Orphan high field superconductivity in non-superconducting uranium ditelluride

Reentrant superconductivity is an uncommon phenomenon in which the destructive effects of magnetic field on superconductivity are mitigated, allowing a zero-resistance state to survive under conditions that would otherwise destroy it. Typically, the reentrant superconducting region derives from a zero-field parent superconducting phase. Here, we show that in UTe2 crystals extreme applied magnetic fields give rise to an unprecedented high-field superconductor that lacks a zero-field antecedent. This high-field orphan superconductivity exists at angles offset between 29o and 42o from the crystallographic b to c axes with applied fields between 37 T and 52 T. The stability of field-induced orphan superconductivity presented in this work defies both empirical precedent and theoretical explanation and demonstrates that high-field superconductivity can exist in an otherwise non-superconducting material.


Introduction
Although uranium ditelluride (UTe2) has been known since the mid-1900's to be a paramagnet, 1,2 its unconventional superconductivity was not reported until 2019. 3,4In most superconductors, applied magnetic fields destroy superconductivity at and above the Pauli limit, the field at which Zeeman splitting destabilizes spin anti-aligned Cooper pairs. 5In UTe2, however, superconductivity survives to fields at least double the Pauli limit when the field is aligned in any crystallographic direction, indicating the presence of unconventional superconductivity. 3,4When the applied field is aligned along the crystallographic b axis, superconductivity persists to a striking value of 35 T, above which it is sharply truncated by a metamagnetic transition into a field polarized state. 4Moreover, superconductivity returns and persists up to an estimated 70 T at off-axis angles of 20 o -40 o from the crystallographic b-to caxes. 6,7This anisotropic and highly robust superconductivity strongly implies that UTe2 is an intrinsic spin-triplet superconductor. 4,7Owing to the potential for spin-triplet superconductors to host non-Abelian Majorana fermions, 8 such materials would be very attractive as building blocks for emergent technologies such as fault tolerant quantum computers. 91][12] Determining the nature of the highest field superconductivity is even more of a challenge, [13][14][15] and the relationship between the low-and high-field superconducting phases is also uncertain.Although this question has been primarily addressed theoretically, there has been some experimental input.For example, NMR Knight-shift measurements suggest that there is a field-induced d-vector rotation involving a switch between B3u and B2u components. 11,16Nonetheless, the most important effect underlying the intense field enhancement of superconductivity remains unclear.Leading explanations include lower dimensionality, 14,15 which can suppress the orbital limiting effects of magnetic fields, or internal exchange fields that counteract the applied external field, 4,7 leading the superconducting phase to experience smaller total magnetic fields.
To explore the relationship between the superconducting phases in UTe2, we prepared samples of nominally non-superconducting UTe2 via chemical vapor transport.The stability of superconductivity was mapped via magnetoresistance measurements that were performed in applied magnetic fields of up to 60 T with the field-angle rotated between the b and c axes.Our results show that these UTe2 samples host an "orphaned" high field stabilized superconductivity without an accompanying low-field superconducting phase.In addition to being the fieldstabilized superconductor, these findings dramatically limit possible explanations for the stability of high-field superconductivity in UTe2, demanding a new theoretical framework.

