Failed Superconductivity Mechanisms

• Failed superconductivity is a phenomenon where superconducting pairing persists but global phase coherence is lost, resulting in finite resistance.
• It encompasses various mechanisms including anomalous metallic states in 2D films, percolation failures, and competing order that prevent full superconductivity.
• Experimental evidence features signatures like vanishing Hall response, resistivity saturation, and filamentary conduction, challenging conventional superconductivity criteria.

Searching arXiv for the specified papers and closely related work on failed superconductivity. arXiv search query: "failed superconductivity anomalous metal bosonic metal particle-hole symmetry" “Failed superconductivity” is a heterogeneous term used in several distinct but related ways in the literature. In one usage, it denotes an anomalous metallic ground state that emerges when superconducting phase coherence is destroyed while strong Cooper-pair correlations persist, so that transport retains key superconducting signatures such as a vanishing Hall response despite a finite low-temperature longitudinal resistivity (Breznay et al., 2017). In a second usage, it denotes systems in which pairing, superconducting fluctuations, or filamentary superconducting paths exist, but bulk zero-resistance superconductivity does not develop because of phase incoherence, percolation failure, competing order, or intrinsic inhomogeneity (Wang et al., 14 Jul 2025). In a third, more critical usage, the phrase is applied to purported superconductors whose reported signatures fail standard criteria such as zero resistance, full Meissner expulsion, internally consistent critical fields, or reproducible thermodynamic evidence (Hirsch et al., 2021).

1. Terminology and defining criteria

In the narrow sense established for disordered two-dimensional films, “failed superconductivity” refers to an anomalous zero-temperature metallic phase that emerges out of a two-dimensional superconductor when superconducting phase coherence is destroyed despite the persistence of strong Cooper-pair correlations (Breznay et al., 2017). A true superconductor exhibits zero longitudinal resistivity $\rho_{xx}$ and perfect particle–hole symmetry, i.e. zero Hall resistivity $\rho_{xy}$, down to $T \to 0$. By contrast, a “failed superconductor” or bosonic metal has a finite, saturation-value longitudinal resistivity $\rho_{xx}(T\to 0)$ much smaller than the normal-state resistance $\rho_N$, together with a vanishing Hall resistivity $\rho_{xy}\approx 0$ over a broad field range.

A broader phenomenological definition appears in the anomalous-metal literature: the resistivity initially drops sharply as temperature is lowered, much as if the system were approaching a superconducting ground state, but then saturates at low temperatures to a value that can be orders of magnitude smaller than the Drude value (Kapitulnik et al., 2017). In that framework, the system behaves as if it were a “failed superconductor” because it develops strong superconducting correlations, vortex dynamics, and finite-$\omega$ superfluid stiffness, yet fails to establish global phase coherence as $T \to 0$.

The term is also used in materials where superconducting fluctuations or local superconducting domains appear, but no infinite superconducting cluster forms. In chemically substituted quasi-two-dimensional $\kappa$-organics, superconducting fluctuations emerge near the bandwidth-tuned Mott metal–insulator transition, yet global superconductivity fails to set in as temperature approaches zero; the data indicate superconducting domains embedded in a metallic percolating cluster that undergo a magnetic-field-tuned quantum superconductor-to-metal transition (Wang et al., 14 Jul 2025). In stripe-ordered cuprates, “failed superconductor” likewise denotes a state with surviving bosonic pairing signatures but finite resistance under high magnetic field (Li et al., 2018).

A distinct, non-bosonic usage appears in critical assessments of claimed superconductors. There, “failed superconductivity” does not mean a metallic Bose phase; it means that the reported evidence does not satisfy the standard litmus test for superconductivity. The defining hallmark invoked in such critiques is the Meissner effect, i.e. complete magnetic-field expulsion below $T_c$, which in a perfect diamagnet implies $\rho_{xy}$0 and $\rho_{xy}$1 in the bulk (Hirsch et al., 2021). This suggests that the phrase has become an umbrella term for several failure modes of superconducting order: failure of phase coherence, failure of percolation, failure of thermodynamic consistency, and failure of evidentiary standards.

