Reentrant Superconducting States

Updated 22 January 2026

Reentrant superconducting states are regimes where superconductivity vanishes and reappears as external parameters exceed critical values, defying conventional trends.
They result from competing effects such as magnetic exchange, FFLO interference, spin-orbit coupling, and density of states modulations, which modify Cooper pairing.
Understanding these states aids in designing advanced superconducting devices and topological quantum systems through engineered material platforms and controlled phase transitions.

Reentrant superconducting states are regimes in which superconductivity vanishes as an external parameter (such as temperature, magnetic field, carrier concentration, or pressure) is varied, but then reappears at a larger value of that parameter—contrary to conventional monotonic suppression. This phenomenon reflects the nontrivial interplay between superconductivity and competing orders (magnetism, spin-orbit coupling, strong correlations, topology, or disorder), manifesting in diverse systems from heavy-fermion compounds and topological heterostructures to engineered Josephson arrays and strongly correlated materials. Reentrant superconductivity is rigorously characterized by nonmonotonic behavior of critical temperature $T_c$ , critical field $H_{c2}$ , or supercurrent $I_c$ , with intermediate parameter regimes where superconductivity is suppressed before returning at more extreme values.

1. Microscopic Mechanisms of Reentrant Superconductivity

Reentrance arises from a variety of microscopic origins:

i. Magnetic Exchange and Compensation Mechanisms:

Magnetic impurities or internal magnetism can induce reentrance via pair breaking and compensation effects. In dilute magnetic alloys, magnetic impurities produce a competing exchange field; as temperature decreases, pair-breaking is maximized near the Kondo scale, suppressing superconductivity, but at lower $T$ the impurities freeze and superconductivity reappears. The Jaccarino–Peter effect is a consequence: superconductivity is restored at certain applied fields due to cancellation between internal and external Zeeman fields (Borycki et al., 2010).

ii. FFLO and Interference States:

Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states involve Cooper pairs with finite center-of-mass momentum due to spin splitting. In S/F or S/F/S heterostructures, the oscillatory proximity-induced pair amplitude leads to destructive or constructive interference, causing $T_c$ to vanish and reenter as ferromagnetic thickness or exchange field are varied (Kehrle et al., 2012, Zdravkov et al., 2011). Van Hove singularities and Fermi surface nesting further stabilize reentrant FFLO phases in lattice systems (Cichy et al., 2017).

iii. Field-Tuned Magnetic Fluctuations in Ferromagnetic Superconductors:

In uranium-based systems (URhGe, UCoGe, UTe $_2$ ), field-tuned enhancement of longitudinal spin fluctuations near tricritical points induces a second, reentrant superconducting dome. Ginzburg–Landau modeling ties the nonmonotonic $T_c(H)$ to the interplay of field-dependent magnetizations, quantum fluctuations, and rotation of the triplet $d$ -vector (Feng et al., 2020, Mineev, 2014, Yu et al., 2021).

iv. Spin-Orbit Coupling and Topological Effects:

In proximity junctions with materials possessing strong Rashba or topological surface states (e.g., $\alpha$ -GeTe), spin-texture engineering via Zeeman field can suppress or restore superconductivity through spin-polarized inverse proximity, yielding reentrance without magnetic order in the normal region (Esin et al., 2023).

v. Fermi Surface Lifshitz Transitions and Density of States Modulation:

Band-structure effects, e.g. van Hove singularities or Lifshitz transitions, can drive reentrance. In 2D interfaces with strong Rashba SOC (LaTiO $_3$ /KTaO $_3$ (Maryenko et al., 2 Oct 2025)) or moiré systems (tWSe $_2$ (Braz et al., 17 Jan 2026)), tuning carrier density or in-plane field shifts the Fermi energy across a VHS, enhancing and then suppressing superconductivity in a nonmonotonic fashion.

vi. Many-Body Screening Effects in Artificial Josephson Arrays:

Granular Al arrays display reentrance as a function of RF power and temperature. Here, screening of the charging energy $E_C$ by thermally excited normal electrons at elevated $T$ enables a reentrant superconducting phase after an intervening insulating regime (Avraham et al., 2 Sep 2025).

vii. Geometric and Interference Effects in Mesoscopic Structures:

In Josephson junctions with non-circular (e.g., polygonal) Corbino geometry, closed-loop flux quantization and interference selectivity create multipartite domains of superconductivity and normal state as flux is swept, with reentrant regions controlled by geometric symmetry and, in topological cases, by Majorana physics (Lesser et al., 20 Jan 2026).

