Reentrant Superconductivity Mechanisms

• Reentrant superconductivity is a phenomenon marked by a non-monotonic response, where the superconducting state is suppressed then reappears as variables like temperature, magnetic field, or pressure change.
• Its mechanisms span exchange-field pair breaking, FFLO oscillations, spin–orbit interactions, pressure-induced transitions, and current-phase interference in engineered geometries.
• Experimental and theoretical studies use transport measurements, magnetic and structural diagnostics, and Josephson junction analyses to unravel the complex interplay between pairing, phase coherence, and control parameters.

Reentrant superconductivity denotes a non-monotonic superconducting response in which superconductivity is first suppressed and then reappears as temperature, magnetic field, pressure, layer thickness, fluxoid number, or another control parameter is varied. In transport language, it may appear as the recovery of a normal-resistive state upon cooling below the nominal critical temperature, followed by a second transition back into the superconducting zero-resistance state; in field- or pressure-tuned systems it appears as a second superconducting pocket or dome after an intervening normal phase. Across current theory and experiment, reentrance is realized by several distinct mechanisms, including exchange-field pair breaking, FFLO-like proximity oscillations, longitudinal magnetic fluctuations near first-order transitions, spin-orbit–assisted field enhancement of pairing, pressure-driven electronic or structural reconstruction, current-phase interference in non-circular Josephson junctions, and competition between Josephson and charging energies in arrays (Singh et al., 2013, Maryenko et al., 2 Oct 2025, Xia et al., 2022, Lesser et al., 20 Jan 2026, Avraham et al., 2 Sep 2025).

1. Defining phenomenology and general forms

In a conventional Bardeen–Cooper–Schrieffer superconductor, an applied magnetic field monotonically suppresses the superconducting transition temperature through Zeeman pair breaking and orbital depairing. Reentrant superconductivity is instead characterized by a non-monotonic $T_c(H)$: superconductivity is first destroyed at a lower field, then re-emerges at a higher field before finally being suppressed again at still larger fields. Historically, reentrant superconductivity was first observed in three-dimensional magnetic superconductors via the Jaccarino–Peter compensation effect, where an internal exchange field is canceled by an external field (Maryenko et al., 2 Oct 2025).

The modern literature uses the same term for several experimentally distinct trajectories. In ferromagnet–superconductor–ferromagnet trilayers, reentrance occurs upon cooling: resistance decreases below the superconducting onset, rises again when ferromagnetic order becomes effective in the interfacial region, and finally falls to zero once the superconducting condensation energy dominates (Singh et al., 2013). In pressure-tuned materials such as $1T$-TiSe$_2$, a low-pressure superconducting dome disappears and a second, entirely separate superconducting region emerges only above $P \approx 15.8$ GPa (Xia et al., 2022). In misfit layered $\mathrm{(SnS)_{1.15}(TaS_2)}$, the low-pressure superconducting phase disappears near $14.7$ GPa, and a distinct superconducting phase reemerges above $80$ GPa (Zhang et al., 26 Feb 2026). In non-circular Corbino Josephson junctions, superconductivity reenters only for discrete fluxoids fixed by geometry, and in topological realizations the reentrance period is halved (Lesser et al., 20 Jan 2026). This variety indicates that “reentrance” is a phenomenological label for reappearance of phase coherence, rather than a synonym for one microscopic mechanism.

2. Exchange fields, magnetic order, and proximity-induced reentrance

A canonical temperature-driven example is the HoNi$_5$–NbN–HoNi$_5$ trilayer. For $d_{\mathrm{NbN}} \simeq 10$ nm and $1T$0 nm $1T$1 nm, the resistance shows onset of superconductivity at $1T$2 K, a resistance minimum at $1T$3 K, a peak at $1T$4 K, and a final drop to $1T$5 below $1T$6 K. The observed reentrance occurs in the range $1T$7, is quenched by increasing the out-of-plane magnetic field and transport current, and is attributed to a delicate balance between the magnetic exchange energy and the condensation energy in the interfacial regions of the trilayer. In the same system, thermally activated flux flow changes systematically from $1T$8 in single NbN to $1T$9 in the F–S bilayer and $_2$0 in the F–S–F trilayer, consistent with progressive weakening of the superconducting condensate by pair breaking at both S–F interfaces (Singh et al., 2013).

