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Black phosphorus as a bipolar pseudospin semiconductor

Nature Materials volume 19, pages 277–281 (2020)Cite this article

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Abstract

Semiconductor devices rely on the charge and spin of electrons, but there is another electronic degree of freedom called pseudospin in a two-level quantum system1 such as a crystal consisting of two sublattices2. A potential way to exploit the pseudospin of electrons in pseudospintronics3,4,5 is to find quantum matter with tunable and sizeable pseudospin polarization. Here, we propose a bipolar pseudospin semiconductor, where the electron and hole states have opposite net pseudospin polarization. We experimentally identify such states in anisotropic honeycomb crystal—black phosphorus. By sublattice interference of photoelectrons, we find bipolar pseudospin polarization greater than 95% that is stable at room temperature. This pseudospin polarization is identified as a consequence of Dirac cones merged in the highly anisotropic honeycomb system6,7. The bipolar pseudospin semiconductor, which is a pseudospin analogue of magnetic semiconductors, is not only interesting in itself, but also might be useful for pseudospintronics.

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Fig. 1: Pseudospin order in anisotropic honeycomb systems.
Fig. 2: Experimental signature of pseudospin polarization.
Fig. 3: Pseudospin polarization patterns.
Fig. 4: Evolution of the pseudospin texture across the topological phase transition.

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Data availability

The data that supports the findings of this study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Research Foundation (NRF) of Korea (grants nos. 2017R1A2B3011368, 2017R1A5A1014862 and 2018K1A3A7A09027641) and the Future-leading Research Initiative of 2019-22-0079 of Yonsei University. The Advanced Light Source is supported by the US Department of Energy, Office of Sciences, under contract no. DE-AC02-05CH11231. We thank K. Moon, B.-J. Yang, Y.W. Son and J.-W. Rhim for helpful discussions and D.Y. Park for help with experiments.

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Author notes

  1. Sung Won Jung

    Present address: Diamond Light Source, Didcot, UK

  2. These authors contributed equally: Sung Won Jung, Sae Hee Ryu, Woo Jong Shin.

Authors and Affiliations

  1. Department of Physics, Yonsei University, Seoul, Korea

    Sung Won Jung, Sae Hee Ryu, Woo Jong Shin, Yeongsup Sohn, Minjae Huh & Keun Su Kim

  2. Department of Physics, Pohang University of Science and Technology, Pohang, Korea

    Sae Hee Ryu, Woo Jong Shin, Yeongsup Sohn & Minjae Huh

  3. Advanced Light Source, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Roland J. Koch, Chris Jozwiak, Eli Rotenberg & Aaron Bostwick

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Contributions

S.W.J., S.H.R., W.J.S., Y.S. and M.H. conducted ARPES experiments with help from R.J.K., C.J., E.R. and A.B. S.W.J. performed tight-binding band calculations and spectral simulations. K.S.K. directed the project. S.W.J., S.H.R. and K.S.K. wrote the manuscript with contributions from all other co-authors.

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Correspondence to Keun Su Kim.

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Extended data

Extended Data Fig. 1 Pseudospin texture in graphene and BP.

The pseudospin texture is calculated with tight-binding models (Methods) and shown in the vector plot for graphene and BP with different Δ marked at the top. The arrows shown in different colours indicate the direction of pseudospin polarization (ϕ is 0, π, ±π/2 for blue, red, green, and yellow arrows, as in Figs. 1e–g and 4a, b). Black dots represent Dirac points.

Extended Data Fig. 2 Experimental geometry and selective excitation of pseudospin polarization.

a, Scattering plane of photon-in (blue arrow) and photoelectron-out (red arrow) aligned to the zigzag (ZZ) axis of BP. With this geometry, linear horizontal (LH) and linear vertical (LV) polarization corresponds to ZZ and AC polarization, respectively. The analyzer slit is rotatable between the horizontal slit to measure ARPES spectra in kZZ and the vertical slit to measure those in kAC with no change in the scattering plane. b, Selective excitation of pseudospin states by variable polarization. The superposition of wavefunctions in A and B sublattices |A〉+eiϕ|B〉 are represented on the Bloch sphere by pseudospin arrows in colour (ϕ is 0, π, ±π/2 for blue, red, green, and yellow arrows). On top of each sphere, the double-head or curved arrows show light polarization allowed to excite corresponding pseudospin states by sublattice interference (Methods).

