4Hb-TaS2: Tantalum Disulfide Heterostructure

• 4Hb-TaS2 is a layered tantalum disulfide polytype composed of alternating 1T and 1H sheets, where the 1T layers form a Star-of-David charge-density-wave structure with correlated Mott physics.
• Interlayer charge transfer from the 1T to 1H layers modulates flat-band occupancy and drives phenomena such as charge ordering and tunable metallic behavior.
• The material displays unconventional, anisotropic multiband superconductivity with chiral signatures, high in-plane upper critical fields, and evidence for a two-component order parameter.

4Hb-TaS2 is a layered tantalum disulfide polytype in which 1T-TaS2 and 1H-TaS2 sheets alternate along the $c$ axis, forming a natural van der Waals heterostructure with space group $P6_3/mmc$. In this architecture, the 1T component carries the $\sqrt{13}\times\sqrt{13}$ Star-of-David charge-density-wave superlattice and the associated narrow-band, Mott-related physics, whereas the 1H component remains metallic and hosts superconductivity. The material has therefore become a model system for interfacial charge transfer, correlated flat-band physics, chiral and charge-ordered states, and unconventional superconductivity in a single stoichiometric crystal (Ribak et al., 2019, Almoalem et al., 2024, Bang et al., 2024).

1. Crystal polytype and layer-resolved electronic structure

The “4Hb” designation denotes an H–T alternation within a hexagonal polytype; the unit cell consists of alternating 1H and 1T layers, and the overall crystal is inversion symmetric, with the inversion center located in the middle of the 1T layer. The 1H layers have trigonal-prismatic coordination and the 1T layers octahedral coordination. In the more detailed stacking description, 1H layers appear in two rotational variants, $1H$ and $1H'$, related by a $180^\circ$ in-plane rotation, while 1T layers appear as $1T$ and $1T'$ variants related by a $60^\circ$ in-plane rotation coupled to a fractional translation along $c$ (Ribak et al., 2019, Gofman et al., 22 Aug 2025).

At low temperature, the 1T layers undergo a commensurate charge-density-wave reconstruction into a Star-of-David superlattice with $P6_3/mmc$0 periodicity. Each cluster contains 13 Ta atoms, and the correlated electronic degree of freedom is associated with the central cluster orbital. The same reconstruction can be described as a $P6_3/mmc$1 superstructure whose principal axes are rotated by $P6_3/mmc$2 relative to the underlying atomic lattice, generating left- and right-handed charge-density-wave variants (Bang et al., 2024, Gofman et al., 22 Aug 2025).

The 1H layers remain metallic, with their own charge-density-wave tendencies. Distinct studies describe $P6_3/mmc$3, $P6_3/mmc$4, and, in Se-substituted material, suppressed $P6_3/mmc$5 or nearly $P6_3/mmc$6 behavior, indicating that the 1H subsystem is sensitive to strain, doping, and interlayer coupling (Bang et al., 2024, Geng et al., 2024). Transport is strongly anisotropic, metallic in plane and semiconducting along $P6_3/mmc$7, with in-plane resistivity reported as $P6_3/mmc$8 smaller than out-of-plane (Ribak et al., 2019). ARPES further shows that the normal-state electronic structure is not a simple superposition of 1T- and 1H-TaS2, but is reshaped by charge transfer and reduced interlayer coupling (Almoalem et al., 2024).

2. Charge transfer, flat bands, and charge ordering in the 1T subsystem

A central property of 4Hb-TaS2 is interlayer charge transfer from the 1T layers to the 1H layers. ARPES identifies a net transfer of $P6_3/mmc$9 electron per Ta, equivalent to $\sqrt{13}\times\sqrt{13}$0 electron per Star-of-David cluster, from the measured Fermi-surface area changes relative to 2H-TaS2. This shifts 1H-derived pockets and drives the 1T layer away from half-filling (Almoalem et al., 2024). Micro-focused ARPES later sharpened this picture by showing that a T-terminated surface remains metallic, whereas a subsurface T layer under an H termination is gapped; that work interpreted the bulk as exhibiting complete charge transfer of $\sqrt{13}\times\sqrt{13}$1 electron per 13 Ta from T to adjacent H layers, with incomplete transfer only at the T-terminated surface (Date et al., 22 Aug 2025).

