Two-dimensional semiconductor and TMD superconductors

Scope

Two-dimensional transition-metal dichalcogenide superconductivity includes gate-doped semiconductors such as MoS2 and WS2, as well as intrinsically metallic NbSe2 and TaS2. They should not all be described as semiconductors or assigned one pairing mechanism. Atomic thickness, the thickness of an accumulated conducting layer and the dimensionality relevant to superconducting coherence are also different properties. Preserve polytype, substrate, layer count and preparation before comparing experiments. R1 R3 R6 R7 R8

Ising protection refers to the influence of spin–orbit coupling on the response of Cooper pairs to an applied field. It does not mean that every paired state is purely singlet, or that a large in-plane critical field proves triplet pairing. Broken inversion can admit mixed components, while additional Fermi pockets, interlayer coupling, scattering and geometry change the interpretation. Topological superconductivity is a further classification, not a synonym for strong spin–orbit coupling. R3 R4 R6

Mathematical assumptions

A local normal-state illustration uses $H_\eta=\eta\lambda\sigma_z+b\sigma_x$, where $\eta=\pm1$ labels opposite valleys and $\sigma$ acts on spin. Here $\lambda$ and $b$ are Hamiltonian energy coefficients: the zero-field spin splitting is $2|\lambda|$, and $|b|=g\mu_B|B_\parallel|/2$ for an isotropic Zeeman coupling. Do not insert a reported full spin splitting directly as $\lambda$ without checking conventions. With $R=\sqrt{\lambda^2+b^2}>0$, the eigenvalues are $\pm R$ and the positive-branch spin directions are $\mathbf n_\eta=(b,0,\eta\lambda)/R$. The field cants both spins in-plane. This illustration omits band dispersion, occupations, other pockets, Rashba coupling and interactions; it is not the full band or pairing calculation of either cited paper. R3 R6

Choose normalized spinors $u_+$ and $u_-$ on the same positive-energy branch. The antisymmetric spin contraction $A=u_+^T i\sigma_yu_-$ obeys

$$|A|^2=\frac{1-\mathbf n_+\cdot\mathbf n_-}{2} =\frac{\lambda^2}{\lambda^2+b^2}.$$

This is a squared matrix element, not a measured fraction of singlet Cooper pairs. For the ordered tensor product $|u_+\rangle\otimes|u_-\rangle$, projection onto the normalized spin singlet $|S\rangle=(|\uparrow\downarrow\rangle-|\downarrow\uparrow\rangle)/\sqrt2$ instead gives

$$P_S=|\langle S|u_+\otimes u_-\rangle|^2 =\frac{|A|^2}{2}.$$

The factor comes from the singlet's normalization, equivalently the spin projector $(1-\boldsymbol\sigma_1\cdot\boldsymbol\sigma_2)/4$. At $b=0$ and $\lambda\ne0$, the opposite-spin product has $|A|^2=1$ but $P_S=1/2$. This does not imply a half-singlet superconducting condensate: an ordered product of two normal-state spinors is not a specified antisymmetrized orbital-spin pair wavefunction or a many-body order parameter. At $\lambda=0$ and $b\ne0$, same-branch spins are parallel and both quantities vanish. At $\lambda=b=0$, the Hamiltonian is degenerate and selects no unique spinors; the ratio is undefined.

Local spinor and spin-projector checks include signed couplings, complex in-plane spin directions, arbitrary spinor phases and common spin rotations. They verify this limited identity, not a gap equation, pairing dominance, topology or critical field. Saito's supplementary model separately includes momentum-dependent bands, a pairing interaction and a linearized gap equation. De la Barrera's discussion compares more complete theories with experiment and retains quantitative disagreements. Their results motivate the example; neither paper is claimed to derive this exact local normalization exercise. R3 R6

The weak-coupling reference $B_P=\Delta_0/(\sqrt2\mu_B)\simeq1.86\,T_c$ uses tesla for field and kelvin for temperature, with $g=2$, negligible spin–orbit effects and $\Delta_0\simeq1.764k_BT_c$. This is a paramagnetic benchmark, not a universal upper bound including orbital effects. Similarly, the BKT transport signature $V\propto I^3$ has a restricted dynamical regime; finite size, heating and inhomogeneity can invalidate a naive exponent-only diagnosis. Neither comparison identifies the pairing interaction. R11 R12

Experimental criteria

Ye's MoS2 study established a gate-controlled superconducting dome in a band insulator. Lu's later Ising study illustrates why the chosen threshold matters: its checked author manuscript uses 90% of normal resistance for the phase diagram and 50% elsewhere. Those temperatures cannot be silently substituted for one another, for a measured zero-resistance temperature or for a fitted BKT temperature. The dome itself is not evidence selecting a unique pairing mechanism. R1 R2