2. Two-dimensional anomalous metals and particle–hole symmetry

The canonical transport realization of failed superconductivity was reported in disordered two-dimensional indium oxide and tantalum nitride films, where a magnetic field tunes the system from a true superconductor to a metallic phase with saturated resistivity (Breznay et al., 2017). The samples were amorphous InO$\rho_{xy}$2 films of thickness $\rho_{xy}$3–$\rho_{xy}$4 nm with nonstoichiometric $\rho_{xy}$5, and amorphous TaN$\rho_{xy}$6 films of thickness $\rho_{xy}$7–$\rho_{xy}$8 nm with $\rho_{xy}$9, both weakly disordered two-dimensional superconductors with zero-field critical temperatures $T \to 0$0–$T \to 0$1 K. Transport was measured in Hall-bar geometries using low-frequency lock-in detection, with magnetic fields up to $T \to 0$2 T and temperatures down to $T \to 0$3 mK.

Below the Kosterlitz–Thouless–like transition $T \to 0$4 at zero field, the films show $T \to 0$5 and $T \to 0$6. Increasing magnetic field suppresses superconductivity. At a well-defined field $T \to 0$7, the system crosses over to an anomalous metallic phase in which $T \to 0$8 saturates to a finite value $T \to 0$9 rather than diverging or remaining zero (Breznay et al., 2017). The low-field vortex-creep regime is thermally activated, with

$\rho_{xx}(T\to 0)$0

and at $\rho_{xx}(T\to 0)$1 mK this crosses over to a temperature-independent plateau $\rho_{xx}(T\to 0)$2. The saturation resistance interpolates smoothly between zero for $\rho_{xx}(T\to 0)$3 and $\rho_{xx}(T\to 0)$4 for $\rho_{xx}(T\to 0)$5, rising exponentially in the intermediate field range $\rho_{xx}(T\to 0)$6.

The key symmetry result is the persistence of a vanishing Hall resistivity deep into the metallic regime. In the superconducting state, $\rho_{xx}(T\to 0)$7 by particle–hole symmetry. Remarkably, in the anomalous metallic regime $\rho_{xx}(T\to 0)$8, the Hall resistivity remains zero to within the noise floor of approximately $\rho_{xx}(T\to 0)$9, despite finite $\rho_N$0 (Breznay et al., 2017). Only above a second field $\rho_N$1, still well below $\rho_N$2, does a finite $\rho_N$3 emerge, marking loss of exact particle–hole symmetry and entry into a vortex-flow-dominated regime. The conductivity relation is

$\rho_N$4

so the particle–hole symmetry condition is

$\rho_N$5

This phenomenology motivated the interpretation of the anomalous metallic phase as a bosonic metal: the pairing amplitude remains finite even as phase stiffness vanishes; short-range superconducting correlations survive; and vortices cross over from thermally activated creep to quantum-tunneling-dominated dynamics at the lowest temperatures (Breznay et al., 2017). The review literature generalizes this to a broad class of anomalous metals in homogeneously disordered thin films, crystalline two-dimensional materials, artificial Josephson-junction arrays, and oxide interfaces, driven by magnetic field, gate voltage, disorder, or film thickness (Kapitulnik et al., 2017). The generic low-temperature form given there is

$\rho_N$6

with $\rho_N$7, together with giant positive magnetoresistance. A common misconception is that finite resistivity at $\rho_N$8 necessarily implies the absence of pairing; these data show instead that dissipation and particle–hole symmetry can coexist.

