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# Topological surface currents accessed through reversible hydrogenation of the three-dimensional bulk

## Abstract

Hydrogen, the smallest and most abundant element in nature, can be efficiently incorporated within a solid and drastically modify its electronic and structural state. In most semiconductors interstitial hydrogen binds to defects and is known to be amphoteric, namely it can act either as a donor (H+) or an acceptor (H) of charge, nearly always counteracting the prevailing conductivity type. Here we demonstrate that hydrogenation resolves an outstanding challenge in chalcogenide classes of three-dimensional (3D) topological insulators and magnets — the control of intrinsic bulk conduction that denies access to quantum surface transport, imposing severe thickness limits on the bulk. With electrons donated by a reversible binding of H+ ions to Te(Se) chalcogens, carrier densities are reduced by over 1020cm−3, allowing tuning the Fermi level into the bulk bandgap to enter surface/edge current channels without altering carrier mobility or the bandstructure. The hydrogen-tuned topological nanostructures are stable at room temperature and tunable disregarding bulk size, opening a breadth of device platforms for harnessing emergent topological states.

## Introduction

The ability to control carrier density—a key parameter of the electronic state of condensed matter—is central to achieving access to the topologically protected surface states in three-dimensional (3D) topological materials (TIs) that ideally are insulating in the bulk1. In the absence of magnetic dopants, the 2D electronic surface states with Dirac-type (linear) energy-momentum dispersion1,2,3 are gapless and fully spin-polarized, with protection against backscattering by local disorder guaranteed by time-reversal symmetry. These important layered van der Waals (vdW) quantum materials have narrow (300 meV) bulk gaps and charge carriers donated by intrinsic lattice defects4. As a result, the conduction through the bulk and its intermixing with the surface channels is what largely denies direct access to the surface currents sought for the implementation in topological spintronics and fault-tolerant quantum computing5.

Recent realizations of a nontrivial quantum anomalous Hall (QAH) state, featuring dissipation-free chiral edge currents6, made it apparent that when long-range magnetism and band topology combine7 the problem of bulk conduction can be particularly acute. Magnetic dopants, by breaking time-reversal symmetry, gap out the Dirac surface channels8, and when the Fermi level is in the Dirac (mass) gap the QAH state is expected to emerge. However, in addition to magnetic moment, the dopants also donate charge. Indeed, QAH was first observed in heavily Cr-doped (Bi,Sb)2Te3 ultrathin films9 in which to minimize bulk conduction a non-stoichiometric alloying of the constituent elements was employed and the film thickness had to be precisely controlled. Moreover, doping disorder restricted QAH temperature to the mK range.

In a newly discovered important class of intrinsic topological magnets (ITM)10 the doping and alloying disorders are avoided because the magnetic dopants are arranged as an atomic layer in a layered vdW crystal structure. For example, the Mn-based ITM MnBi2Te4 consists of Te–Bi–Te–Mn–Te–Bi–Te septuple layers (SLs), separated by vdW gaps and coupled antiferromagnetically11. As a consequence, the anomalous Hall (near) quantization was observed at somewhat higher temperatures12. However, such materials show high bulk carrier densities (typically > 1020 cm−3)13,14, and observation of QAH required delicate tuning of charge density that was again only possible in ultrathin (3–5 nm) samples with odd number of SLs. In thicker (hundreds of nanometers) samples ferromagnetism and quantization could be achieved when SLs were separated by a topological spacer15 yet tuning to quantization of either ferromagnetic (FM) or antiferromagnetic (AFM) ITMs without imposing severe thickness constraints is a major obstacle to realizing novel topological states.

Here we demonstrate a remarkably efficient and facile way to reversibly tune bulk carrier densities by over  1020 cm−3 in different classes of layered TIs4 by using insertion and extraction of ionic hydrogen to achieve access to topological surface states. The source of H+ ions is a dilute aqueous hydrochloric acid (HCl) solution, which leaves the TI crystal structure as well as electronic bands intact and has an extra benefit of removing native surface oxide while passivating surfaces and preventing reoxidation under exposure to air. We show that H+ in TIs, by preferentially forming an H–Te(Se) moiety within vdW gaps, donates electrons to the system and moves Fermi level EF from the bulk valence (BVB) to bulk conduction (BCB) bands, crossing the bulk bandgap to display an ambipolar p- to n-type conductance conversion at the charge neutrality point. The process is fully reversible, as hydrogen-chalcogen moiety can be disassociated by a low-temperature annealing protocol under which hydrogen is easily removed. It is also multiply-cyclable and reproducible, thereby resolving one of the key limitations of magnetic and nonmagnetic TIs. In contrast with charge compensation by doping or alloying during growth14,16, the post-growth hydrogenation can tune EF to charge neutrality without altering the band structure and can be effective in single crystals and in nano-devices, where the evolution of resistance under hydrogenation is easily monitored over time.

