Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ by angle-resolved photoemission and terahertz spectroscopy

Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator ${Bi}_{2} {Te}_{3}$ by angle-resolved photoemission and terahertz spectroscopy

Bumjoo Lee, Yukiaki Ishida, Jonghyeon Kim, Jinsu Kim, Na Hyun Jo, So Yeun Kim, Inho Kwak, Min-Cheol Lee, Kyungwan Kim, Jae Hoon Kim, Myung-Hwa Jung, Shik Shin, Tae Won Noh, and Hyunyong Choi

Phys. Rev. B 106, 195430 – Published 29 November 2022

Abstract

Photoexcited carriers in three-dimensional topological insulators (3D TIs) decay rapidly through the electron-electron and electron-phonon scattering. While most studies focus on such fast dynamics, recent experiments find the slow photovoltage (PV) dynamics arising from the band-bending potentials, in which the optical transitions in two-dimensional electron gas (2DEG) are effective. Although early investigations speculated the existence of multiple band-bending structures from the TI surface to the TI bulk, how PV and 2DEG are correlated in the presence of such multiple band bendings has been less explored. Here, we employ the combination of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and ultrafast time-resolved terahertz (tr-THz) spectroscopy to investigate the PV and 2DEG dynamics in the prototypical topological insulator ${Bi}_{2} {Te}_{3}$ . Our tr-ARPES analysis identifies two spatially separated PV dynamics associated with two types of band bending: one is the well-known surface PV, and another PV is formed deep within the bulk, which we call “internal bulk PV.” For the surface PV, our tr-THz spectra substantiate that the $μ s$ -long transient signal arises from the surface-PV-induced increase of the TSS and 2DEG carrier density, which appears as a transient blueshift of a Fermi cutoff and an increased ARPES intensity in the tr-ARPES measurements. In contrast, the effect of the internal bulk PV shows only marginal changes in the 2DEG and TSS carrier densities but shifts the entire binding energy of the near-surface bands.

Received 1 July 2022
Accepted 7 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.195430

Physics Subject Headings (PhySH)

Photovoltaic effect

Topological insulators

Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bumjoo Lee ^1,2, Yukiaki Ishida^1,3, Jonghyeon Kim ⁴, Jinsu Kim^5,*, Na Hyun Jo^5,6, So Yeun Kim^1,2,†, Inho Kwak ^1,2, Min-Cheol Lee ^1,2, Kyungwan Kim ⁷, Jae Hoon Kim ⁴, Myung-Hwa Jung ⁵, Shik Shin³, Tae Won Noh^1,2, and Hyunyong Choi ^2,8,‡

¹Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Republic of Korea
²Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
³Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Department of Physics, Yonsei University, Seoul 03722, Republic of Korea
⁵Department of Physics, Sogang University, Seoul 04107, Republic of Korea
⁶Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
⁷Department of Physics, Chungbuk National University, Cheongju 28644, Republic of Korea
⁸Institute of Applied Physics, Seoul National University, Seoul 08826, Republic of Korea

^*Present address: Physical Engineering Division, Busan Institute, National Forensic Service, Yangsan 50612, Korea.
^†Present address: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, 61801 IL, USA.
^‡Corresponding author: hy.choi@snu.ac.kr

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Vol. 106, Iss. 19 — 15 November 2022