3. Granularity, percolation, and quantum superconductor-to-metal transitions

A second major route to failed superconductivity is intrinsic inhomogeneity. In quasi-two-dimensional $\rho_N$9-[(BEDT-TTF)$\rho_{xy}\approx 0$0(BEDT-STF)$\rho_{xy}\approx 0$1]$\rho_{xy}\approx 0$2Cu$\rho_{xy}\approx 0$3(CN)$\rho_{xy}\approx 0$4, bandwidth tuning by S$\rho_{xy}\approx 0$5Se substitution drives the system across a first-order Mott metal–insulator transition at ambient pressure without intervening magnetic, charge, or structural order (Wang et al., 14 Jul 2025). Superconductivity appears only in the immediate vicinity of this transition, within a phase-coexistence region between the Mott insulator and a correlated Fermi liquid. Magnetotransport down to $\rho_{xy}\approx 0$6 mK and up to $\rho_{xy}\approx 0$7 T shows that for $\rho_{xy}\approx 0$8–$\rho_{xy}\approx 0$9, $\omega$0 has a downturn at $\omega$1–$\omega$2 K signaling onset of superconducting fluctuations, but $\omega$3 never reaches zero; instead it saturates or upturns below a lower temperature $\omega$4. AC susceptibility measured down to approximately $\omega$5 K finds a diamagnetic drop at $\omega$6 K but a total shielding fraction $\omega$7, indicating only a tiny superconducting volume.

The phenomenology is modeled by a Ginzburg–Landau–type free-energy functional for an order parameter $\omega$8,

$\omega$9

where $T \to 0$0, $T \to 0$1, $T \to 0$2, and $T \to 0$3 represents random local fields due to substitutional disorder (Wang et al., 14 Jul 2025). The sample is then treated as a binary mixture of superconducting domains of fraction $T \to 0$4 with resistivity $T \to 0$5 and metallic background of fraction $T \to 0$6 with $T \to 0$7. Within the two-dimensional effective-medium approximation,

$T \to 0$8

The extracted superconducting fraction satisfies $T \to 0$9, confirming isolated superconducting islands rather than a percolating superconducting network (Wang et al., 14 Jul 2025).

Within each superconducting domain, the resistivity displays a field-tuned quantum phase transition at $\kappa$0, where $\kappa$1 changes sign. The scaling collapse is

$\kappa$2

with extracted exponent $\kappa$3 on both sides of $\kappa$4 for all samples (Wang et al., 14 Jul 2025). Assuming $\kappa$5, the result $\kappa$6 is stated to be consistent with disordered two-dimensional quantum phase transition theories. The high-field normal state exhibits reproducible universal conductance fluctuations $\kappa$7 in millimeter-sized samples, with root-mean-square amplitude $\kappa$8, attributed to mesoscopic metallic regions separated by insulating domains.

Granular In/InO$\kappa$9 composites show a related but explicitly self-dual phenomenology. There, resistivity saturation is found on both superconducting and insulating sides of an avoided magnetic-field-tuned superconductor-to-insulator transition, with the material modeled as a random Josephson-junction system having broad distributions of Josephson coupling $T_c$0 and charging energy $T_c$1 (Zhang et al., 2022). The phase-only effective action includes a Caldeira–Leggett dissipation term,

$T_c$2

and the empirical low-temperature resistivity on the superconducting side is written

$T_c$3

with $T_c$4 and $T_c$5 (Zhang et al., 2022). At the crossover field $T_c$6 Oe, the measured saturation resistance is approximately $T_c$7, essentially the Cooper-pair quantum resistance $T_c$8.

These results collectively establish percolation failure and quantum phase fluctuations as central microscopic routes by which superconductivity can “fail” without reverting immediately to a conventional insulator or normal metal.

4. Competing order, stripes, and pseudogaps in correlated materials

In cuprates, failed superconductivity is tied not only to disorder and percolation but also to intertwined order. In stripe-ordered La$T_c$9Ba$\rho_{xy}$00CuO$\rho_{xy}$01 at $\rho_{xy}$02, suppressing superconductivity with magnetic field yields a sequence of low-temperature phases: three-dimensional superconductor, reentrant two-dimensional superconductor, ultra-quantum metal, and in one misaligned sample a failed-insulator regime (Li et al., 2018). The operational sheet resistance per CuO$\rho_{xy}$03 layer is defined as $\rho_{xy}$04 with $\rho_{xy}$05 Å, and is compared to the Cooper-pair quantum resistance $\rho_{xy}$06. In the ultra-quantum metal, identified as a failed superconductor, the resistance saturates at $\rho_{xy}$07 for $\rho_{xy}$08, while the Hall coefficient remains approximately zero at low temperature and high field (Li et al., 2018). At $\rho_{xy}$09 K, the reported characteristic fields are $\rho_{xy}$10 T, $\rho_{xy}$11 T, and $\rho_{xy}$12 T.