## Results

### Reaching charge neutrality and beyond in Bi2Te3 by hydrogenation

The ultralight hydrogen diffuses rapidly and easily incorporates into many materials17, although it shows qualitatively different behavior in different hosts18. Widely practiced in technology to passivate Si dangling bonds or enhance catalytic activity19, hydrogenation is also known to modify both electronic and structural states20 in a variety of diverse materials systems21,22—it was found effective in turning graphene into graphane23, inducing new magnetic phases in complex perovskites24, and modulating insulator-to-metal transition in a correlated Mott oxide VO225. To ascertain the effects of hydrogen uptake on charge transport in the TIs we first chose well-characterized Bi2Te3 crystals with the conductivity flavor initially of a net acceptor type. The level of hydrogenation was controlled by timing the diffusion of H+ ions from a dilute HCl solution kept at room temperature (see Fig. 1a, b and “Methods”).

Our key and a most immediately notable result shown in Fig. 1 is a nearly two orders of magnitude increase in the low-temperature longitudinal resistance Rxx as a function of HCl exposure time to a maximum $${R}_{xx}^{\max }$$ and a subsequent decrease as the exposure time is prolonged (Fig. 1c). The resistance maximum $${R}_{xx}^{\max }$$ (conductance minimum) is at the charge-neutral point (CNP) where conduction is converted from p- to n-type, as determined from the corresponding Hall resistance (Fig. 1d). We surmise then that hydrogen, through the process of in-diffusion into the bulk (Supplementary Note 1), indeed donates electrons. This process is not self-limiting: at long (≥24 h) exposure times a decrease in Rxx on the deep n-side slows down yet continues. The observed ambipolar conduction, with well-distinguished p (hole) and n (electron) conduction regions, can be reproducibly reversed when hydrogen is removed by a low-temperature anneal (sketch in Fig. 1b) in the easily accessible range that depends on sample thickness. For the ~121-nm-thick Bi2Te3 crystal shown here the de-hydrogenation and a return from n-type across the CNP back to p-type is obtained within ~100 °C. Importantly, the carrier mobility during the entire process is not affected—e.g. in the sample in Fig. 1 it remains at 7000 cm2 V−1 s−1 (Supplementary Table 1).

After each annealing step, the system is room temperature stable and can be further finetuned by the conventional electrostatic gating. Figure 1e shows that once the carrier density is sufficiently reduced by H+, the vicinity of the CNP can be reproducibly explored by applying a gate voltage Vg. Rxx(Vg) is precisely reversible upon changing the direction of the Vg sweep—the absence of hysteresis is a clear indication that hydrogenation does not create surface traps26 and is consistent with hydrogen permeating the bulk. We emphasize that in thick (≥100 nm) materials, far away from the CNP where carrier densities are in the high ~1019 cm−3 range, the CNP can not be reached by gating within a practically accessible voltage sweep (Fig. 1f).

### Salient features of 2D transport in Bi2Te3 under hydrogen

The type conversion on hydrogenation and de-hydrogenation is clearly seen in the magnetic field dependence of Hall resistance Rxy (Fig. 2a), with Rxy flipping its slope dRxy/dH and Hall coefficient $${R}_{{{{{\rm{H}}}}}}=-\frac{1}{{n}_{b}e}$$ changing sign in the conversion region, where nb is the carrier density obtained from the linear part of the high-field slope of Rxy (see Supplementary Fig. 1). As we approach the CNP, weak antilocalization (WAL) quantum correction to ‘classical’ conductivity at low magnetic fields emerges from a parabolic (B2) background as a positive magnetoresistance cusp (Fig. 2b), characteristic of a TI27. The number nQ of quantum conduction channels contributing to WAL can be estimated from 2D localization theory28 $${{\Delta }}G(B)\simeq \alpha \frac{{e}^{2}}{2{\pi }^{2}\hslash }f(\frac{{B}_{\phi }}{B})$$, where ΔG(B) is the low-field quantum correction to 2D magnetoconductance, coefficient α = nQ/2 equals to 1/2 for a single 2D channel, f(x) ≡ lnx − ψ(1/2 + x), ψ is the digamma function, and field $${B}_{\phi }=\frac{\hslash }{4e{l}_{\phi }^{2}}$$ is related to the dephasing length lϕ of interfering electron paths. The fit to WAL conductance (see Fig. 2e and Supplementary Figs. 2 and 3) yields α 1.004 ± 0.005, corresponding to two 2D quantum channels we associate with top and bottom surfaces27. Figure 2c schematically depicts the Bi2Te3 band structure2 as the Fermi level EF moves from BVB to BCB (hydrogen in) and in reverse (hydrogen out). The 2D character of WAL cusp when EF is within the bulk gap is apparent in the scaling with the transverse component of magnetic field $${H}_{\perp }=H\cos \theta$$ (Fig. 2d and Supplementary Fig. 2), and in the characteristic 2D temperature dependence of $${l}_{\phi }\propto 1/\sqrt{T}$$ (Fig. 2f). The Drude-like B2 contribution to magnetoresistance is consistent with the anisotropy of bulk Bi2Te3 (Supplementary Fig. 4).