STM/STS has, however, resolved a non-half-filled regime in which the 1T surface shows two distinct Star-of-David sites arranged in a $\sqrt{13}\times\sqrt{13}$2 superstructure on the Star-of-David lattice. In that study, the average occupancy was inferred as $\sqrt{13}\times\sqrt{13}$3, corresponding to a hole density $\sqrt{13}\times\sqrt{13}$4 per Star-of-David cluster. Differential-conductance maps at $\sqrt{13}\times\sqrt{13}$5 mV showed contrast inversion, establishing an out-of-phase relation between the local spectral gap features and the local charge density. The local spectra were interpreted as consistent with $\sqrt{13}\times\sqrt{13}$6 and $\sqrt{13}\times\sqrt{13}$7 clusters rather than $\sqrt{13}\times\sqrt{13}$8, implying a charge-ordered insulating state rather than a correlated metal at intermediate doping (Bang et al., 2024).

This charge-order phenomenology was interpreted using an extended Hubbard model on the triangular Star-of-David lattice,

$\sqrt{13}\times\sqrt{13}$9

with a charge-order parameter

$1H$0

Within this description, the competition between on-site $1H$1 and nearest-neighbor $1H$2 favors $1H$3-type charge order near $1H$4, and the local tunneling conductance obeys $1H$5, allowing the charge modulation to be read directly from the LDOS maps (Bang et al., 2024).

Taken together, these results establish that the 1T-derived flat band is not generically a half-filled, isolated Mott band in 4Hb-TaS2. Instead, its occupancy is termination-, depth-, and sample-dependent, and the resulting states range from metallic surface flat-band remnants to charge-ordered insulating configurations and, in some interpretations, nearly completely depleted bulk T layers (Almoalem et al., 2024, Bang et al., 2024, Date et al., 22 Aug 2025).

3. Superconductivity: transition temperature, anisotropy, and gap structure

Bulk superconductivity in 4Hb-TaS2 occurs at $1H$6 K, substantially above the $1H$7 of 2H-TaS2 cited as $1H$8 K or $1H$9 K in comparative discussions. Specific heat exhibits exponential low-temperature behavior and was fitted by a fully gapped BCS $1H'$0-wave form with $1H'$1 meV. Transport and thermodynamic measurements further showed strong anisotropy, with $1H'$2, $1H'$3 remaining linear from $1H'$4 down to 30 mK and up to 18 T, and exceeding the BCS Pauli limit by about a factor of 4 (Ribak et al., 2019).

High-field transport on bulk 4Hb-TaS2 and 4Hb-TaS$1H'$5Se$1H'$6 later described both $1H'$7 and $1H'$8 as linear in temperature down to 0.3 K and interpreted the data using 3D anisotropic Ginzburg–Landau orbital depairing. For 4Hb-TaS2, the fitted zero-temperature fields were $1H'$9 T and $180^\circ$0 T, with $180^\circ$1 Å and $180^\circ$2 Å. This formulation emphasizes bulk three-dimensional superconductivity with dominant orbital depairing, even while retaining very large in-plane critical fields (Meng et al., 2023).

Ultralow-temperature thermal conductivity added a different constraint on the superconducting state. In 4Hb-TaS$180^\circ$3Se$180^\circ$4, a small residual linear term $180^\circ$5 was observed in zero field, while the low-field evolution of $180^\circ$6 was slow and the full-field dependence was S-shaped. That work ruled out line and point nodes, argued for multiple nodeless gaps, and interpreted the residual density of states as evidence for multiband gapless superconductivity in which some Fermi surfaces remain gapless while others are fully gapped (Wang et al., 2024). A related theoretical study proposed that this behavior can arise from pocket-dependent pair-breaking scattering rates on distinct Fermi-surface pockets, producing a robust residual density of states and $180^\circ$7-linear low-temperature specific heat without requiring nodal pairing (Dentelski et al., 2021).

Accordingly, the superconductivity of 4Hb-TaS2 is experimentally established as strongly anisotropic and multiband, but its low-energy excitation structure remains under active discussion. The main alternatives in the current literature are a fully gapped two-component state compatible with thermodynamics and $180^\circ$8SR, and a multiband gapless state arising from selective pair breaking on parts of the Fermi surface (Ribak et al., 2019, Dentelski et al., 2021, Wang et al., 2024).

4. Time-reversal symmetry breaking and other unconventional superconducting signatures

Zero-field $180^\circ$9SR provided the earliest bulk evidence for unconventional superconductivity in 4Hb-TaS2. The muon depolarization rate $1T$0 shows an abrupt increase at $1T$1, corresponding to an internal field width of $1T$2 G below the transition. Because the onset coincides with $1T$3, that study argued against a lower-temperature secondary transition and interpreted the result as evidence for a chiral superconducting state, with two-component order parameters in the $1T$4 representation allowing chiral $1T$5 or $1T$6 combinations (Ribak et al., 2019).

