Proximity-induced magnetism and superconductivity in heterostructures involving topological insulators (TIs) and magnetic or superconducting materials have emerged as a rich field of study due to the unique electronic properties of TIs. These heterostructures exploit the spin-momentum locked surface states of TIs, which can lead to novel phenomena when coupled with magnetic or superconducting order. The proximity effect enables the transfer of magnetic or superconducting correlations from one material to another without direct chemical doping, preserving the intrinsic properties of the TI while introducing new functionalities.

In TI/ferromagnet (FM) bilayers, the proximity effect induces an exchange interaction at the interface, which can align the spins of the TI surface states with the magnetization of the FM layer. This interaction arises due to the overlap of electronic wavefunctions at the interface, leading to a spin-dependent potential that modifies the electronic structure of the TI. The induced magnetism can open a gap in the Dirac surface states, breaking time-reversal symmetry and creating an energy gap at the Dirac point. The size of the gap depends on the strength of the exchange coupling, which is influenced by factors such as interfacial quality, magnetic layer thickness, and temperature. For example, in Bi2Se3/EuS heterostructures, a gap of approximately 15 meV has been observed at low temperatures, demonstrating the potential for engineering magnetic order in TIs.

The proximity effect in TI/FM systems can also lead to chiral edge states, analogous to those in quantum anomalous Hall insulators. These edge states are dissipationless and robust against backscattering, making them attractive for spintronic applications. The critical temperature for observing these effects is determined by the Curie temperature of the FM layer and the strength of the interfacial coupling. In some cases, the proximity effect can persist up to room temperature, as seen in Bi2Se3/Y3Fe5O12 (YIG) heterostructures, where spin-polarized currents have been measured at 300 K.

Superconductivity can also be induced in TIs through proximity coupling to conventional superconductors (SCs). In TI/SC heterostructures, Cooper pairs from the superconductor can tunnel into the TI, leading to superconducting correlations in the surface states. This effect is particularly intriguing because the spin-momentum locking of the TI surface states can give rise to unconventional pairing symmetries, including p-wave superconductivity. The induced superconducting gap in the TI typically follows the BCS temperature dependence of the parent superconductor, but with modifications due to the unique electronic structure of the TI. For instance, in Bi2Se3/NbSe2 heterostructures, a superconducting gap of around 1 meV has been observed, with evidence of topological superconductivity.

One of the most striking consequences of proximity-induced superconductivity in TIs is the potential for Majorana zero modes (MZMs), which are quasiparticles that obey non-Abelian statistics and are of interest for topological quantum computing. MZMs are predicted to appear at vortex cores or edges of proximitized TI films when the superconducting gap is sufficiently large and the Fermi level is tuned to the Dirac point. Experimental signatures of MZMs have been reported in TI/SC heterostructures, including zero-bias conductance peaks in tunneling spectroscopy measurements. However, definitive proof of their non-Abelian nature remains an ongoing challenge.

The interfacial quality plays a crucial role in determining the strength of the proximity effect in both magnetic and superconducting heterostructures. Atomic-scale defects or disorder can suppress the induced order by scattering electrons and breaking coherence. Techniques such as molecular beam epitaxy (MBE) and careful surface preparation are essential for achieving high-quality interfaces. For example, in-situ growth of TI and SC layers under ultrahigh vacuum conditions has been shown to enhance the proximity effect by minimizing interfacial contamination.

The thickness of the TI layer is another critical parameter. If the TI is too thick, the proximity effect may be confined to the interface, leaving the bulk states unaffected. Conversely, if the TI is too thin, quantum confinement can modify the electronic structure, potentially altering the desired properties. Optimal thicknesses are typically in the range of 5-10 nm for maintaining strong proximity effects while preserving the topological surface states.

External fields can further modulate the proximity-induced phenomena. In TI/FM heterostructures, an applied magnetic field can switch the magnetization of the FM layer, thereby controlling the induced gap in the TI. Similarly, in TI/SC systems, magnetic fields can create vortices that host MZMs. Electric fields, on the other hand, can tune the Fermi level of the TI, enabling control over the superconducting or magnetic correlations.

The interplay between magnetism and superconductivity in TI-based heterostructures can lead to exotic phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs acquire finite momentum in the presence of a magnetic field. While evidence for such states in TIs is still limited, theoretical studies suggest that the strong spin-orbit coupling and unique band structure of TIs could stabilize these phases under specific conditions.

Practical applications of proximity-induced phenomena in TI heterostructures include low-power spintronic devices, topological qubits, and highly sensitive magnetic sensors. The ability to engineer these effects without chemical doping makes them particularly attractive for integration into existing semiconductor technologies. However, challenges such as interfacial disorder, thermal stability, and scalability must be addressed before widespread adoption becomes feasible.

In summary, proximity-induced magnetism and superconductivity in TI heterostructures offer a versatile platform for exploring novel quantum states and developing next-generation electronic devices. The combination of strong spin-orbit coupling, topological protection, and tunable interfacial interactions makes these systems a fertile ground for both fundamental research and technological innovation. Continued advances in material synthesis and characterization will be essential for unlocking their full potential.