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Visualization of bulk and edge photocurrent flow in anisotropic Weyl semimetals

Abstract

Materials that rectify light into current in their bulk are desired for optoelectronic applications. In Weyl semimetals that break inversion symmetry, bulk photocurrents may arise due to nonlinear optical processes that are enhanced near the Weyl nodes. However, the photoresponse of these materials is commonly studied by scanning photocurrent microscopy, which convolves the effects of photocurrent generation and collection. Here we directly image the photocurrent flow inside the type-II Weyl semimetals WTe2 and TaIrTe4 using high-sensitivity quantum magnetometry with nitrogen-vacancy centre spins. We elucidate a mechanism for bulk photocurrent generation, which we call the anisotropic photothermoelectric effect, where unequal thermopowers along different crystal axes drive intricate circulations of photocurrent around the photoexcitation. Using overlapping scanning photocurrent microscopy and magnetic imaging at the interior and edges of the sample, we visualize how the anisotropic photothermoelectric effect stimulates the long-range photocurrent collected in our WTe2 and TaIrTe4 devices through the Shockley–Ramo mechanism. Our results highlight a widely relevant source of current flow and will inspire photodetectors that utilize bulk materials with thermoelectric anisotropy.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.

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Acknowledgements

We thank Q. Ma, M. Jung and P. C. Jerger for valuable discussions. B.B.Z. acknowledges support from the National Science Foundation (NSF) under award nos. DMR-2047214 and ECCS-2041779. This material is based on work supported by the Air Force Office of Scientific Research under award nos. FA2386-21-1-4095 and FA2386-21-1-4059. Y.R. acknowledges support from the NSF award no. DMR-1712128. C.L. and D.B. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE-SC0021071 (ab initio calculations of band structure and Seebeck coefficients of WTe2). Z.L. acknowledges support from the Singapore National Research Foundation—Competitive Research Program under awards NRF-CRP22-2019-0007 and NRF-CRP21-2018-0007. This work was performed, in part, at the Integrated Sciences Cleanroom and Nanofabrication Facility at Boston College and at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network, which is supported by the NSF under award no. ECCS-0335765. CNS is part of Harvard University.

Author information

Authors

Contributions

Y.-X.W. and B.B.Z. devised the experiments. Y.-X.W. fabricated the photocurrent devices and performed the SPCM and PCFM experiments. Y.R. conceived and demonstrated the theoretical model, with final implementation by Y.-X.W. C.L. and D.B. performed the ab initio calculations. X.Y. and F.T. synthesized the WTe2 samples. R.D. and Z.L. synthesized the TaIrTe4 samples. Y.-X.W. and B.B.Z analysed the data. Y.-X.W. built the experimental setup, with assistance from X.-Y.Z. and T.K.M.G. B.B.Z., Y.-X.W., D.B. and C.L. wrote the manuscript with input from all authors. B.B.Z. supervised the project.

Corresponding author

Correspondence to Brian B. Zhou.

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Nature Physics thanks Matt Graham, Amit Finkler and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Coincident SPCM and PCFM imaging of WTe2 Device B.

(a) Experimental SPCM image of Iglobal in WTe2 Device B for P = 100 μW at 661 nm. (b) Experimental SPCM image of Iglobal for P = 300 μW at 515 nm. The collected photocurrents have identical spatial patterns regardless of optical power or wavelength (see also Fig. 4a of main text). The intensity is slightly higher at 515 nm likely due to better objective transmission and sample absorption at shorter wavelengths. (c) The streamlines for the weighting field ψ within Device B. We solve 2ψ = 0 with equipotential surfaces ψ = 1 and ψ = 0 around two localized positions on the upper (current collecting) and lower (grounded) electrical contacts, respectively. The background colormap denotes the potential ψ. (d) Linear dependence of Iglobal on the optical power P at 661 nm for fixed photoexcitation locations on the $$\langle 1\overline{1}0\rangle$$ (red) or 〈110〉 (blue) edges in Device B. The global electrical measurement is consistent with the local magnetic measurement (Δφ) presented in Fig. 2b of the main text. (e) PCFM image of J(r) when photoexciting the region of high interior Iglobal near the upper gold (Au) electrical pad. The four-fold APTE pattern is negligibly changed from the center of the flake. (f) PCFM image for photoexcitation at the corner between the 〈110〉 and $$\langle 1\overline{1}0\rangle$$ edges. The locations for the measurements (d-f) within Device B are labeled in the SCPM image shown in a).