Phase-sensitive mesoscopic measurements strengthened the two-component interpretation. Little–Parks oscillations in single-crystal rings showed both conventional “0-ring” behavior and reproducible $1T$7-shifted oscillations in “$1T$8-rings,” with 4 out of 9 rings exhibiting a $1T$9 shift. The same work also found that $1T'$0 can be enhanced as a function of out-of-plane field when a constant in-plane field is applied. These observations were analyzed with a two-component Ginzburg–Landau free energy,

$1T'$1

and were taken as evidence that the superconducting order belongs to a two-dimensional irreducible representation (Almoalem et al., 2022).

STM and angle-resolved transport then revealed a chiral-to-nematic crossover phenomenology. A quasi-periodic one-dimensional conductance modulation with median period $1T'$2 nm defines a macroscopic axis on the surface, while the in-plane $1T'$3 develops a $1T'$4 two-fold modulation near $1T'$5. By contrast, averaged vortex cores at 0.4 K are nearly circular. These observations were reconciled by a two-component Ginzburg–Landau theory in which a uniaxial-strain term favors nematicity near $1T'$6, whereas a quartic term with $1T'$7 favors a low-temperature chiral state (Silber et al., 2022).

A still more field-driven variant was proposed from hard x-ray diffraction, ARPES, and transport under in-plane field. In that work, 4Hb-TaS2 was described as a locally noncentrosymmetric bulk superconductor with negligible $1T'$8 dispersion, $1T'$9 meV, $60^\circ$0, and a field-induced superconducting-to-superconducting transition from a uniform state to an orbital-driven finite-momentum pairing state. The high-field phase breaks continuous rotational symmetry down to the sixfold crystal symmetry, and its Ginzburg–Landau description contains a magnetoelectric term

$60^\circ$1

This analysis identifies $60^\circ$2 as the induced pairing momentum (Yang et al., 2024).

Theoretical alternatives remain active. One proposal attributes the magnetic memory and superconducting TRSB to interlayer equal-spin pairing with a gap whose phase winds by an integer multiple of $60^\circ$3, giving a magnetization amplification below $60^\circ$4 (Liu et al., 2023). Others interpret the magnetic memory in terms of vison–vortex nucleation from $60^\circ$5 topological order or spinon–vortex transmutation mediated by Kondo coupling to a chiral quantum spin liquid in the 1T layers (Luo et al., 2022, Lin, 2022). These proposals do not negate the superconducting anomalies; rather, they show that the microscopic origin of the broken-symmetry state remains unsettled.

5. Local probes, Kondo-related phenomena, defects, and chiral charge order

Low-temperature STM/STS has repeatedly emphasized the richness of the 1T-derived states. On 1T terraces, one study identified a Kondo resonance associated with screening of the unpaired electrons in the Star-of-David clusters by itinerant electrons in adjacent 1H layers. The resonance was fitted by a thermally convolved Fano line shape, and its width followed $60^\circ$6 with $60^\circ$7 K. The same work showed that evaporating Pb atoms onto the 1T surface can shift the resonance toward $60^\circ$8 and strongly enhance its intensity (Shen et al., 2022).

A later STM study identified two coexisting correlated electronic states on the 1T surface: a depleted flat-band state and a “Kondo cluster” state on $60^\circ$9 of charge-density-wave sites. The Kondo state exhibited a zero-bias conductance peak with Fano fit parameters $c$0, $c$1 meV, and $c$2 meV, as well as satellite peaks with $c$3 meV and $c$4 meV. That work reported a first-order quantum phase transition between the Kondo cluster and flat-band states, tunable by temperature, electric field, and tip-controlled interlayer coupling (Nayak et al., 2023).

Native defects provide another tuning axis. STM/S combined with first-principles calculations identified two defect classes in the 1T charge-density-wave lattice. Type 1 defects, attributed to sulfur vacancies in the 1T layer, distort the local Star-of-David structure and suppress the flat-band peak. Type 2 defects, attributed to sulfur vacancies in the 1H layer, reduce interlayer charge transfer, split the flat band into lower and upper Hubbard-like features separated by $c$5 meV, and generate a zero-bias Kondo-like resonance. The same study demonstrated the controlled writing and erasing of individual defects by STM manipulation (Yang et al., 30 Jul 2025).