Extended Data Fig. 3 Temperature dependence of pseudospin polarization in BP.

ARPES spectra of BP at 30 K (top) and 300 K (bottom), taken with linearly polarized light marked at the top. Red and blue curves show the expected locations of VB and CB, respectively. Corresponding line profiles taken at k = 0 are shown on the right.

Extended Data Fig. 4 Photon-energy dependence of pseudospin polarization in BP.

ARPES spectra of BP taken along the AC direction with the photon energy of 60–200 eV. The photon energy is converted to k in the out-of-plane axis (kz) with the inner potential of 10 eV. Constant-energy maps as a function of kAC and kz are shown at –0.23 eV, where the uniform intensity of VB in data of AC-polarized light is suppressed at k < ±0.1 Å−1 in that of ZZ-polarized light. This suppression is unexceptionally observed in all the photon energies, ruling out the possibility of final-state effects. The dispersion along kz is due to the bulk bandstructure of BP, and the fringe patterns near kz = 4.2–4.3 Å−1 is due to the overlap of core-level spectra excited by the second harmonic photons.

Extended Data Fig. 5 Evolution of pseudospin polarization in BP across the band inversion.

A series of ARPES data taken from bulk BP with Δ controlled by surface doping, as marked at the top. ARPES data in the top row were taken along kZZ with AC- polarized light (AC-pol), and those in the middle row were taken with ZZ-polarized light (ZZ-pol). Shown at the bottom row is the difference of ARPES intensity taken by AC-polarized light (IAC) and ZZ-polarized light (IZZ) after normalization. Red and blue dotted lines show the expected locations of hole and electron states, respectively. Black dotted lines indicate the charge-neutrality energy.

Extended Data Fig. 6 Experimental pseudospin polarization in band-inverted BP.

a,b, ARPES data taken from surface-doped bulk BP with Δ = –0.6 eV with AC-polarized light (AC-pol) and zigzag-polarized light (ZZ-pol). c, Difference of ARPES intensity taken with AC-pol. (IAC) and ZZ-pol. (IZZ) after normalization. d, Difference of those taken with LC-polarized (ILC) and RC-polarized (IRC) light. e-h, Constant-energy maps at –0.45 eV taken with the corresponding polarization conditions as marked at the top.

Extended Data Fig. 7 Pseudospin order in anisotropic honeycomb systems across the topological phase transition.

a, Bandstructure of anisotropic honeycomb systems for the three representative cases, Δ > 0 for the normal state, Δ = 0 for the critical point, and Δ < 0 for the Dirac semimetal state. The arrows overlaid show pseudospins in the same colour as defined in Extended Data Fig. 2b. b, Corresponding pseudospin textures calculated with the tight-binding model of BP as a function of Δ controlled by vertical electric field (Methods). c, Corresponding pseudospin textures calculated by the tight-binding model of graphene as a function of Δ controlled by uniaxial strain (Methods).

Extended Data Fig. 8 Quantum tunnelling through the pseudospin interface.

a, Band diagram of BP made in a form of the pseudospin interface. The pseudospin polarization is shown in the same colour as in Extended Data Fig. 7. Owing to the pseudospin conservation as in the p-n junction of bilayer graphene29, the current passing through this pseudospin interface was predicted to exhibit anti-Klein tunnelling and giant pseudo-magnetoresistance, the key mechanism of a pseudospin valve with a large on-off ratio3. b, Conceptual diagram of a pseudospin valve that can be switched on and off by the gate polarity in the middle region.

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Jung, S.W., Ryu, S.H., Shin, W.J. et al. Black phosphorus as a bipolar pseudospin semiconductor. Nat. Mater. 19, 277–281 (2020). https://doi.org/10.1038/s41563-019-0590-2

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