Extended Data Fig. 2 Absence of any detectable photo-Nernst effect in WTe2 at room temperature.

(a) NV center phase image Δφ(r) in WTe2 Device A for an external dc magnetic field, Bext = + 28.2 mT. (b) Δφ(r) image for the opposite field direction, Bext = − 28.2 mT. By flipping the direction of Bext, we probe the projection of the photocurrent’s magnetic field, BPC, along opposite NV axes. Afterwards, the NV center’s acquired phase simply changes sign everywhere, indicating that the current flow is independent of the magnetic field direction. (c) Reconstructed J(r) for Bext = + 28.2 mT. (d) Reconstructed J(r) for Bext = − 28.2 mT. (e) The difference between the experimental photocurrent patterns at positive and negative external field: J(r, + Bext) − J(r, − Bext). The difference highlights the field-antisymmetric component of the photocurrent flow, which isolates the photo-Nernst effect1,29. The overlaid false colormap denotes the magnitude of the difference, which is experimentally consistent with noise. (f,g) Simulated photocurrent pattern J(r) when including both the APTE term and a possible Nernst term ($$\propto {B}_{\rm{ext,z}}\hat{z}\times \nabla T$$) for f) positive and g) negative Bext (see Supplementary Section 7). (h) The difference J(r, + Bext) − J(r, − Bext) between the simulated patterns clearly shows a chiral photocurrent vortex due to the photo-Nernst effect, which is absent in the experiment. The colormaps in (f-h) denote the magnitude J(r).

Extended Data Fig. 3 Ab initio calculations of the band structure and in-plane thermopower of WTe2.

(a) Electronic band structure calculated within density functional theory, including spin-orbit coupling. (b) Fermi surface of WTe2 with an outer electron pocket shown in cyan and an outer hole pocket shown in purple. (c) Electronic density of states for WTe2, displaying an electron-hole asymmetry about E = 0, defined at the chemical potential μ(300 K). (d) Calculated Seebeck coefficients Sa and Sb along the a- and b-axes of WTe2 versus temperature T. Both Sa and Sb are negative at 300 K, with Sa < Sb as observed in experiment. The difference Sa − Sb diverges with increasing temperature up to 500 K: the thermopower along the a-axis is dominated by electron contributions due to the high velocities of the low-lying conduction bands along this direction, but the smaller velocities along the b-axis do not compensate for the increasing hole contribution that is probed at higher temperatures, due to the rapidly rising density of states on the hole side away from the chemical potential.

Extended Data Fig. 4 APTE photocurrent in TaIrTe4 Devices A and B.

(a) Optical micrograph of TaIrTe4 Device A, with thickness 440 nm. (b) NV center phase image Δφ(r) for photoexcitation in the interior of TaIrTe4 with P = 90 μW. The reconstructed J(r) from Δφ(r) is shown in Fig. 3d of the main text. (c) Phase image Δφ(r) for photoexcitation of the 〈100〉 edge in TaIrTe4 with P = 90 μW. The photoexcitation locations of b) and c) are labeled in the optical micrograph shown in a). (d) Reconstructed PCFM image of J(r) near the 〈100〉 edge, corresponding to Δφ(r) in c). (e) Dependence of the edge photocurrent Iglobal on the optical power P at 661 nm for an oblique 〈110〉 edge in TaIrTe4. The data are taken on TaIrTe4 Device B with thickness of 280 nm, whose optical micrograph is shown as the inset. (f) Experimental SPCM image of TaIrTe4 Device B. Similar to WTe2, global edge photocurrent is detected along the right 〈110〉 edge, while interior photocurrents are detected throughout the device. Far away from the contacts, the edge photocurrent is nearly vanishing along the left 〈100〉 edge, as expected from mirror symmetry and a gradient field ψ that becomes slowly-varying over the local photocurrent extent. (g,h) PCFM image of J(r) for photoexciting: g) the 〈100〉 edge, and h) the 〈110〉 edge in TaIrTe4 Device B, both with P = 85 μW. The photoexcitation locations for g) and h) are labeled on the SPCM image in f).