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Figure 1
(a) Schematic illustration of our experiment and the band structure. The time-dependent changes of the upward band bending in $n$ -type TI are associated with the PV dynamics. On the contrary, prior reports on the two-dimensional electron gas (2DEG) require a downward band bending, which is related to the surface PV. (b)–(e) Time-dependent band structure dynamics measured by tr-ARPES. Each panel represents the tr-ARPES image recorded at different pump-probe delay $τ$ . (b) On top of the linear dispersion of the topological surface state (TSS), a small contribution from the quadratic band was observed at delay $τ = - 1.73$ ps (black circle). After the arrival of the pump pulse (c)–(e), the quadratic band whose energy bottom is at $E - E_{F} \sim 0.1$ eV (black circle) becomes visible.
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Figure 2
The Dirac point and Fermi cutoff shift observed via tr-ARPES (a) Energy distribution curves (EDCs) near $Γ$ point (integrated from $- 0.02 to 0.02 Å^{- 1}$ ) recorded at $τ = - 1.73$ ps. The black and red arrows indicate the peak of the Dirac point and the quadratic band, respectively. (b) EDC near $Γ$ point measured at 1.07 ps (red solid line). For easy comparison, we show the data at $τ = - 1.73$ ps (black solid line) on top of it. After the pump arrival, the ARPES intensity in the unoccupied side ( $E - E_{F} < 0$ ) is reduced while the intensity around $E - E_{F} \sim 0.1$ eV (red arrow) is enhanced. (c) The fluence ( $F$ ) dependent EDC shift at the negative delay $τ = - 0.13$ ps. Compared to the equilibrium (no pump excitation, $0 μ {J / cm}^{2}$ ), the TSS binding energy is increased ( $Δ V_{U} > 0)$ with increasing $F$ (left panel). We attribute $Δ V_{U} > 0$ to the internal bulk PV in the upward band bending. The blue arrow indicates the increased quadratic band in the ARPES intensity (right panel). (d) The Fermi cutoff shift relative to the Dirac point at a negative delay $τ = - 0.13$ ps. No Fermi cutoff shift was seen. (e) EDC near $Γ$ point is shown at $τ$ of −1.73 ps (black solid line) and 340 ps (red solid line). In contrast to (c), the reduced TSS binding energy $| Δ V_{D} |$ of 2.3 meV is observed under the same $F$ of $10 μ {J / cm}^{2}$ (left panel). We attribute $(Δ V_{D} < 0)$ to the surface PV in the downward band bending. The blue arrow has the same meaning as the right panel of (c). (f) The Fermi cutoff shifts relative to the Dirac point at $τ = - 1.73$ ps (black solid line) and at 340 ps (red solid line). A positive Fermi cutoff shift $δ_{D}$ of 2.4 meV is observed at $τ = 340$ ps. Note that the relative shift was compared to the Dirac point energy.
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Figure 3
Schematics of the band structure and the energy band diagram. (a) The energy band diagram (blue solid line) in an “equilibrium” state, i.e., no pump excitation. The energy level of Fermi cutoff $E_{F}$ is indicated by black dotted lines. The bulk state is assumed to be an $n$ -doped semiconductor. The spatial distance of the downward band bending ( $l_{D}$ ) and the upward band bending ( $l_{U}$ ) is indicated by the black bidirectional arrows. (b) Photocarrier distribution on top of the energy band diagram in a “quasiequilibrium” state at negative $τ$ . The effect of the prepump pulses (4 $μ s$ ahead) is to build up the DC component of $V_{DC}$ . The solid red dots indicate the photoexcited electrons and the blue solid dots are the photoexcited holes. The TSS binding energy is enhanced by the internal bulk PV (red arrow) compared to the no pump case. The energy band diagram of the quasiequilibrium (blue solid line) is compared to the equilibrium (blue dotted line). (c) The photocarrier dynamics at about a few hundreds of picoseconds. We call this energy band diagram a “nonequilibrium” one to distinguish this state from the other two states. The photoexcited carriers result in two spatially distinct PVs; one is the surface PV near TSS and another is the internal bulk PV occurring deep into the TI bulk. Both PVs reduce the band bending compared to the quasiequilibrium. The surface PV (red arrow) reduces the TSS band binding energy compared to the quasiequilibrium case. The purple arrows intend to describe the electron-hole recombination. Blue dotted lines are for the energy band diagram in the quasiequilibrium state, and blue solid ones are for the nonequilibrium state.
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Figure 4
The ARPES intensity distribution curves of 2DEG bands and band configuration. (a) Momentum distribution curve (MDC, black circles) measured at $E - E_{F} = 239.6 meV$ when $τ$ is 1.07 ps and the corresponding fit using two Lorentz oscillators (red solid line for the total fit, and blue dotted lines for each oscillator). (b) The black dotted line is the binding energy to obtain the MDC curve. (c) EDC (black circles) at $Γ point$ and the corresponding fit using two Lorentz oscillators multiplied by the Fermi-Dirac distribution (red solid line for the total fit and blue dotted lines for each Lorentz oscillator). (d) The calculated 2DEG subbands with the Rashba-type band split (white lines) are overlapped with the experimental tr-ARPES results.
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Figure 5
The equilibrium THz conductivity and the pump-induced tr-THz conductivity changes. (a) Left: the real part $σ_{1} (ω)$ . Right: the imaginary part $σ_{2} (ω)$ . Red solid lines are fits (see Supplemental Material S6 [34]) using the surface Drude (orange solid line), bulk Drude (black solid line), and Fano-like oscillator (blue solid line). The surface Drude exhibits a scattering rate of $26 c m^{- 1}$ and the bulk Drude exhibits a scattering rate of $150 c m^{- 1}$ . (b), (c) The measured optical conductivity changes (black circle) in the real part $Δ σ_{1} (ω)$ (left panel) and imaginary part $Δ σ_{2} (ω)$ (right panel) at a delay $τ = - 20 ps$ (b) and $τ = 800 ps$ (c) after excitation. Red solid lines are fits (see Supplemental Material S6 [34]) using the differential changes of the surface Drude (orange solid line) and the bulk Drude (black solid line). The reference spectrum is the equilibrium conductivity in (a).
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Physical Review B

covering condensed matter and materials physics

Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator ${Bi}_{2} {Te}_{3}$ by angle-resolved photoemission and terahertz spectroscopy

Bumjoo Lee, Yukiaki Ishida, Jonghyeon Kim, Jinsu Kim, Na Hyun Jo, So Yeun Kim, Inho Kwak, Min-Cheol Lee, Kyungwan Kim, Jae Hoon Kim, Myung-Hwa Jung, Shik Shin, Tae Won Noh, and Hyunyong Choi

Phys. Rev. B 106, 195430 – Published 29 November 2022

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Physical Review B

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Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator Bi2Te3 by angle-resolved photoemission and terahertz spectroscopy

Bumjoo Lee, Yukiaki Ishida, Jonghyeon Kim, Jinsu Kim, Na Hyun Jo, So Yeun Kim, Inho Kwak, Min-Cheol Lee, Kyungwan Kim, Jae Hoon Kim, Myung-Hwa Jung, Shik Shin, Tae Won Noh, and Hyunyong Choi

Phys. Rev. B 106, 195430 – Published 29 November 2022

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Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator ${Bi}_{2} {Te}_{3}$ by angle-resolved photoemission and terahertz spectroscopy