconductivity in the antiferromagnetic insulator λ-(BETS) 2 FeCl 4 . Chemical substitution experiments show that the high-field range of the superconductivity is decreased when antiferromagnetism is destabilized and have been interpreted to indicate that λ-(BETS) 2 FeCl 4 may have a "hidden" superconducting phase that competes with the antiferromagnetic internal field 49 .

It was pointed out previously that the Jaccarino-Peter mechanism is likely not appropriate for UTe 2 3 because this effect requires localized moments and is typically observed in experiment over a narrow angular field range 48 . This contrasts sharply with the weak paramagnetic response of UTe 2 , the substantial angular range of SC FP , and the very large magnetic field scale. This inconsistency is reinforced by the new observations of Orphan SC FP . The absence of zero field superconductivity without magnetic order to generate a negative exchange field at H > 0 almost entirely precludes the compensationeffect as the primary field-stabilizing mode in UTe 2 Another proposed explanation is that SC FP is stabilized by ferromagnetic fluctuations 2 , similar to field-reinforced superconductivity observed in ferromagnetic superconductors UCoGe 50 and URhGe 51 (Fig. 4). In this model, stabilizing longitudinal spin fluctuations arise near a second-order ferromagnetic transition driven by magnetic field 52 . Low field magnetometry measurements at ambient 38 and high pressure 53 imply that UTe 2 lies similarly at the cusp of magnetic order. However, UTe 2 strongly differs from the superconductors described by the spin-fluctuation model; these materials exhibit both long range magnetic order and low-field superconductivity which precede a fieldreentrant superconducting phase 50,51 For example, spin fluctuations near a metamagnetic spin reorientation lead to reentrant superconductivity in URhGe, and strongly enhance T cRE over the H = 0 critical temperature. The low field and reentrant superconducting transition temperatures in URhGe are highly sensitive to sample quality 26,54 . However, when the initial T c boost from enhanced magnetic fluctuations near the metamagnetic field is accounted for, the ordering temperatures of the two phases are almost equally affected by disorder. In fact, the reentrant phase appears to be the slightly more fragile of the two 26 .

Another mechanism for stabilizing high field superconductivity involves field-induced Landau level broadening near the quantum limit 43 . Mean field theory predicts that in applied fields strong enough to constrain electrons to the lowest Landau levels, T c will increase in an oscillatory manner as a function of applied field, reflecting an enhancement of superconducting stability due to the Landau-level structure 43 (Fig. 4). It has even been hypothesized that approaching the extreme quantum limit could suppress the negative effects of disorder on T c in the high-field regime 43 . Typically the field strength required for this is far beyond the Pauli limit for spin-singlet superconductors 43,55 . Landau-level stabilized superconductivity is therefore most likely to be realized in spin-triplet superconductors. Indeed, high pressure measurements of resistance in low-field-superconducting UTe 2 show possible precursor effects quantized with the signature 1/H relation to SC 1 and SC FP

. However, this model is not without controversy: it has been argued that "unless the [Landé] g-factor is exactly 0 56 ," which is not true in UTe 2 , "re-entrant superconductivity can be expected only if there is a superconducting transition in zero field 56 ." Moreover, a lowdimensional electronic structure is usually assumed for models of superconductivity near the quantum limit 43 , and such a structure could not be inferred in UTe 2 from angle-resolved photoemission spectroscopy 57 . Recent de Haas van Alphen oscillation measurements of low-field superconducting UTe 2 suggest quasi-two-dimensional cylindrical electron and hole Fermi surface sections 58 . However, the Fermi surface has three-dimensional characteristics [59][60][61] , and the inverse-field periodicity implies a small orbit that has yet to be conclusively demonstrated. A separate theoretical analysis has proposed that SC FP in UTe 2 may be stabilized near the quantum limit by a Hofstadter butterfly regime of Landau level quantization with large superlattices 62 . This stabilization regime would, if accurate, indicate the existence of an even higher field phase beyond SC FP , located at approximately 90 T 22,62 , and moreover that the quantum limit field has somehow been lowered from the H > 100 T region inferred from recently reported 59,60 quantum oscillation frequencies. Furthermore, confirmation of this model would ideally involve observation of superconductivity in multiple Landau levels, requiring challenging measurements performed at significantly higher magnetic fields. The above inconsistencies show that SC FP is likely not a fieldstabilized version of SC 1 and its pairing state should be considered separately. In other words, SC FP and SC 1 are substantially different superconducting phases, could involve different superconducting pairing mechanisms, and their gap structure and size are different. The lack of a parent superconducting instability makes it more remarkable that SC FP is stable at such high magnetic fields, as the dominant theoretical descriptions of high-field superconductivity presuppose a lowfield antecedent. While none of the three scenarios we have discussed anticipate oSC FP , other potential explanations such as the invocation of "hidden" superconductivity in UTe 2 , similar to that in the Chevrel 47 case, would require even more a priori assumptions and cannot be considered useful models at this stage. We must conclude that further understanding of SC FP specifically, and field stabilized superconductivity as a whole, demand the further development of models of high-field superconductivity that do not evolve from a low field superconducting phase.

All samples were grown as single crystals via chemical vapor transport with iodine oas the transport agent. Orphan UTe 2 crystals were grown over one week as thin plates approximately 3 mm in length from a 2:3 U:Te ratio in a two zone furnace set to 800 o C and 710 o C in the charge and growth zones, respectively. The Low-R and High-R samples were grown in a two zone furnace at 900 o C (charge zone) and 830 o C (growth zone) over two weeks with starting U:Te ratios of 5:9 and 2:3, respectively. At the end of the growth period, transport was quenched by turning off power to the heating elements. Crystallographic orientation was identified from the crystal habit.

Zero-field resistance measurements to 100 mK were performed on a Quantum Design Physical Property Measurement System (PPMS) using the adiabatic demagnetization refrigerator (ADR) option. For high field measurements, crystals were mounted on a cryogenic single axis goniometer 63 at the National High Magnetic Field Laboratory (NHMFL), Los Alamos, NM and rotated between the (010) and (001) faces at applied fields of up to 55 T or up to 60 T. Both high field magnetoresistance and proximity diode oscillator measurements were performed using a 65 T short-pulse magnet. Identification of commercial equipment does not imply recommendation or endorsement by NIST.