Bulk or composite magnetic superconductors realize the same competition on different energy scales. In Eu$_2$1, a superconducting transition below $_2$2 K is followed by a resistivity reentrance peaking at $_2$3 K, caused by ordering of the Eu$_2$4 moments; low-field magnetization still shows a prominent diamagnetic signal despite the large ordered moments (Paramanik et al., 2013). In the YBa$_2$5Cu$_2$6O$_2$7–Tb oxalate composite, the initial superconducting transition remains at $_2$8 K, but the diamagnetic signal is lost below a characteristic reentrance temperature, estimated as $_2$9–$P \approx 15.8$0 K for the $P \approx 15.8$1 wt% YBCO composite and $P \approx 15.8$2–$P \approx 15.8$3 K for the $P \approx 15.8$4 wt% composite. The extracted critical fields, $P \approx 15.8$5 Oe and $P \approx 15.8$6 kOe, are dramatically reduced relative to pure YBCO, reflecting strong pair breaking by the magnetic Tb phase (López-Romero et al., 2017).

In proximity structures, reentrance can arise even without a bulk magnetic transition in the superconducting component. Nb/Cu$P \approx 15.8$7Ni$P \approx 15.8$8 bilayers realize the FFLO-like state predicted for S/F proximity systems: by varying $P \approx 15.8$9, the measured $\mathrm{(SnS)_{1.15}(TaS_2)}$0 curves span shallow suppression, broad extinction regions, and even double extinction of superconductivity, evidencing multiple reentrant behavior (Zdravkov et al., 2011). In Ho/S bilayers with a conical spiral exchange field, self-consistent Bogoliubov–de Gennes calculations give a strictly reentrant window in temperature, $\mathrm{(SnS)_{1.15}(TaS_2)}$1, with the condensation free energy vanishing at both transitions and an interval where the superconducting state is less ordered than the normal state according to the entropy difference (Wu et al., 2011). These systems place reentrance in the general class of oscillatory proximity effects and exchange-driven entropy–energy competition.

3. High-field reentrance in triplet and spin-orbit-coupled systems

In uranium-based heavy-fermion materials, reentrant superconductivity is strongly tied to field-tuned magnetic structure. For URhGe, Landau theory shows that a magnetic field applied perpendicular to the easy magnetization axis changes the ferromagnet–paramagnet transition from second order to first order; the longitudinal susceptibility corresponding to magnetic fluctuations strongly increases in the vicinity of the first-order transition, stimulating reentrance of the superconducting state. The reentrant superconductivity observed near that first-order line exists both in ferromagnet and paramagnet states, and the critical temperature falls down at intersection with the ferromagnet–paramagnet phase boundary (Mineev, 2014). A broader Ginzburg–Landau treatment for URhGe, UCoGe, and UTe$\mathrm{(SnS)_{1.15}(TaS_2)}$2 reaches the same qualitative conclusion: magnetizations along the easy and hard axis have opposite effects on superconductivity, the reentrant state is induced by fluctuations parallel to the direction of the magnetic field, and the theory predicts both field-dependent rotation of the triplet $\mathrm{(SnS)_{1.15}(TaS_2)}$3-vector and a metastable state associated with the appearance of reentrance (Feng et al., 2020).

UTe$\mathrm{(SnS)_{1.15}(TaS_2)}$4 has become a central test case because several mechanisms compete. A quasi-two-dimensional spin-triplet theory explains the extremely large initial slope $\mathrm{(SnS)_{1.15}(TaS_2)}$5 T/K and the recovery of superconductivity for $\mathrm{(SnS)_{1.15}(TaS_2)}$6 above $\mathrm{(SnS)_{1.15}(TaS_2)}$7 T, eventually surviving up to $\mathrm{(SnS)_{1.15}(TaS_2)}$8–$\mathrm{(SnS)_{1.15}(TaS_2)}$9 T, through suppression of orbital depairing when $14.7$0 (Mineev, 2020). However, specifically prepared non-superconducting UTe$14.7$1 crystals exhibit an orphan high-field superconducting dome between $14.7$2 T and $14.7$3 T, over a smaller angular range than in superconducting samples, despite the absence of a zero-field parent superconducting phase. That observation challenges standard explanations based on compensation, fluctuation enhancement alone, or Landau-level/FFLO repetition, and instead underscores the likelihood of a field-induced modification of the electronic structure (Frank et al., 2023). A recent two-sublattice spin-orbit model further argues that neither Jaccarino–Peter nor magnetic-fluctuation mechanisms can entirely explain the SC$14.7$4 phase of UTe$14.7$5: avoided band crossings at finite field maximize the intraband pairing matrix element in one spin-split band, and a $14.7$6 pairing state reproduces the highly anisotropic reentrant phase diagram (Lee et al., 22 Jun 2026).