Results and Discussion
UTe2 crystalizes in a centrosymmetric orthorhombic structure (Immm, No. 71) with D2h point group symmetry.The anisotropy of this structure, coupled with the strong spin orbit coupling of 5f uranium, leads to strongly anisotropic response to applied magnetic field.Low-field superconductivity in UTe2 persists to at least 8 T in all directions; superconductivity survives to the highest fields (~35 T) when H || b, the low-field magnetic hard axis.Whether the superconductivity along the b-axis consists of more than one phase is an open question. 12,17,18 the UTe2 samples studied here, there is no evidence of superconductivity in any orientation for magnetic field smaller than 35 T. Instead, the samples are paramagnetic metals.Zero-field resistance measurements demonstrate Fermi-liquid T 2 dependence below 10 K (See Supplementary Information, Fig S .2) without evidence of a superconducting transition down to 110 mK, or 1/19 of the expected critical temperature, 3,4,7,[19][20][21][22][23] reflecting the absence of zero-field superconductivity.One measure of the disorder in this sample is given by the residual resistivity ratio (RRR) of 7.5, which compares to a typical RRR of 18 -30, as first discussed by Ran et al, 3 and recent high RRR (RRR ≈1000) grown via salt flux.19 Absent superconductivity, the dominant feature in the data (Fig. 1) is the metamagnetic transition at applied field, Hm.At Hm, the magnetization along the b-axis jumps discontinuously, and the system enters a field-polarized state.As shown in Fig. 1, the metamagnetic transition occurs just below 35 T along the b axis.This value is slightly lower than previous observations of Hm reported from typically superconducting samples of UTe2.4,7,18,[24][25][26] The onset field of the metamagnetic transition in UTe2 is of similar energy scale to the temperature at which there is a maximum in the magnetic susceptibility with field along b, Tχ max ≈ 35 K, previously reported for both nonsuperconducting 27 and superconducting 6 UTe2. The agreement between the energy scales associated with Tχ max and Hm is also important in UTe2 24,25,29 and reflects the Kondo hybridization energy scale, as further observed in scanning tunneling microscopy 29 and magnetic excitations in inelastic neutron scattering experiments.30 These results show that the heavy fermion state in UTe2 is a robust characteristic.
We now consider the orphaned field-induced orphan superconducting phase (SCFP) that occurs at fields greater than Hm in the field polarized state.This SCFP phase, with boundaries defined 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 orphan SCFP is striking when compared to previously published data from typically superconducting UTe2, which extends from 25 o to 42 o4,24,25,31 (Fig. S.6 in Supplementary Information).The orphan SCFP phase only survives to 52 T, compared to extrapolated values above 65 T in other reports. 4,7,32Nevertheless, magnetoresistance (Fig. 1b) shows that the transition into the SCFP state is qualitatively similar to that in other samples.Note two important features: wider 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 , suggesting that there is no direct relationship between the stability of SCFP and the crystallographic (0 1 1) direction, situated at 23.7 o .
The temperature dependence of orphan SCFP gives further information about the robustness of the superconductivity.The zero resistance state, measured at a 38.7 o offset from b to c, persists to 0.5 K (Fig. 2), 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. 4Previously, the similar Tc's of low-field and SCFP states lead to the inference that the two phases must involve similar pairing energies. 4The presence of orphan SCFP suggests that this interpretation is incorrect, or that additional mechanisms must be considered, such as substantial differences in the effects of the same disorder on the smearing of the superconducting energy gaps, perhaps due to differences in gap structure.
The challenge of identifying any theoretical mechanism for field stabilization of SCFP is made more difficult by the absence of low-field superconductivity.Existing relevant theoretical attempts to describe high field superconductivity generally require the presence of zero-field superconductivity, 3,4,7,[13][14][15]33 . It s instructive to review these mechanisms in light of the recontextualization demanded by the orphan SCFP phase.The magnetic field dependence of the superconductivity due to these mechanisms is illustrated in Fig. 3.
5][36] This mechanism involves an internal exchange field generated by the short-range magnetic fluctuations of localized moments which opposes the applied magnetic field, stabilizing reentrant superconductivity (Fig. 3). 37For example, in the chevrel phase Eu0.75Sn0.25Mo6S7.2Se0.8,zero-field superconductivity appears below 3.9 K and is suppressed by 1 T. 34 Above 4 T, the external field begins to adequately compensate for the internal exchange field, and superconductivity returns, persisting to approximately 22 T. 34 A similar mechanism is believed relevant to field-stabilized superconductivity in the antiferromagnetic insulator λ-(BETS)2FeCl4.Chemical substitution experiments show that the high field range of the superconductivity is decreased when antiferromagnetism is destabilized, and further indicate that λ-(BETS)2FeCl4 may have a "hidden" superconducting phase that competes with the antiferromagnetic internal field. 38wever, it was pointed out previously that the Jaccarino-Peter mechanism is likely not appropriate for UTe2 4 because this effect requires localized moments and is typically observed in experiment over a narrow angular field range. 37This conclusion is reinforced by the new observations of orphan SCFP.The absence of zero field superconductivity without magnetic order to generate a negative exchange field at H = 0 almost entirely precludes the compensation-effect as the primary field stabilizing mode in UTe2.Another possible explanation is that SCFP is stabilized by ferromagnetic fluctuations, 3 similar to field-reinforced superconductivity observed in ferromagnetic superconductors UCoGe 39 and URhGe 40 (Fig 3).In this model, stabilizing longitudinal spin fluctuations arise near a second-order ferromagnetic transition driven by magnetic field. 41At ambient conditions, UTe2 is also inferred to lie on the cusp of magnetic order, based on low field magnetometry at ambient 27 and high pressure 42 .However, an important caveat is that superconductors described by the spin-fluctuation model exhibit long range magnetic order in zero field, and show low-field superconductivity in addition to a magnetically reinforced superconducting phase. 39,40More importantly, experiments show that the high-field phases in the ferromagnetic superconductors are more readily suppressed by temperature and disorder than the zero field phases, 39,40 so it is surprising to see the presumptive fragile phase without its more robust neighbor in UTe2.
Another mechanism for stabilizing high field superconductivity involves field-induced Landau levels. 33In this model, the field-induced orbits of conduction electrons are quantized, and eventually the increased cyclotron radii of quasiparticles orbiting the Fermi surface extends the coherence range of paired electrons, and thus the stability field of HC2 (Fig 3).Hypothetically, superconductivity could be stabilized in this way at any temperature with sufficient field; however, typically the field strength required for this is far beyond the Pauli limit for spin-singlet superconductors. 33,43Landau-level stabilization is most likely to be realized in low dimensional spin-triplet superconductors, and high pressure measurements of resistance in typical UTe2 show phase transitions quantized with the signature 1/H relation. 44A lowdimensional electronic structure may be inferred from angle-resolved photoemission spectroscopy, 45 and recent de Haas van Alphen oscillation measurements of low-field superconducting UTe2 suggest quasi-two-dimensional cylindrical electron and hole Fermi surface sections. 46However, the Fermi surface has three-dimensional characteristics 47,48 and whether the electronic structure has sufficiently low-dimensional character for relevant theories to apply remains an open question.Theoretical analysis has proposed that SCFP in UTe2 is stabilized near the quantum limit by a Hofstadter butterfly regime of Landau level quantizations with large superlattices. 49This stabilization regime implies the existence of an even higher field phase beyond SCFP, located at approximately 90 T. 44,49 Possible signatures of precursor effects related to Landau level stabilized superconductivity were reported in a previous high-field pressure study (ref 7).However, confirmation of this model would ideally involve observation of superconductivity in multiple Landau levels, requiring challenging measurements performed at significantly higher magnetic fields.