Chemical substitution also tunes the flat-band occupancy. In 4Hb-TaSe$c$6S$c$7, Se substitution increases the interlayer spacing, reduces the 1T–1H surface-potential contrast from $c$8 mV to $c$9 mV, decreases the interfacial transfer from $P6_3/mmc$00 per Star-of-David in pristine 4Hb-TaS2 to $P6_3/mmc$01 per Star-of-David at $P6_3/mmc$02, and produces coexisting electron-filled and electron-void Star-of-David clusters. For 4Hb-TaSe$P6_3/mmc$03S$P6_3/mmc$04, the bright-Star-of-David fraction is $P6_3/mmc$05, consistent with $P6_3/mmc$06, and the real-space configurations show stripe-like patterns, short-range $P6_3/mmc$07 pairs, and “anti-seven magic number” clusters, indicating interactions beyond pure long-range Coulomb repulsion (Geng et al., 2024).

Micro-ARPES added a complementary mesoscale view of the charge order by resolving coexisting left- and right-handed commensurate charge-density-wave domains in the 1T layers. Four spectral patterns arise from chirality and rotational stacking, and the interlayer coupling of the chiral order is calculated to be only $P6_3/mmc$08 meV per Star-of-David in 4Hb-TaS2, versus $P6_3/mmc$09 meV per Star-of-David in bulk 1T-TaS2. The 1T-derived bands in 4Hb-TaS2 also show negligible out-of-plane dispersion, with total $P6_3/mmc$10 bandwidth $P6_3/mmc$11 meV and $P6_3/mmc$12 meV, underscoring the quasi-two-dimensional character of the 1T subsystem (Gofman et al., 22 Aug 2025).

6. Competing interpretations, unresolved questions, and emerging applications

The most persistent unresolved issue concerns the actual correlated state of the 1T layers in the bulk material. STM/S has reported an intermediate-doping, $P6_3/mmc$13 charge-ordered insulating state with $P6_3/mmc$14 and $P6_3/mmc$15 holes per Star-of-David (Bang et al., 2024). Other STM work identified flat-band and Kondo-cluster states on the 1T surface and a first-order transition between them (Nayak et al., 2023). By contrast, micro-ARPES argued that the bulk T layers are completely depleted by charge transfer, that the flat band is emptied in the subsurface and bulk, and that cluster Mott localization is excluded in both bulk and surface, except for incomplete transfer at the T termination (Date et al., 22 Aug 2025). These are not minor differences in language; they correspond to distinct microscopic starting points for theories of superconductivity.

A second unresolved issue is the relation between superconductivity and the 1T subsystem. One line of work regards the doped, frustrated 1T layer as a fluctuation-rich correlated insulator that may enhance pairing in adjacent 1H layers (Bang et al., 2024). Another argues that superconductivity arises primarily from Josephson-like tunneling between 1H layers across effectively insulating T layers (Date et al., 22 Aug 2025). Yet another stresses pocket-selective gapless superconductivity produced by pair breaking from slow magnetic fluctuations in T-derived states (Dentelski et al., 2021). The available data therefore constrain, but do not yet uniquely determine, the interfacial pairing mechanism.

The material has also begun to enter device physics. A flux-tunable transmon employing an Al/AlO$P6_3/mmc$16/4Hb-TaS$P6_3/mmc$17 Josephson junction has been realized in a three-dimensional copper cavity. The flux-dependent spectrum is reproduced by a standard dressed transmon–cavity Hamiltonian, and measured devices showed $P6_3/mmc$18 values from $P6_3/mmc$19 to $P6_3/mmc$20s, while Ramsey measurements indicated dephasing faster than 16 ns. That work also found a pronounced discrepancy between the Josephson energy inferred from spectroscopy and the Ambegaokar–Baratoff estimate based on room-temperature resistances, suggesting nontrivial junction physics in the hybrid system (Blumenthal et al., 27 Jan 2026). This does not yet resolve the condensate symmetry, but it establishes 4Hb-TaS2 as a practical platform for circuit-QED experiments sensitive to unconventional and subgap excitations.

Across these debates, several points are already secure. 4Hb-TaS2 is an intrinsic 1T/1H heterostructure; interlayer charge transfer is large; the 1T layer is not a simple half-filled Mott plane; superconductivity is strongly anisotropic and multiband; and multiple experiments detect broken symmetries or phase-sensitive anomalies not expected for a conventional single-component bulk $P6_3/mmc$21-wave superconductor. What remains open is which microscopic description best unifies the charge order, chiral or planar-chiral density-wave textures, magnetic memory, and superconducting state within one consistent framework.