Dual quantum confinement and anisotropic spin splitting in the multivalley semimetal ${\mathrm{PtSe}}_{2}$

Dual quantum confinement and anisotropic spin splitting in the multivalley semimetal ${PtSe}_{2}$

O. J. Clark, F. Mazzola, J. Feng, V. Sunko, I. Marković, L. Bawden, T. K. Kim, P. D. C. King, and M. S. Bahramy

Phys. Rev. B 99, 045438 – Published 25 January 2019

Abstract

We investigate the electronic structure of a two-dimensional electron gas created at the surface of the multivalley semimetal $1 T - {PtSe}_{2}$ . Using angle-resolved photoemission and first-principles-based surface space-charge calculations, we show how the induced quantum well sub-band states form multiple Fermi surfaces, which exhibit highly anisotropic Rashba-like spin splittings. We further show how the presence of both electronlike and holelike bulk carriers causes the near-surface band bending potential to develop an unusual nonmonotonic form, with spatially segregated electron accumulation and hole accumulation regions, which in turn amplifies the induced spin splitting. Our results thus demonstrate the novel environment that semimetals provide for tailoring electrostatically induced potential profiles and their corresponding quantum sub-band states.

Received 19 October 2018
Revised 2 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.045438

Physics Subject Headings (PhySH)

Electronic structure Spin-orbit coupling

Semimetals Two-dimensional electron gas

Angle-resolved photoemission spectroscopy Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

O. J. Clark¹, F. Mazzola¹, J. Feng^1,2, V. Sunko^1,3, I. Marković^1,3, L. Bawden¹, T. K. Kim⁴, P. D. C. King^1,*, and M. S. Bahramy^5,6,†

¹SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
²Suzhou Institute of Nano-Tech. and Nanobionics (SINANO), CAS, 398 Ruoshui Road, SEID, SIP, Suzhou, 215123, China
³Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
⁴Diamond Light Source, Harwell Campus, Didcot, OX11 0DE, United Kingdom
⁵Quantum-Phase Electronics Center and Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
⁶RIKEN center for Emergent Matter Science (CEMS), Wako 351-0198, Japan

^*philip.king@st-andrews.ac.uk
^†bahramy@ap.t.u-tokyo.ac.jp

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Vol. 99, Iss. 4 — 15 January 2019

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Figure 1
(a) Three-dimensional Fermi surface of bulk ${PtSe}_{2}$ , extracted from DFT calculations. Additional $k_{x} - k_{y}$ contours are displayed for $k_{z} = \pm 0.6 \frac{π}{c}$ as extracted from photon energy-dependent ARPES, left ( $h ν = 120$ eV and 99 eV, $E_{F} \pm 30$ meV) and from DFT, right. (b) ARPES dispersions along the $\bar{M} - \bar{K} - \bar{Γ} - \bar{M}$ path ( $h ν = 53$ eV). (c) Equivalent dispersions extracted from DFT calculations, projected as a function of $k_{z}$ between 0 and $0.7 \frac{π}{c}$ (see color bar), which are in good agreement with the experimental measurements. No additional states are present in this energy range for other $k_{z}$ values.
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Figure 2
(a) Schematic representation of near-surface charge accumulation when Rb atoms are deposited on a surface. (b) Measured Fermi surface of Rb-dosed ${PtSe}_{2}$ ( $E_{F} \pm 12$ meV, $h ν = 37$ eV). (c) Equivalent Fermi surface resulting from a self-consistent band bending calculation.
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Figure 3
(a) Pristine (left) and Rb-dosed (right) ARPES dispersions ( $h ν = 37$ eV) measured along the $\bar{Γ} - \bar{M}$ direction. (b) Orbitally projected surface slab calculations over an equivalent range as for (a). The inset shows the spin polarization of the confined Rashba-split pair along $\bar{Γ} - \bar{M}$ , projected onto the perpendicular (i.e., chiral) spin component. (c) Bulk orbitally projected band structure of pristine ${PtSe}_{2}$ calculated along the in-plane $\bar{Γ} - \bar{M}$ direction for $k_{z} = 0.6 \frac{π}{c}$ . The dashed lines show schematically the expected band structure in the absence of hybridisation between the $p_{x, y}$ and $p_{z}$ orbitals.
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Figure 4
Calculated (a) potential profile and (b) charge density profile for surface-doped ${PtSe}_{2}$ with a surface sheet carrier density $N_{ss} \approx 1 \times 10^{14} {cm}^{- 2}$ . In (b), $ρ_{h}$ and $ρ_{e}$ denote the individual contribution of the hole and electron bands to the charge density, respectively. (c), (d) Schematic illustration of quantum confinement of surface states in a compensated semimetal, considering (c) a conventional band bending potential and (d) a real potential satisfying the Poisson's equation for such a double-carrier system.
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Figure 5
(a) Comparison of calculated charge density profile resulting from all Fermi pockets of ${PtSe}_{2}$ vs a hypothetical case where only the electron ( $K$ -) pocket and hole ( $Γ$ -) pockets are included in the space-charge calculations. (b) The corresponding potential profile for each case. For all three cases, the total sheet carrier density is fixed at $10^{14} {cm}^{- 2}$ .
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Figure 6
Expected potential profile of surface-doped ${PtSe}_{2}$ at sheet carrier densities (a) $1 \times 10^{14} {cm}^{- 2}$ , (b) $2.2 \times 10^{14} {cm}^{- 2}$ , and (c) $4.3 \times 10^{14} {cm}^{- 2}$ . (d)–(f) The respective spin-resolved surface electronic structures along the $\bar{Γ} - \bar{M}$ direction. Here, spin projection direction is set to be normal to both the momentum direction and the gradient of the bending potential. The size of the spin splitting grows with increasing magnitude of the near-surface potential gradient, indicating that the asymmetric band bending potential is the dominant driver of the Rashba-like spin splitting here.
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Physical Review B

covering condensed matter and materials physics

Dual quantum confinement and anisotropic spin splitting in the multivalley semimetal ${PtSe}_{2}$

O. J. Clark, F. Mazzola, J. Feng, V. Sunko, I. Marković, L. Bawden, T. K. Kim, P. D. C. King, and M. S. Bahramy

Phys. Rev. B 99, 045438 – Published 25 January 2019

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Physical Review B

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Dual quantum confinement and anisotropic spin splitting in the multivalley semimetal PtSe2

O. J. Clark, F. Mazzola, J. Feng, V. Sunko, I. Marković, L. Bawden, T. K. Kim, P. D. C. King, and M. S. Bahramy

Phys. Rev. B 99, 045438 – Published 25 January 2019

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Dual quantum confinement and anisotropic spin splitting in the multivalley semimetal ${PtSe}_{2}$