Saito's high-field MoS2 device gives a particularly clear warning. Its reported transition near 6.5 K and in-plane critical field near 52 T at 1.5 K use a 75%-of-normal-resistance criterion; that device did not reach zero resistance. The separate low-field sample's 9.7 K transition uses 50%. The 55 T pulsed-field ceiling is not identical to the extracted 52 T boundary. The experiment and band calculations support spin–valley protection, while neither these criteria nor the measurement temperature establish triplet order. R3

Costanzo's atomically thin MoS2 experiments demonstrate a monolayer resistance drop to the measured zero level, but only one contact pair in the illustrated device shows it. Other monolayers show no transition down to the 1.5 K base temperature. Different contact regions reveal substantial density variation, associated with frozen-liquid detachment. A tendency toward weaker monolayer superconductivity in this set of devices is therefore not a universal prohibition on strong two-dimensional pairing. The critical-field comparison uses half the normal resistance. R7

In NbSe2, Xi's Ising paper extracts an Aslamazov–Larkin fit scale close to half the normal resistance; its current-excitation BKT estimate lies closer to the one-percent criterion. The roughly 3 K monolayer fit scale must not be relabelled as a direct BKT temperature. The paper considers reduced interlayer pairing and argues that the competing CDW effect on this trend is likely weak. That interpretation differs from asserting that enhanced CDW necessarily causes the superconducting suppression. R4

The frequently quoted monolayer CDW scale of $145\pm3$ K comes from a separate Xi Raman/transport paper. The selected analysis follows a CDW amplitude mode and extrapolates its intensity to zero, with mean-field fits used as guides. This is neither a superconducting transition nor an independent direct measurement of the pairing interaction. Contrasting thickness trends of CDW and superconductivity motivate competing-order tests; a correlation alone does not determine their causal coupling. R5

De la Barrera compares metallic 2H-TaS2 and NbSe2 down to atomic thickness. The resistive curves use 50% criteria; the reported monolayer TaS2 boundary remains above the 34.5 T instrument limit below 2 K. A 65.6 T coefficient fitted near the transition is not a measured zero-temperature critical field. Even-layer enhancement also survives despite restored inversion symmetry, emphasizing the balance of interlayer and spin–orbit coupling. Encapsulation, aging and distinct thickness trends remain part of the sample record. R6

Lu's CVD monolayer WS2 dome uses an effective gate coordinate assembled from ionic-gate states and back-gate sweeps. It is not a directly applied kilovolt voltage across the ionic liquid, and Hall carrier density is nonmonotonic across the dome. The high-field study uses a separate sample B, whose optimal 50%-resistance transition is 3.15 K. Its low-edge 1.54 K state changes by only 0.08 K at 35 T. Neither number supplies a universal WS2 transition or proves that all tungsten dichalcogenides behave alike. R8

Limits and disputes

Sajadi's monolayer WTe2 device connects gate-controlled superconductivity with a quantum-spin-Hall material platform, while retaining resistance thresholds and a finite measurement floor. Qi's pressure-dependent MoTe2 study instead follows bulk structural regimes, including low-pressure Td and high-pressure 1T-prime behavior. These are distinct geometries and phases. A topological normal-state description plus superconductivity is a reason to investigate the paired state, not sufficient demonstration of a topological superconducting gap or Majorana modes. R9 R10

A September 2026 theory by Marini, Cudazzo and Calandra attributes gated-TMD domes to ionic disorder, reduced screening and enhanced Coulomb repulsion, comparing its calculations with experiment. This is a model explanation, not a new experimental transition or universal proof about every superconducting dome. Complete scientific acceptance remains open here: its full equations, other cited final-version comparisons, supplements, chemical controls and raw-data analyses are unfinished. The present checks are restricted to the named primary passages, figures and spinor model. R1 R3 R5 R7 R8 R13

Discovery implications

Treat the device as part of the material: record layer count, polytype, contacts, electrolyte, gating temperature, voltage history and field orientation. Compare onset, midpoint, measured zero, phase-ordering and spectroscopic scales separately. Establish whether charge tuning also changes disorder or chemistry, and test proposed spin protection against the actual bands and geometry. The strongest next experiment distinguishes competing explanations on characterized devices instead of ranking isolated critical-field or transition-temperature numbers. R2 R3 R6 R7 R8 R12

Related topics

Electrostatic gating, Pauli limit, Spin–orbit coupling, BKT transitions, and Topological candidates.

Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.