Methods
Single crystals of UTe2 were grown as thin plates approximately 3 mm in length by chemical vapor transport with iodine as the transport agent.Approximately 1 g total of elemental U and Te in a 2:3 atomic ratio were sealed in an evacuated quartz ampule with 30 mg of iodine.The ampule was loaded into a two-zone horizontal furnace and the temperature was slowly increased to 800 o C and 710 o C in the charge and growth zones, respectively.Temperature was maintained for 1 week, after which transport was quenched by turning off power to the heating elements.Crystals grew as thin black plates in the ab plane (Fig. S.1 in Supplementary Information).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.Crystals were mounted on a cryogenic single axis goniometer, 50 and high field magnetoresistance measurements were performed at the National High Magnetic Field Laboratory (NHMFL), Los Alamos, NM using a 65 T short-pulse magnet.Identification of commercial equipment does not imply recommendation or endorsement by NIST.

Funding
This work was supported in part by the National Science Foundation under the Division of Materials Research Grant NSF-DMR 2105191.A portion of this work was performed at the National High Magnetic Field Laboratory (NHMFL), which is supported by National Science Foundation Cooperative Agreements DMR-1644779 and DMR-2128556, and the Department of Energy (DOE).JS acknowledges support from the DOE BES program "Science of 100 T", which permitted the design and construction of much of the specialized equipment used in the high-field studies.The authors declare no competing financial interest.

Figures
Figures

Fig. 1
Fig. 1 (a) The angle dependence of the magnetoresistance (b to c, degrees) of orphan superconductivity in UTe2 by applied field (H) at base temperature (approximately 0.5 K), with color indicating total resistance.Dark blue regions between 30-44 o are where the sample resistance falls below the low field normal state value and the darkest color indicates zero resistance.Superconducting transitions (defined by 50% of the transition) are shown as purple hexagons, and transitions from the low field normal state to the field polarized normal state are indicated by blue hexagons.Lines are guides to the eye.(b) Magnetoresistance of orphan superconductivity at select angles near the SCFP phase (angles are in degrees from b to c).The large jumps in resistance near 35 T indicate the metamagnetic transition at applied fields Hm.
Fig. 1 (a) The angle dependence of the magnetoresistance (b to c, degrees) of orphan superconductivity in UTe2 by applied field (H) at base temperature (approximately 0.5 K), with color indicating total resistance.Dark blue regions between 30-44 o are where the sample resistance falls below the low field normal state value and the darkest color indicates zero resistance.Superconducting transitions (defined by 50% of the transition) are shown as purple hexagons, and transitions from the low field normal state to the field polarized normal state are indicated by blue hexagons.Lines are guides to the eye.(b) Magnetoresistance of orphan superconductivity at select angles near the SCFP phase (angles are in degrees from b to c).The large jumps in resistance near 35 T indicate the metamagnetic transition at applied fields Hm.

Fig. 2
Fig. 2 (a) The temperature dependence of the magnetoresistance of orphan superconductivity in UTe2 at 38.7 o between b and c versus applied field (H).Large jumps in resistance near 45 T indicate the metamagnetic transition.(b) The field-temperature phase diagram of orphan superconductivity.Open circles are features taken from data shown in a), and the R = 0 regions are highlighted in dark blue.Purple, orange barred, and light green crossed circles respectively indicate 50%, 10%, 90% of the transitions between superconducting and normal state or superconducting and field polarized state.

Fig. 3 .
Fig. 3. Magnetic field -temperature schematic phase diagrams for superconductivity stabilized by different possible mechanisms.(3.a)The Jaccarino-Peter compensation effect.An internal exchange field (HEx, blue) opposes the applied field (HApp) resulting in reentrant superconductivity when the total internal field (HT, purple) is smaller than Hc2.(3.b) Stabilization of ferromagnetic superconductivity near a quantum critical point.Strong magnetic fluctuations due to the destabilization of long-range magnetism enhance the superconducting pairing.Superconductivity can survive at and on either side of the QCP.(3c) Landau level stabilized superconductivity.The upper critical field of reentrant superconductivity is oscillatory in inverse field. a.