The bosonic interpretation rests on several transport signatures. Vanishing Hall response across the two-dimensional-superconductor to ultra-quantum-metal evolution is taken to imply particle–hole symmetry of the transport carriers. Saturation of $\rho_{xy}$13 at simple multiples of $\rho_{xy}$14 points to bosonic conduction channels. By contrast, a fermionic quasiparticle picture would produce finite $\rho_{xy}$15 and very large anisotropy $\rho_{xy}$16, contrary to observation (Li et al., 2018). Theoretical language in that context includes a Bose–Hubbard Hamiltonian for surviving but incoherent pairs,

$\rho_{xy}$17

as well as coupled-Luther–Emery descriptions of stripes and a pair-density-wave state $\rho_{xy}$18.

A different cuprate manifestation appears in La$\rho_{xy}$19Ba$\rho_{xy}$20CuO$\rho_{xy}$21, described as a “failed high-$\rho_{xy}$22 superconductor” in angle-resolved photoemission work (0812.3882). There, the ground-state pseudogap deviates strongly from a simple $\rho_{xy}$23-wave form. In a pure $\rho_{xy}$24-wave superconductor one expects

$\rho_{xy}$25

Instead, the low-energy nodal sector is parameterized by a $\rho_{xy}$26-wave slope $\rho_{xy}$27 with $\rho_{xy}$28, or equivalently $\rho_{xy}$29 near the node, whereas beyond a crossover near $\rho_{xy}$30 the gap jumps to a large antinodal value $\rho_{xy}$31 (0812.3882). The nodal gap is thermally smeared out by $\rho_{xy}$32–$\rho_{xy}$33 K, in agreement with the onset of two-dimensional superconducting fluctuations, but the antinodal gap is essentially temperature-independent up to at least $\rho_{xy}$34 K and lacks a sharp quasiparticle peak.

The interpretation offered there is that the nodal sector retains a precursor pairing gap, while the abrupt antinodal pseudogap has a different origin and destroys the global phase coherence needed for superconductivity (0812.3882). This suggests a correlated-electron analogue of failed superconductivity in which the local pairing scale is not the limiting factor. Instead, phase stiffness is blocked by stripe order, Fermi-surface fragmentation, or an entangled antinodal state. A common misconception is that underdoped cuprates fail to superconduct simply because pairing is weak; the cited data argue more specifically for a breakdown of coherent long-range order in the presence of a robust nodal pairing amplitude.

5. Apparent superconductivity without bulk superconductivity

Another important class of failed superconductivity comprises systems in which zero resistance or magnetic signatures arise from minority phases, filamentary paths, or non-bulk effects rather than from the nominal host material. Arc-melted Nb–B samples close to 1:1 composition illustrate this clearly. Powder X-ray diffraction shows that all samples are non-stoichiometric and comprise two crystal phases: a majority orthorhombic NbB-type phase and traces of a minor body-centered-cubic Nb-rich phase Nb$\rho_{xy}$35 with stoichiometry close to Nb$\rho_{xy}$36B$\rho_{xy}$37 (Abud et al., 2017). Backscattered-electron micrographs show that the minority phase forms bright filamentary veins and networks around the dark NbB grains, constituting a three-dimensional percolation path. The resistivity shows a sharp drop to zero with onset $\rho_{xy}$38 K, and magnetization in chunk samples shows an apparent diamagnetic onset near $\rho_{xy}$39 K, but the shielding fraction is only about $\rho_{xy}$40 in zero-field cooling and the Meissner fraction is $\rho_{xy}$41 at $\rho_{xy}$42 K. Powdering the material reduces the diamagnetic signal by two orders of magnitude, consistent with destruction of the percolative filament network (Abud et al., 2017).

