Proximity-induced superconductivity in graphene has emerged as a significant area of research due to its potential for hosting exotic quantum states, including Majorana fermions. When graphene is coupled with a superconducting material such as niobium diselenide (NbSe₂), Cooper pairs from the superconductor can penetrate the graphene layer, inducing superconducting correlations. This effect is highly sensitive to the interface quality, doping, and twist angle between the layers. NbSe₂, with its relatively high critical temperature (T_c) of around 7-8 K, serves as an effective proximity partner, enabling the study of superconducting transport in graphene at accessible temperatures. The induced superconducting gap in graphene typically ranges from 0.1 to 1 meV, depending on coupling strength and sample conditions.

Twisted bilayer graphene (TBG) introduces additional complexity and opportunity. At specific "magic angles" (approximately 1.1°), the moiré pattern formed between the two graphene layers creates flat electronic bands, leading to strongly correlated states. When proximitized by a superconductor, these systems can exhibit unconventional superconducting phases. Experiments have shown that TBG coupled to NbSe₂ can display signatures of superconductivity even without intrinsic pairing mechanisms, though the T_c remains constrained by the parent superconductor’s properties. The interplay between twist-induced correlations and proximity effects opens pathways for engineering higher-T_c hybrid systems, though no verified room-temperature superconductivity has been achieved in such configurations.

Critical temperature limitations in proximity-coupled graphene systems are primarily dictated by the parent superconductor’s T_c and the efficiency of Cooper pair transfer. NbSe₂’s T_c of ~7 K sets an upper bound, but factors such as interfacial disorder, charge inhomogeneity, and phonon scattering further suppress the effective T_c in graphene. Recent studies have explored alternatives like magnesium diboride (MgB₂, T_c ~39 K) or high-T_c cuprates to enhance the induced gap, yet challenges in interface engineering persist. The superconducting coherence length in graphene, typically exceeding hundreds of nanometers, allows for long-range proximity effects but also makes the system susceptible to phase-breaking scattering.

Majorana fermion research in these systems focuses on creating and detecting these quasiparticles, which are pivotal for topological quantum computing. Proximity-induced superconductivity in graphene, combined with spin-orbit coupling and magnetic fields, can theoretically support Majorana zero modes at vortex cores or junction interfaces. Experiments have reported zero-bias conductance peaks—a potential Majorana signature—in graphene-NbSe₂ heterostructures under applied magnetic fields. However, conclusive evidence remains elusive due to competing explanations, such as Andreev bound states or disorder effects. Refining device fabrication to minimize extrinsic influences is critical for unambiguous Majorana detection.

The table below summarizes key parameters in proximity-coupled graphene systems:

| Parameter | Typical Range | Influencing Factors |
|-------------------------|-----------------------------|-----------------------------|
| Induced gap (Δ) | 0.1 - 1 meV | Coupling strength, doping |
| Coherence length (ξ) | 100 - 500 nm | Temperature, purity |
| Critical temperature | <7 K (NbSe₂-based) | Parent T_c, interface quality |
| Majorana signature | Zero-bias conductance peak | Field, spin-orbit coupling |

Future directions include optimizing twist-angle control in TBG-superconductor hybrids to enhance correlation-driven superconductivity and integrating stronger spin-orbit coupling materials to stabilize Majorana modes. Advances in cryogenic scanning probe techniques will further elucidate the microscopic mechanisms governing these phenomena. While challenges remain in achieving higher T_c and robust topological states, the synergy between graphene’s tunability and superconducting proximity effects continues to drive progress in quantum material engineering.