High pressure has emerged as a powerful tool for probing and manipulating the electronic structure of quantum materials, particularly in inducing topological phase transitions. Among the materials exhibiting such behavior, bismuth selenide (Bi2Se3) serves as a prototypical example, undergoing distinct electronic rearrangements under compression. These transitions are driven by modifications in band inversion, spin-orbit coupling, and lattice symmetry, leading to experimentally observable signatures in transport, optical, and spectroscopic measurements.

At ambient conditions, Bi2Se3 is a well-known topological insulator with a rhombohedral crystal structure (space group R-3m) and a bulk bandgap of approximately 0.3 eV. The topological surface states are protected by time-reversal symmetry, with the Z2 invariant ν0 = 1. Under applied pressure, the interplay between orbital hybridization and lattice contraction alters the electronic landscape. The first significant change occurs around 3-4 GPa, where the bandgap begins to close due to increased overlap between the conduction and valence bands. This marks the onset of a topological phase transition, where the material evolves from a topological insulator to a trivial semiconductor or semimetal.

The critical pressure for complete bandgap closure in Bi2Se3 typically lies between 8-10 GPa, as confirmed by high-pressure angle-resolved photoemission spectroscopy (ARPES) and X-ray diffraction (XRD). Beyond this threshold, the material enters a metallic state with a Lifshitz transition, characterized by a change in the Fermi surface topology. The loss of band inversion eliminates the topological protection, and the surface states merge into the bulk continuum. Further compression (above 15 GPa) often induces structural phase transitions, such as the rhombohedral-to-monoclinic transformation observed near 25 GPa in Bi2Se3. These structural changes further modify the electronic dispersion, sometimes leading to superconductivity at higher pressures.

The electronic structure crossover under pressure is primarily governed by two competing mechanisms. First, the increased kinetic energy of electrons due to lattice compression enhances band dispersion, favoring metallic behavior. Second, spin-orbit coupling, which is responsible for the initial band inversion, remains strong but becomes insufficient to maintain the topological phase as the lattice parameters shrink. The relative strength of these effects determines the critical pressure for the phase transition. In Bi2Se3, the persistence of spin-orbit coupling ensures that the transition is not abrupt but occurs over a finite pressure range, as evidenced by gradual changes in transport properties.

Experimental signatures of these transitions are manifold. Electrical resistivity measurements reveal a non-monotonic pressure dependence, with an initial increase due to bandgap narrowing, followed by a drop upon entering the metallic state. Hall effect data show carrier concentration changes, reflecting the Lifshitz transition and Fermi surface reconstruction. Optical spectroscopy detects shifts in the absorption edge and plasmonic features, correlating with the bandgap closure and metallization. Raman spectroscopy provides additional insights by tracking phonon mode softening or disappearance, which accompanies the structural and electronic transitions.

High-pressure XRD and neutron scattering are indispensable for correlating electronic changes with lattice dynamics. In Bi2Se3, the compression reduces the c/a ratio of the unit cell, increasing interlayer coupling and diminishing the van der Waals gap. This dimensional crossover from quasi-2D to more 3D behavior further destabilizes the topological phase. The emergence of new diffraction peaks at higher pressures signals symmetry lowering, which can gap out previously protected surface states.

The pressure-induced topological transition is not unique to Bi2Se3 but is observed in related compounds like Bi2Te3 and Sb2Te3, albeit with different critical pressures due to variations in spin-orbit coupling and compressibility. For instance, Bi2Te3 undergoes a similar insulator-to-metal transition near 7 GPa, while Sb2Te3 requires higher pressures due to its stronger spin-orbit interaction. These differences highlight the tunability of topological phases via chemical substitution and external pressure.

Beyond the binary chalcogenides, high-pressure studies have extended to ternary and quaternary topological materials, where additional degrees of freedom enable richer phase diagrams. For example, the Bi2Se3-derivative Bi2Te2Se exhibits pressure-driven transitions involving both topological and magnetic ordering, as indicated by anomalies in magnetoresistance and specific heat. Such complexity underscores the need for multi-probe experimental approaches to disentangle competing effects.

Theoretical frameworks like density functional theory (DFT) and tight-binding models have been instrumental in predicting and interpreting these transitions. Calculations often reveal that pressure not only closes the bandgap but can also induce new topological phases through band reordering. In some cases, a re-entrant topological insulating state is predicted at ultra-high pressures, though experimental confirmation remains challenging due to technical limitations.

Practical implications of these findings extend to the design of pressure-tunable devices and the exploration of exotic quantum states. The ability to reversibly switch between topological and trivial phases offers potential applications in reconfigurable electronics and sensors. Moreover, the proximity to superconductivity in pressurized Bi2Se3 suggests a possible interplay between topological and superconducting order parameters, relevant for fault-tolerant quantum computing.

In summary, high pressure serves as a clean tuning parameter for investigating topological phase transitions in materials like Bi2Se3. The electronic structure evolves through distinct regimes—topological insulator, trivial semiconductor, and metallic phases—each with characteristic experimental fingerprints. These studies not only advance fundamental understanding of topological matter but also pave the way for engineering novel quantum phases under extreme conditions. Future research directions may explore higher pressure regimes, combined stress geometries, and dynamic compression techniques to uncover additional hidden phases and transitions.