Specific heat provides the decisive bulk criterion. The normal-state data fit

$\rho_{xy}$43

with $\rho_{xy}$44 for one NbB sample, close to values reported for non-superconducting NbB (Abud et al., 2017). The specific-heat jump satisfies $\rho_{xy}$45, only about $\rho_{xy}$46 of the BCS weak-coupling value $\rho_{xy}$47, whereas a nearly pure Nb$\rho_{xy}$48 sample yields $\rho_{xy}$49. An $\rho_{xy}$50-model fit gives $\rho_{xy}$51, $\rho_{xy}$52 meV, and residual $\rho_{xy}$53, implying that roughly $\rho_{xy}$54 of the electrons remain ungapped. The conclusion is that bulk NbB does not superconduct; the apparent superconductivity comes from Nb$\rho_{xy}$55 filaments (Abud et al., 2017).

Hydride and related ambient-condition claims have generated a parallel literature of “absence of superconductivity” studies. In sulfur and lanthanum hydrides under high pressure, the standard argument against superconductivity is the absence of a proper field-cooled Meissner effect and the internal inconsistency of inferred magnetic parameters (Hirsch et al., 2021). The defining London relations are

$\rho_{xy}$56

which imply

$\rho_{xy}$57

For a type-II superconductor, complete field-cooled flux expulsion requires $\rho_{xy}$58, with

$\rho_{xy}$59

The critique emphasizes that field-cooled curves in the cited hydride work show no plateau, precursor samples exhibit nearly identical field-cooled/zero-field-cooled splitting, and even conservative $\rho_{xy}$60 estimates imply $\rho_{xy}$61–$\rho_{xy}$62 and density-of-states values far above density-functional predictions (Hirsch et al., 2021).

Related critiques of carbonaceous sulfur hydride emphasize non-zero low-temperature resistance, lack of field-induced broadening, and implausible Ginzburg–Landau parameter extraction (Hirsch et al., 2020). One argument uses

$\rho_{xy}$63

together with inferred $\rho_{xy}$64 nm and allegedly extracted $\rho_{xy}$65 nm, which would imply $\rho_{xy}$66, inconsistent with a disordered multigrain type-II hydride sample (Hirsch et al., 2020). A separate analysis estimates instead $\rho_{xy}$67 nm and $\rho_{xy}$68, then argues that transitions with $\rho_{xy}$69 at all fields up to $\rho_{xy}$70 T are inconsistent with strongly type-II behavior (Dogan et al., 2020).

The same evidentiary logic is applied to Lu–H–N and LK-99. In Lu–H–N synthesized from lutetium foil in H$\rho_{xy}$71/N$\rho_{xy}$72, X-ray diffraction identifies FCC-1 and FCC-2 hydride phases and Lu metal, but resistance from $\rho_{xy}$73 to $\rho_{xy}$74 K remains metallic with no abrupt drop to $\rho_{xy}$75, and ac susceptibility is essentially flat or weakly temperature-dependent with $\rho_{xy}$76 and no $\rho_{xy}$77 (Cai et al., 2023). A companion study repeatedly reproduced the near-room-temperature sharp resistance change and attributed it not to superconductivity but to a metal-to-poor-conductor transition, explicitly noting that the measured resistance jumps upward rather than falling to zero (Peng et al., 2023). In phase-pure LK-99, SQUID magnetization shows only linear diamagnetism with no Meissner onset and no levitation signature, despite Cu-doped apatite structure verified by PXRD and Rietveld refinement (Kumar et al., 2023). A FLEX study of Pb$\rho_{xy}$78Cu$\rho_{xy}$79(PO$\rho_{xy}$80)$\rho_{xy}$81O reaches a complementary theoretical conclusion: in the two-band Cu $\rho_{xy}$82 model, the largest superconducting eigenvalue in self-consistent FLEX remains below $\rho_{xy}$83 even at $\rho_{xy}$84 K, excluding electronically driven spin- or orbital-fluctuation superconductivity within that framework (Witt et al., 2023).