Extended Data Fig. 5 Power dependence of SPCM and PCFM imaging in TaIrTe4 Device C.

(a) Optical micrograph of TaIrTe4 Device C, with thickness 224 nm. Deliberate point-like side contact is made to the 〈100〉 edge. (b) Calculated weighting field ψ within TaIrTe4 Device C by assuming point-like equipotential surfaces ψ = 1 and ψ = 0 around the upper and lower locations, respectively, where the gold pads make grazing contact to the sample. c) Full simulation of the SPCM image of the collected photocurrent in Device C using Shockley-Ramo theory. The ψ used is shown in b), and the local Jph is assumed to be due to the APTE with a conductivity anisotropy σa/σb = 4 for TaIrTe4 (Fig. 3d,e of the main text). (d,e,f) Experimental SPCM images using 661 nm photoexcitation at powers of 200 μW, 100 μW, and 50 μW, respectively. The spatial pattern is nearly identical across optical powers. g) Linear dependence of the collected Iglobal on the optical power P at three particular locations R1, R2, and R3. The locations of the points are labeled in d). (h,i) PCFM images of the photocurrent flow when exciting the 〈100〉 edge in TaIrTe4 Device C with P = 100 μW and 50 μW, respectively. The location of the photoexcitation is labeled in e) and f). Although vanishing global photocurrent is collected, as expected from Shockley-Ramo theory for this high-symmetry 〈100〉 edge far from the contacts, the local photocurrent still displays APTE circulation.

Extended Data Fig. 6 PCFM imaging of edge photocurrent in WTe2 Device A.

(a) Zoomed-in optical micrograph of WTe2 Device A. The photoexcitation locations for the PCFM and NV phase images to follow are labeled by their figure panel. (b) PCFM image of J(r) for photoexciting the $$\langle 1\overline{1}0\rangle$$ edge with P = 70 μW. (c) PCFM image for photoexciting the 〈110〉 edge with P = 120 μW. (d) NV center phase map Δφ(r) for photoexciting the 〈100〉 edge in Device A, corresponding to the reconstructed J(r) shown in Fig. 4d of the main text. (e) Phase map Δφ(r) corresponding to the J(r) image in b). (f) Phase map Δφ(r) corresponding to the J(r) image in c).

Extended Data Fig. 7 Novel photodetector designs based on the APTE.

(a) Geometry for enhanced Shockley-Ramo collection of bulk APTE photocurrents. We choose the contact configuration to maximize the dot product between ψ, shown as the streamlines, and Jph due to the APTE in the center of the device. An array of such individual pixels could potentially be used for imaging applications in the mid-infrared or terahertz wavelengths. (b) Simulated Iglobal as a function of the incident beam position for the design in a). The beam size is shown as the green circle and can be realized with an attached microlens. (c) Single-chip, four-quadrant APTE photodetector based on sign-switching, crystal-axes-aligned APTE photocurrents. Photocurrents I13, between contacts 1 and 3, or I24, between contacts 2 and 4, are alternatively measured with the other contact pair floating. The modeled beam size is shown as the green circle. The material and beam properties are the same between designs shown in b) and c), which allows a comparison of the amplitude of Iglobal. (d) The binary pair corresponding to the signs of I13 and I24 uniquely identifies on which quadrant of the detector the beam is incident. The orientation of the crystal a/b-axes for each design is diagrammed.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12, Table 1 and Sections 1–9.

Source data

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical and simulation source data.

Source Data Fig. 4

Statistical and simulation source data.

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Wang, YX., Zhang, XY., Li, C. et al. Visualization of bulk and edge photocurrent flow in anisotropic Weyl semimetals. Nat. Phys. (2023). https://doi.org/10.1038/s41567-022-01898-0

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