2. Experimental Realizations and Diagnostics

Systematic Table of Representative Realizations

Material/System	Control Parameter	Reentrant Mechanism
URhGe, UCoGe, UTe $_2$	Magnetic field (transverse)	Spin-fluctuation enhancement
LaTiO $_3$ /KTaO $_3$ (110) interface	In-plane field, gating	Van Hove/Chern/SOC
$\alpha$ -GeTe SNS junctions	In-plane field	Spin-polarized Rashba surface
S/F/S, S/F bilayers (Nb/Cu $_{41}$ Ni $_{59}$ )	F-layer thickness, B-field	Proximity FFLO interference
HoNi $_5$ -NbN-HoNi $_5$ trilayers	Temperature	Exchange-condensation interplay
Twisted WSe $_2$ bilayers (%%%%23 $_2$ 24%%%%)	Carrier concentration	Spin-valley Stoner instability
TTG	Field, carrier density	Quantum Lifshitz, finite- $q$ pairing
Granular-Al Josephson arrays	RF power, B, T	Screening of $E_C$ , many-body
Corbino Josephson junctions (3DTI)	Magnetic flux	Geometric/mode selection, Majorana

Experimental diagnostics for reentrant behavior include precise mapping of $R(T, H, n, P_{\rm RF})$ , $I_c(B)$ , and $T_c$ as a function of the relevant control, typically displaying a “double-dome” or “butterfly” profile. Advanced probes include spin-resolved tunneling, STM for triplet order detection, quantum oscillation for Lifshitz transitions, and device-integrated Josephson measurements for interference and flux dependence.

3. Theoretical Frameworks and Mean-Field Descriptions

Specific theoretical formalisms used across systems include:

Ginzburg–Landau Theories: Multi-component order-parameter expansions capturing competition between magnetic, superconducting, and fluctuation/inhomogeneity effects—key for uranium-based triplet superconductors and fluctuation-driven first-order transitions (Feng et al., 2020, Yu et al., 2021).
Usadel Equation Formalism: Describes spatially modulated superconductivity due to FFLO-like pair amplitudes in S/F and S/F/S heterostructures, predicting oscillatory $T_c(d_{\rm F})$ and reentrance (Kehrle et al., 2012, Zdravkov et al., 2011).
Microscopic BdG and Mean-Field Models: Hamiltonians incorporating Rashba SOC, Zeeman fields, and orbitally selective interactions to model gap equations and density-of-states effects (Maryenko et al., 2 Oct 2025, Esin et al., 2023, Cichy et al., 2017).
Stoner-RPA Susceptibility Calculations: Matrix susceptibility approach to identify spin-valley-ordered regimes and fluctuation-mediated pairing in moiré materials (Braz et al., 17 Jan 2026).
Josephson Array Models with Phase-Charge Duality: Effective Hamiltonians of coupled junction arrays, including many-body screening by normal electrons and criticality between coherent and insulating phases (Avraham et al., 2 Sep 2025).
Landau Theory for Tricritical Points: Mapping phase boundaries and enhancement of susceptibility in field-tuned Ising ferromagnets (Mineev, 2014).
Analytical Models for Geometric Reentrance: Derivation and selection rules for reentrant critical current in noncircular Corbino geometries, including topological (Majorana) period halving (Lesser et al., 20 Jan 2026).

Key mathematical criteria for reentrance involve nonmonotonicity of $T_c(x)$ , $I_c(B)$ , or a Landau coefficient $a(B,T)$ , with minima or zeros intervening between superconducting domains.

4. Topological, Correlated, and Device-Engineering Implications

Topological Heterostructures and Majorana Physics:

Reentrant superconductivity mediated by spin-polarized or chiral surface states is foundational for realizing topological quasiparticles. In $\alpha$ -GeTe interfaces and 3DTI-based Josephson devices, field-tunable reentrance allows selective on/off supercurrent switching—critical for quantum circuitry and manipulation of Majorana zero modes (Esin et al., 2023, Lesser et al., 20 Jan 2026).