More generic high-field theories abstract this material-specific phenomenology into symmetry conditions on pairing. In a spin-triplet Bogoliubov–de Gennes model with a $14.7$7 vector, a spin-orbit vector, and a Zeeman field, when the three vectors are perpendicular to one another the spin-orbit interaction suppresses superconductivity in weak Zeeman fields and enhances superconductivity in strong Zeeman fields; the instability and stability of the superconducting state are characterized by odd-frequency and even-frequency Cooper pairs, respectively (Sano et al., 16 Feb 2026). A minimal two-component Ginzburg–Landau theory similarly shows that competition between a spinful instability and a spin-polarized instability generically yields a nonmonotonic, reentrant $14.7$8 curve independent of microscopic details (Goryo, 30 Dec 2025).

Two-dimensional platforms provide closely related but experimentally distinct routes. At the epitaxial $14.7$9-oriented LaTiO$80$0–KTaO$80$1 interface, superconductivity is first suppressed by a few hundred mT, then re-emerges at $80$2 T across the entire gate range; the resistive cusp at $80$3 T is independent of both $80$4 and temperature, and the proposed mechanism is the interplay between strong Rashba spin–orbit coupling and magnetic-field-driven modification of the Fermi surface near an extended van Hove singularity (Maryenko et al., 2 Oct 2025). In magic-angle twisted trilayer graphene, superconductivity is destroyed around $80$5 T and reappears for $80$6 T, with the high-field phase argued to be associated with a quantum Lifshitz transition and finite-momentum pairing in a singlet–triplet superposition (Lake et al., 2021). These two-dimensional cases are explicitly distinguished from Jaccarino–Peter compensation.

4. Pressure-driven reentrance and electronic or structural reconstruction

Pressure can generate reentrance either by changing crystal structure or by reconstructing the Fermi surface without symmetry breaking. In $80$7-TiSe$80$8, the well-known low-pressure superconducting dome emerges in the range $80$9–$_5$0 GPa and peaks with maximal $_5$1 K, while a second superconducting transition starts around $_5$2 GPa and reaches $_5$3 K by $_5$4 GPa. High-pressure X-ray diffraction and Raman spectroscopy identify a first-order structural phase transition from $_5$5 to $_5$6, with phase coexistence, reversible recovery on decompression, a discontinuity in the unit-cell volume per formula, and new Raman modes $_5$7 and $_5$8 appearing above $_5$9 GPa. First-principles calculations show that conventional electron–phonon coupling accounts for low-pressure superconductivity with $_5$0, $_5$1 meV, and $_5$2 K, but in the high-pressure $_5$3 phase the coupling drops to $_5$4 and the predicted $_5$5 K, far below the observed $_5$6 K. The high-pressure reentrant state is therefore inferred to have an unconventional, non-phononic origin (Xia et al., 2022).

The misfit layered compound $_5$7 presents the complementary case. At ambient pressure it is a bulk superconductor with $_5$8 K and $_5$9 K; superconductivity is gradually weakened and disappears near $d_{\mathrm{NbN}} \simeq 10$0 GPa, then a second high-pressure superconducting dome reenters above $d_{\mathrm{NbN}} \simeq 10$1 GPa and persists up to $d_{\mathrm{NbN}} \simeq 10$2 GPa. The Hall coefficient decreases with pressure, crosses zero at $d_{\mathrm{NbN}} \simeq 10$3 GPa, and becomes negative for $d_{\mathrm{NbN}} \simeq 10$4 GPa, while in situ powder X-ray diffraction to $d_{\mathrm{NbN}} \simeq 10$5 GPa shows continuous lattice contraction but no new reflections, splitting, or peak disappearance. The proposed interpretation is a pressure-induced electronic Lifshitz transition driven by enhanced interlayer charge transfer, rather than a structural phase transition (Zhang et al., 26 Feb 2026). Taken together, these two studies show that pressure-induced reentrance may be either structure-driven or purely electronic.

5. Geometry-controlled and array-based reentrant superconductivity

Reentrance can be encoded directly into phase winding and current-phase interference. In Corbino Josephson junctions, fluxoid quantization fixes the superconducting phase winding, and the critical current is determined by integrating a local sinusoidal current-phase relation around the annulus. For a circular junction with constant width, $d_{\mathrm{NbN}} \simeq 10$6, and the total Josephson current vanishes for any integer $d_{\mathrm{NbN}} \simeq 10$7; equivalently, imposing quantization on the Fraunhofer-type formula gives $d_{\mathrm{NbN}} \simeq 10$8 for all nonzero fluxoids. In a non-circular junction, however, the local enclosed area varies with $d_{\mathrm{NbN}} \simeq 10$9, the phase acquires corner-induced kinks, and a minimal analytic model $1T$00 yields a reentrance condition $1T$01, where the period of the lobes is set by the number of corners. In the topological case, coupling of counter-propagating Majorana modes depends on $1T$02, generates a $1T$03 harmonic, and halves the reentrance condition to $1T$04. Numerically, for a square junction, the conventional case peaks at $1T$05, while the topological case peaks at $1T$06 (Lesser et al., 20 Jan 2026).