Across these examples, the unifying issue is that apparent superconducting signatures can be generated by filamentary conduction, minority phases, structural or electronic transitions, or data-processing artifacts without any bulk superconducting state.

6. Theoretical frameworks, thermodynamic limits, and unresolved issues

Several theoretical frameworks have been used to rationalize failed superconductivity, but the literature also emphasizes that none yet provides a universally accepted account. In the anomalous-metal review, a solvable paradigm consists of superconducting puddles embedded in a metallic matrix, characterized by puddle susceptibility $\rho_{xy}$85, Josephson coupling $\rho_{xy}$86, and effective coupling

$\rho_{xy}$87

with a quantum superconductor-to-metal transition when an infinite cluster of puddles with $\rho_{xy}$88 percolates (Kapitulnik et al., 2017). For two puddles separated by $\rho_{xy}$89 in two dimensions,

$\rho_{xy}$90

while the puddle susceptibility time can be exponentially large, $\rho_{xy}$91 (Kapitulnik et al., 2017). The same review argues, however, that classical percolation requires implausibly fine tuning, local bosonic descriptions tend to yield a superconductor–insulator transition rather than an intervening metal, and existing resistively shunted junction models rely on unphysical assumptions.

Self-duality has become another organizing principle. In granular Josephson-junction systems, the magnetic-field-tuned superconductor-to-insulator transition is described as self-dual at the critical field, with bosonic Cooper-pair and vortex descriptions interchanged under $\rho_{xy}$92 and $\rho_{xy}$93, and critical sheet resistance

$\rho_{xy}$94

in the formulation given for that system (Zhang et al., 2022). The dual action is written

$\rho_{xy}$95

and scaling near the transition is expressed as

$\rho_{xy}$96

although the scaling is stated to fail as $\rho_{xy}$97 in the avoided transition (Zhang et al., 2022).

At the opposite extreme from failed superconductors lies the “failed insulator” or finite-temperature insulator. In amorphous InO, conductivity near the field-tuned insulating state is described phenomenologically by

$\rho_{xy}$98

with best-fit parameters at $\rho_{xy}$99 T of $T \to 0$00 K and $T \to 0$01 K, while at high fields the data follow Efros–Shklovskii variable-range hopping,

$T \to 0$02

with $T \to 0$03 K and $T \to 0$04 at $T \to 0$05 T (Ovadia et al., 2014). This literature frames the superinsulating state and the anomalous metallic state as dual cutoffs to conductivity or resistivity divergence, respectively.

Not all failures are dynamical or percolative. Berger identified what is explicitly called a thermodynamic failure of the Ginzburg–Landau approach to fluctuation superconductivity in nonuniform loops above $T \to 0$06 (Berger, 2022). Starting from the quadratic GL functional

$T \to 0$07

and combining the induced supercurrent with Ohm’s law, the analysis yields a local power density

$T \to 0$08

whose canonical and time averages satisfy $T \to 0$09 in different parts of a loop held at uniform temperature (Berger, 2022). The author interprets this as a violation of the Second Law in the GL-plus-Ohm’s-law framework. A plausible implication is that some fluctuation-superconductivity treatments may be internally inconsistent unless electromagnetic fluctuations, quartic terms, or microscopic vertex corrections are treated more fully.

The combined literature therefore presents failed superconductivity not as a single mechanism but as a family of phenomena at the boundary of superconducting order. In some systems, Cooper pairs survive but long-range phase coherence fails. In others, superconducting islands or filaments exist but never form a bulk condensate. In still others, the evidence for superconductivity itself fails under scrutiny. What remains unresolved is whether the anomalous metallic state is a generic bosonic phase of matter, a percolative crossover stabilized by dissipation and disorder, or a manifestation of a broader theoretical structure that existing models only partially capture (Kapitulnik et al., 2017).