Illuminating the three-dimensional topological insulator Bi2Se3 with polarized light generates photocurrents whose helicity and linear-polarization dependence was traced to the helical Dirac surface states (McIver et al., 2011). However, the original 1.56 eV measurements necessarily coexcite bulk carriers, photon-drag currents, and possibly Rashba-split inversion-layer states, so the Dirac-cone (topological-surface-state) contribution has never been isolated quantitatively, and the proposal that the circular photogalvanic effect measures the surface Berry phase remains unconfirmed. Later work has delivered a microscopic theory of the surface-state linear photogalvanic effect (2023), terahertz/infrared photogalvanic spectroscopy of the surface states (2018), photon-drag theory and experiments (2016), and Dirac-surface-state attribution of terahertz nonlinear responses with topologically trivial controls (2024). What survives is the quantitative core: a model-validated separation of the topological-surface-state photogalvanic response from all competing channels in regimes where only intra-Dirac-cone transitions occur, quantitative bounds on non-topological contributions, and a determination of whether — and by what quantitative signature — the isolated response encodes an intrinsic topological quantity such as the surface Berry phase.

Background

A three-dimensional topological insulator (3D TI) is a bulk insulator whose surfaces host an odd number of gapless, spin-polarized Dirac-cone bands in which the electron spin is locked perpendicular to its momentum (spin-momentum locking), protected by time-reversal symmetry. Bi2Se3 is the archetypal 3D TI, with a single helical Dirac cone on each surface and a bulk band gap of roughly 0.3 eV. The photogalvanic effect is the generation of a dc current (under zero bias) by normally absorbed light: the circular photogalvanic effect (CPGE) is driven by the helicity of circularly polarized light and requires an asymmetric (spin-split) distribution of states in momentum space, while the linear photogalvanic effect (LPGE) is governed by the orientation of the polarization plane. A related mechanism, the photon drag effect, produces currents via photon momentum transfer and is also allowed in the bulk. In spin-orbit-coupled Rashba-split quantum wells (spin splitting from structural inversion asymmetry, which produces two oppositely spin-polarized Fermi surfaces), the CPGE and LPGE are observed together and have long served as probes of the spin splitting (Ganichev and Prettl, 2003), and it was shown theoretically that their combined magnitude measures the trivial Berry phase of the quantum-well spin texture (Moore and Orenstein, 2010); the Berry phase is the geometric phase accumulated by a spin as it winds around the Fermi surface, equal to pi for a single helical Dirac cone. Hosur (2011) predicted analogously that the CPGE on a TI surface is Berry-curvature-dependent, so polarization-resolved photocurrents could measure the non-trivial (pi) Berry phase of the topological surface states, but this requires the surface contribution to be isolated quantitatively, since the CPGE of Rashba-split bands largely cancels between their two Fermi surfaces while a Dirac cone has only one. McIver, Hsieh, Steinberg, Jarillo-Herrero and Gedik (2011) provided the experimental starting point: illuminating Bi2Se3 with 795 nm (1.56 eV) femtosecond pulses, they decomposed the photocurrent into a helicity-dependent term C (which vanishes at normal incidence as required by the threefold rotational symmetry of the Bi2Se3 surface, confirming its spin-momentum-locked origin), a linear-polarization term L1 that tracks the temperature dependence of C and was argued to share the Dirac-cone origin, and terms D and L2 of bulk (photon-drag-like) origin. Their stated obstacles were: depopulating the Dirac cone with 1.56 eV light necessarily excites bulk-like states carrying their own photocurrents; no comprehensive theory of the LPGE for topological surface states existed; features of the polarization- and temperature-dependent data lacked a detailed microscopic model (excited-state and relaxation physics, spin-dependent photon-drag-type processes at the surface); and Rashba-split quantum-well states known to occur in the inversion layer of some Bi2Se3 samples were not quantitatively constrained as CPGE contributors, although they were argued to be small.

Problem Statement

Establish, quantitatively and with microscopic-theoretical validation, the Dirac-cone (topological-surface-state) photogalvanic response of Bi2Se3-family three-dimensional topological insulators, and determine whether — and by what quantitative signature — it encodes an intrinsic topological quantity such as the surface Berry phase (or show that it does not). Concretely, building on the helicity- and linear-polarization-controlled photocurrents reported by McIver et al. (Nature Nanotechnology 7, 66 (2012)) with 1.56 eV excitation, whose circular term C and linear term L1 were attributed to the helical Dirac fermions while D and L2 are of bulk (photon-drag-type) origin: (a) measure the polarization-resolved photocurrents in regimes where only the topological surface states respond, or else separate the surface and bulk contributions quantitatively; (b) construct and test the microscopic theory of the circular and linear photogalvanic effects of the topological surface states — including shift and ballistic/injection mechanisms, hexagonal warping, excited-state populations, relaxation and scattering channels, and possible spin-dependent photon-drag processes at the surface — against the full polarization, temperature, and photon-frequency dependence of the data; (c) place quantitative bounds on all non-topological contributions, including bulk photocurrents and photon drag, thermoelectric and demodulation currents, and the Rashba-split inversion-layer quantum-well states present in some Bi2Se3 samples, whose circular photogalvanic contribution has never been measured; and (d) determine, at a quantitative, model-verified level, whether — and by what measurable signature — the isolated Dirac-cone photogalvanic response encodes an intrinsic topological quantity such as the non-trivial (pi) Berry phase or the Berry-curvature-weighted response of the helical surface spin texture proposed by Hosur (Physical Review B 83, 035309 (2011)), or that it does not. These sub-goals are jointly posed: the topological-surface-state response is to be separated from the bulk, photon-drag, thermoelectric, and Rashba contributions at uncertainties small compared with the extracted surface response.

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