A different engineered route appears in granular aluminum, treated as a naturally occurring Josephson junction array. The nanobridge contains $1T$07 junctions in series per chain, shows giant Shapiro steps at low temperature, and can be tuned by RF power from a coherent superconducting state to a phase-fluctuating insulating state. At $1T$08 MHz, an insulating tongue opens above $1T$09 dBm; for $1T$10 dBm, the resistance drops to zero at $1T$11 K, rises again at $1T$12 K, and returns to zero at $1T$13 K, while for $1T$14 dBm the SC$1T$15I$1T$16SC sequence persists with a narrower reentrant step. The proposed microscopic picture is that RF power renormalizes the Josephson coupling $1T$17, whereas elevated temperatures screen the charging energy $1T$18 through the Efetov mechanism, re-establishing global phase coherence in a system that had entered an insulating, charge-fluctuating regime (Avraham et al., 2 Sep 2025). This is reentrance generated by many-body phase dynamics rather than by pair-breaking in a single homogeneous condensate.

6. Theoretical descriptions, diagnostics, and unresolved questions

The theoretical descriptions of reentrant superconductivity are correspondingly heterogeneous. Current work employs Landau and Ginzburg–Landau functionals for magnetic superconductors and multicomponent triplet order parameters, self-consistent Bogoliubov–de Gennes calculations for conical ferromagnets and spin-orbit/Zeeman models, extended Usadel and single-mode approximations for S/F proximity systems, linearized gap equations for quasi-two-dimensional triplet states, Migdal–Eliashberg and Allen–Dynes estimates for pressure-tuned dichalcogenides, and DMFT plus static mean-field and a noninteracting dual model for reentrant $1T$19-wave superconductivity in the periodic Anderson lattice (Mineev, 2014, Wu et al., 2011, Zdravkov et al., 2011, Mineev, 2020, Xia et al., 2022, Oei et al., 2020). The periodic Anderson study is notable because it finds a finite-temperature superconducting window $1T$20 driven predominantly by competition between static pairing and single-particle hybridization, rather than by many-body Kondo screening (Oei et al., 2020).

Experimental identification is likewise mechanism-specific. Transport remains central: non-monotonic $1T$21, $1T$22, or $1T$23 establishes reentrance in F–S–F trilayers, uranium compounds, oxide interfaces, and moiré graphene (Singh et al., 2013, Mineev, 2014, Maryenko et al., 2 Oct 2025, Lake et al., 2021). Magnetization and susceptibility locate competing magnetic order in Eu$1T$24 and magnetic composites (Paramanik et al., 2013, López-Romero et al., 2017). Hall sign reversal and nonmonotonic normal-state resistance diagnose electronic reconstruction in $1T$25 (Zhang et al., 26 Feb 2026). High-pressure XRD and Raman resolve whether pressure acts through a structural transition, as in TiSe$1T$26, or without crystallographic symmetry breaking, as in the misfit layered compound (Xia et al., 2022, Zhang et al., 26 Feb 2026). In mesoscopic settings, exact zeros and discrete reentrant lobes of $1T$27 versus fluxoid distinguish trivial and topological Corbino junctions, while giant Shapiro steps and zero-bias resistance peaks separate stiff-phase and phase-fluctuating regimes in granular aluminum (Lesser et al., 20 Jan 2026, Avraham et al., 2 Sep 2025).

Several unresolved issues recur. In $1T$28-TiSe$1T$29, electron–phonon coupling is too weak to account for the observed $1T$30 K, implying an unconventional origin of the high-pressure reentrant state (Xia et al., 2022). In UTe$1T$31, orphan high-field superconductivity and the anisotropic SC$1T$32 phase are not fully explained by Jaccarino–Peter compensation or by a change of magnetic fluctuation strength alone (Frank et al., 2023, Lee et al., 22 Jun 2026). In $1T$33, the phenomenology points to a Lifshitz-type transition, but no microscopic band-structure calculation is provided (Zhang et al., 26 Feb 2026). These cases suggest that reentrant superconductivity is best treated as a family of phenomena in which superconductivity reappears because a control parameter reorganizes the balance among pair breaking, phase stiffness, density of states, and pairing symmetry.