Proximity-induced topological states in heterostructures represent a fascinating intersection of condensed matter physics and materials science, where the unique properties of topological insulators (TIs) are modified or enhanced through interactions with adjacent materials. By coupling TIs with superconductors or magnetic layers, novel quantum states emerge, enabling advanced applications in quantum computing and low-energy electronics. This article explores the mechanisms and experimental realizations of such proximity effects, focusing on systems like Bi₂Se₃/EuS while avoiding overlap with broader discussions on heterostructures or spintronics.

Topological insulators are materials with an insulating bulk and conducting surface states protected by time-reversal symmetry. These surface states exhibit Dirac-like dispersion and are robust against non-magnetic perturbations. When a TI is interfaced with a superconductor or ferromagnet, the proximity effect can induce superconducting correlations or break time-reversal symmetry, leading to exotic phenomena such as Majorana fermions or quantum anomalous Hall effects.

Superconducting proximity effects in TIs arise when Cooper pairs tunnel from a conventional superconductor into the topological surface states. This induces a superconducting gap in the Dirac cone, potentially creating a topological superconductor. For instance, when Bi₂Se₃ is coupled to NbSe₂, the superconducting gap of NbSe₂ (approximately 1 meV) propagates into the TI surface states. The resulting system may host Majorana bound states at vortices or edges, which are pivotal for fault-tolerant quantum computing. Experiments have observed signatures of induced superconductivity in such heterostructures through tunneling spectroscopy, where a zero-bias conductance peak suggests the presence of Majorana modes.

Magnetic proximity effects, on the other hand, break time-reversal symmetry in TIs, lifting the degeneracy of the Dirac cone and opening an exchange gap. A notable example is the Bi₂Se₃/EuS heterostructure, where EuS, a ferromagnetic insulator with a Curie temperature of 16.5 K, magnetizes the surface states of Bi₂Se₃. Measurements using angle-resolved photoemission spectroscopy (ARPES) reveal a gap opening at the Dirac point, confirming the magnetic coupling. The induced exchange interaction can reach magnitudes of 10-20 meV, depending on interface quality and temperature. This system exhibits the quantum anomalous Hall effect (QAHE) at sufficiently low temperatures, where the Hall conductance quantizes to e²/h without an external magnetic field.

The interface quality in these heterostructures is critical for observing robust proximity effects. Atomic-scale defects or intermixing can suppress the desired phenomena. For example, in Bi₂Se₃/EuS, ideal interfaces are achieved using molecular beam epitaxy (MBE) with careful control of growth parameters. High-resolution transmission electron microscopy (TEM) studies show that sharp interfaces preserve the magnetic and topological properties, whereas intermixing leads to diluted effects. Similarly, in superconducting heterostructures, tunnel barriers or oxide layers are sometimes introduced to optimize the coupling strength.

Beyond Bi₂Se₃, other TIs like Sb₂Te₃ and Bi₂Te₃ have been explored in proximity-coupled systems. For instance, Sb₂Te₃ grown on NbN exhibits induced superconductivity with a critical temperature tunable by the NbN thickness. The superconducting gap in these systems typically ranges from 0.5 to 1.5 meV, as measured by scanning tunneling microscopy (STM). Magnetic proximity effects have also been studied in Mn-doped Bi₂Te₃, where the intrinsic magnetism eliminates the need for an external ferromagnetic layer, though control over uniformity remains challenging.

Theoretical models provide a framework for understanding these effects. The Bogoliubov-de Gennes (BdG) Hamiltonian describes superconducting proximity effects by incorporating pairing terms into the TI surface state Hamiltonian. For magnetic proximity, the Dirac Hamiltonian is modified with an exchange field term, leading to gap opening and QAHE under specific conditions. Numerical simulations based on these models predict the existence of chiral edge states in magnetic TI heterostructures, which have been experimentally verified through transport measurements.

Practical challenges remain in realizing scalable devices based on proximity-induced topological states. Temperature stability is a key limitation; most effects are observed at cryogenic temperatures due to the low Curie or critical temperatures of the coupled materials. For example, the QAHE in Bi₂Se₃/EuS is typically observed below 2 K, far from room-temperature applicability. Material combinations with higher energy scales, such as Cr-doped (Bi,Sb)₂Te₃, have pushed the QAHE observation to temperatures around 50 K, but further improvements are needed.

Another challenge is the precise control of interfacial coupling. In superconducting heterostructures, the transparency of the interface governs the induced gap magnitude. Techniques like in situ electrode deposition or van der Waals stacking of two-dimensional materials offer improved interface quality. For magnetic systems, achieving uniform magnetization without parasitic effects like magnetic domains is essential. Advances in epitaxial growth and interface engineering continue to address these issues.

Future directions include exploring proximity effects in newer topological materials, such as magnetic topological insulators or Weyl semimetals. Heterostructures combining type-II superconductors with TIs may offer higher critical temperatures, while multiferroic layers could enable electric-field control of magnetic proximity effects. Additionally, integrating these systems with existing semiconductor platforms could facilitate their adoption in hybrid quantum devices.

In summary, proximity-induced topological states in heterostructures unlock rich physics and potential applications by marrying the properties of TIs with superconductors or magnets. Systems like Bi₂Se₃/EuS demonstrate the feasibility of engineering quantum phenomena through interfacial coupling, though challenges in temperature stability and interface control persist. Continued research in materials synthesis and theoretical modeling will be crucial for harnessing these effects in next-generation technologies.