Physics of the spin-orbit coupling at the surface of the model topological insulators <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Bi</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Se</mml:mi> <m

The dispersion of topological surface states in three-dimensional topological insulators (TIs) is commonly attributed to the atomic spin-orbit coupling (SOC) of the constituent elements. Whether the observable surface-state dispersion reflects this bare atomic value, or instead an effective SOC renormalized by surface–bulk hybridization, remains an open question. Here, we investigate this issue for the occupied and unoccupied surface-state dispersion in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Bi</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi>Se</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>Bi</b:mi> <b:mn>2</b:mn> </b:msub> <b:msub> <b:mi>Te</b:mi> <b:mn>3</b:mn> </b:msub> </b:mrow> </b:math> by combining angle-resolved photoemission (ARPES) and time-resolved (tr-ARPES) at a fixed 1 ps delay time with one-step photoemission calculations. Comparison between experimental and calculated spectra indicates that the SOC governing the surface-state dispersion deviates from the atomic expectation, with this effect more clearly resolved in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>Bi</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi>Se</c:mi> <c:mn>3</c:mn> </c:msub> </c:mrow> </c:math> than in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>Bi</d:mi> <d:mn>2</d:mn> </d:msub> <d:msub> <d:mi>Te</d:mi> <d:mn>3</d:mn> </d:msub> </d:mrow> </d:math> . The calculations, which explicitly include hybridization between topological surface states and bulk-derived surface resonance states, provide a microscopic framework for this behavior. These results indicate that the spin-orbit interaction governing topological surface states is effectively shaped by surface–bulk hybridization and can vary significantly across materials.