Cryogenic optoelectronics leverages the unique properties of materials at ultra-low temperatures to enable high-performance quantum sensors and single-photon detectors. Two-dimensional (2D) materials, with their atomic-scale thickness and tunable electronic properties, have emerged as promising candidates for such applications. Their exceptional defect tolerance, coupled with controllable charge transport mechanisms at cryogenic temperatures, makes them ideal for next-generation optoelectronic devices operating in extreme conditions.

At cryogenic temperatures, typically below 77 K, the behavior of charge carriers in 2D materials undergoes significant changes. Thermal noise is drastically reduced, leading to enhanced carrier mobility and longer coherence times. For instance, monolayer molybdenum disulfide (MoS₂) exhibits a mobility increase from approximately 30 cm²/Vs at room temperature to over 1000 cm²/Vs at 4.2 K. This improvement is attributed to the suppression of phonon scattering, which dominates carrier transport at higher temperatures. Similar trends are observed in other transition metal dichalcogenides (TMDCs), such as tungsten diselenide (WSe₂), where low-temperature measurements reveal ballistic transport over micrometer-scale distances.

Defect tolerance is a critical factor in cryogenic optoelectronic applications. Unlike bulk semiconductors, where defects often lead to severe performance degradation, 2D materials demonstrate remarkable resilience. The reduced dimensionality confines defect-induced scattering, while the strong Coulomb interactions at low temperatures facilitate efficient exciton formation even in the presence of imperfections. For example, in hexagonal boron nitride (hBN)-encapsulated graphene, charge carriers maintain high mobility despite substrate-induced disorder due to the screening effect of the hBN layers. This defect tolerance is particularly advantageous for single-photon detectors, where even minor imperfections can compromise detection efficiency.

Single-photon detection is one of the most demanding applications for cryogenic optoelectronics. 2D materials like graphene and TMDCs offer ultrafast response times and broadband spectral sensitivity. Graphene-based photodetectors have demonstrated picosecond-level response times at 4 K, enabled by the rapid extraction of photoexcited carriers. Meanwhile, TMDCs exhibit strong excitonic effects at low temperatures, leading to high quantum efficiencies. In tungsten disulfide (WS₂), bound exciton states become stable below 50 K, allowing for efficient photon absorption and carrier multiplication. These properties are exploited in superconducting nanowire single-photon detectors (SNSPDs), where 2D materials serve as the active sensing layer, achieving detection efficiencies exceeding 90% in the near-infrared spectrum.

Quantum sensors based on 2D materials also benefit from cryogenic operation. Nitrogen-vacancy (NV) centers in diamond have long been used for magnetometry, but 2D materials provide new opportunities for miniaturization and integration. For instance, defects in monolayer TMDCs, such as sulfur vacancies in MoS₂, exhibit spin-dependent photoluminescence that can be manipulated at low temperatures. These defects act as atomic-scale sensors for magnetic fields, with reported sensitivities approaching 1 μT/√Hz at 10 K. Additionally, the valley degree of freedom in TMDCs enables optical readout of magnetic information without the need for complex microwave control, simplifying sensor design.

The interplay between charge transport and defect dynamics in 2D materials at cryogenic temperatures is governed by several mechanisms. At temperatures below 20 K, hopping conduction becomes negligible, and band-like transport dominates. In graphene, this results in a quantized Hall effect, while in TMDCs, the formation of tightly bound excitons leads to sharp photoluminescence peaks. Defects that act as trapping centers at room temperature often become inactive at cryogenic temperatures due to the freeze-out of non-radiative recombination pathways. This phenomenon is observed in selenium-deficient WSe₂, where photoluminescence intensity increases by two orders of magnitude upon cooling to 4 K.

Thermal management is another crucial consideration for cryogenic optoelectronics. The low heat capacity of 2D materials allows for rapid thermalization with the substrate, minimizing thermal gradients that could degrade performance. However, self-heating effects under high photon fluxes can still pose challenges. Studies have shown that in graphene-based bolometers operating at 1.5 K, the electron temperature can rise significantly above the lattice temperature due to weak electron-phonon coupling. Mitigating this requires careful design of thermal anchors and the use of high-thermal-conductivity substrates like diamond.

The integration of 2D materials with superconducting circuits opens new avenues for hybrid quantum devices. Proximity-induced superconductivity has been demonstrated in graphene and TMDCs when coupled to niobium or aluminum contacts. These hybrid structures exhibit gate-tunable supercurrents and Andreev reflection at temperatures below the critical temperature of the superconductor. Such devices are being explored for single-photon detection and quantum information processing, where the combination of superconductivity and 2D material properties enables novel functionalities.

Despite the progress, challenges remain in scaling cryogenic 2D optoelectronic devices for practical applications. Uniform material growth over large areas, precise defect engineering, and stable encapsulation techniques are critical for achieving reproducible performance. Advances in atomic layer deposition and van der Waals assembly have addressed some of these issues, but further optimization is needed. Additionally, the development of cryogenic-compatible readout electronics is essential for real-world deployment.

The future of cryogenic optoelectronics with 2D materials lies in the exploration of new material systems and device architectures. Emerging materials like twisted bilayer graphene and moiré superlattices exhibit correlated electron states at low temperatures that could revolutionize quantum sensing. Similarly, the integration of 2D materials with photonic circuits promises to enable compact, high-performance systems for quantum communication and computing. As the understanding of low-temperature charge transport and defect tolerance deepens, the potential applications of these materials will continue to expand.