Superconducting Spintronics and Spin-Valve Cores:

Multiple reentrant and deep $T_c$ oscillations in S/F/S trilayers enable large, magnetic-alignment-sensitive shifts of superconductivity, greatly amplifying spin-valve effects for device applications (Kehrle et al., 2012).

Strongly Correlated and Moiré Quantum Matter:

In twisted TMD moiré systems (tWSe $_2$ ), reentrant superconducting domes flank regions of spin-valley order near VHS-induced Lifshitz transitions, reflecting the role of enhanced fluctuations and unconventional pairing (Braz et al., 17 Jan 2026). In twisted trilayer graphene, reentrance is tied to finite-momentum pairing and quantum Lifshitz transitions, with mixed singlet-triplet states naturally realized (Lake et al., 2021).

Quantum Simulation and Criticality in Artificial Arrays:

Josephson junction arrays with reentrant regimes provide a quantum simulational platform for disorder, localization, and interaction-tuned transitions, unifying single-junction and many-body physics (Avraham et al., 2 Sep 2025).

5. Distinct Types of Reentrant Phenomena and Phase Diagrams

Reentrance is classified by the control parameter and underlying mechanisms:

Field-Tuned Reentrance:

Heavy fermion ferromagnetic superconductors (URhGe, UCoGe) exhibit reentrant $T_c(H)$ domes at high transverse fields due to divergence of longitudinal susceptibility near FM–PM transitions. In 2D oxide interfaces, $T_c(B)$ displays a minimum with double superconducting lobes due to Rashba SOC and van Hove band structure (Maryenko et al., 2 Oct 2025, Mineev, 2014).

Thickness/Proximity-Tuned Reentrance:

S/F/S and S/F bilayers demonstrate extinction and revival of superconductivity, with two or more reentrant zones controlled by ferromagnetic layer thickness, interference conditions, and exchange splitting (Kehrle et al., 2012, Wu et al., 2011).

Pressure-Induced Reentrant SC:

1T-TiSe $_2$ displays two disconnected superconducting domes in $P$ – $T$ phase space, separated by a structurally driven region with different electronic order: SC–I (phononic) and SC–II (unconventional, possibly excitonic or interband pairing) (Xia et al., 2022).

Carrier Density and Quantum Geometry-Tuned Reentrance:

In twisted WSe $_2$ and TTG, reentrant sequences emerge as the Fermi level crosses VHS lines, flanked by superconducting and spin-ordered states, manifesting as two SC domes at different fillings (Braz et al., 17 Jan 2026, Lake et al., 2021).

Illustrative phase diagrams typically feature domes (or "butterflies") of superconductivity in a given parameter plane (field, pressure, carrier density, etc.) separated by non-superconducting or competing order regions.

6. Perspectives and Future Directions

Reentrant superconducting phases provide crucial insight into nontrivial interplay between superconductivity, magnetism, strong correlations, spin-orbit coupling, and topology. Emerging directions include:

Engineered Material Platforms: Design and control of reentrance via heterostructure geometry, thickness, interface engineering, and electrostatic gating.
Quantum Simulation and Manipulation: Use of Josephson arrays and hybrid devices to simulate nonequilibrium and strongly correlated regimes, with potential for topologically protected quantum operations.
Detection and Control of Majorana Modes: Geometric reentrance and period halving in Josephson critical currents are promising signatures of non-Abelian quasiparticles in topological platforms.
Moiré Flat-Band and Quantum Materials: Understanding VHS-driven instabilities and fluctuation-enhanced pairing in 2D engineered lattices, especially where tunability enables exploration of fundamental physics and device integration.
Theoretical Extensions: Incorporation of fluctuation effects, disorder, and competing multiband and multicomponent order parameters in theoretical modeling.

The universality and diversity of reentrant superconductivity across platforms reinforce its fundamental significance at the intersection of superconductivity, magnetism, quantum geometry, and topological phenomena.