Near the CNP, where the net residual bulk carrier density is very low, Rxy displays a characteristic low-field ambipolar behavior (Supplementary Fig. 5a). The change in the net carrier density induced by hydrogenation is reflected in the Shubnikov-de Haas (SdH) quantum oscillations of Hall resistance at higher fields (Supplementary Fig. 5). An estimate of the Fermi surface size obtained from the change of the oscillation period in ∂ΔRxy/∂μ0H (Supplementary Fig. 5c, d) shows that the Fermi vector kF is much reduced after hydrogenation—near the CNP kF ≈ 0.014Å−1 and the corresponding surface carrier density n2D 6.3 × 1011 cm−2 is very low (see Supplementary Table 2). We note that the 2DEG states arising from the subsurface band-bending of bulk channels present just below the BCB (Fig. 2c and Supplementary Fig. 5b) may also contribute to the 2D WAL. A conventional methodology we use to estimate Berry phase φB = 2πβ from the SdH oscillations29 yields Berry factor β 0.5 near the CNP and after 5.8 hours of exposure to hydrogen. Thus, the topological π-Berry phase1 (see inset in Fig. 2f and discussion following Supplementary Fig. 6) appears robust under hydrogen and not measurably affected by 2DEG.

### Preferential location of hydrogen in the van der Waals gaps

Next we ask, where does hydrogen go? Our transport experiments demonstrate that in Bi2Te3 hydrogen donates electrons and stabilizes in its positive charge state as H+. To optimize its Coulomb interaction with the host electrons, it will tend to locate in the regions of higher electron charge density, i.e. in the vicinity of a more electronegative Te. To chase its physical presence we first utilize time-of-flight secondary ion mass spectrometry (ToF-SIMS), focusing on Te (Fig. 3a–d and Supplementary Fig. 7). A negative bias mass spectrum of secondary ions (see Methods) ejected from Bi2Te3 shows a cluster of peaks in the 120–130 amu (atomic mass unit) range (Fig. 3c) that belong to several naturally occurring isotopes of Te, see Supplementary Table 3. A closer look at the Te isotope cluster (Fig. 3d) clearly shows additional peaks that differ from each Te isotope by exactly Δamu = 1, consistent with each isotope binding with one hydrogen.

On a microscopic scale, we confirm the affinity between H and Te by x-ray photoelectron spectroscopy (XPS), see “Methods”. XPS spectra near the Bi 4f and Te 3d core levels show that the Bi core levels30 are unperturbed by hydrogen (Fig. 3e), while the spectral shapes of Te 3d peaks are quantifiably modified (Fig. 3f, g). The upshift Δ = 1 eV in binding energy due to [Te–H] moiety is easily distinguished from free hydrogen or surface oxidation, as seen, for example, during hydrogen electro-catalysis31, where Bi 4f spectral shapes are upshifted by ~2 eV and both Bi2O3 and TeO2 peaks are present. By contrast, XPS shows that HCl cleanly removes surface oxide, Cl is entirely absent, and annealing restores the original state (Supplementary Fig. 8 and Table 4). Importantly, the surface morphology is preserved, with RMS roughness of ≈ 0.2 nm (Fig. 3h and Supplementary Fig. 9).

The observed electron-donor action of hydrogen in a vdW TI through formation of hydrogen-chalcogen moiety is rationalized by the density functional theory (DFT) calculations (Supplementary Note 2 and Supplementary Figs. 1012). The DFT band structures of Bi2Te3 (Fig. 4a–c) show that after hydrogenation the Dirac bands are preserved while the Fermi level EF is upshifted into the BCB. This n-type doping is independent of whether H+ goes in interstitially or into the vdW gaps, however, the H–Te moiety appears most stable within the vdW gap (the formation energies are in line with XPS). The calculated local density of states (DOS) (Fig. 4d) highlights the shift of EF relative to the Dirac point (DP). It also anticipates the opposite doping action of Cl, which in our experiments is not detected (Supplementary Table 4). Bi2Te3 structure maintains charge balance within each quintuple layer (QL) of atoms Te(1)–Bi–Te(2)–Bi–Te(1), where the superscripts distinguish the inequivalent Te sites (see Supplementary Fig. 11a). The Te–Bi bonds are polar-covalent while only weak vdW type bonding exists between the neighboring Te(1)–Te(1) planes with relatively weak and highly polarizable bonds. The hydrogen prefers going to the region between these planes, while the crystal structure remains intact (Supplementary Fig. 13).

## Discussion

The Fermi level tuning by hydrogenation demonstrated here is very general, indeed it is remarkably effective in other p-type chalcogen-based TI. We have achieved the type conversion across the CNP in Se-containing materials, such as Bi2Te2Se (Supplementary Fig. 14) and Ca-doped Bi2Se3 (Supplementary Figs. 15 and 16). Our DFT calculations confirm that a stable [H–Se] moiety similarly acts to move the Fermi level towards the conduction bands (Supplementary Figs. 11 and 12).

The technique is also very powerful in magnetic TI, and particularly in a very promising ITM class. One example is the intrinsic FM MnBi2Te4/Bi2Te3 superlattice15 where initial bulk carrier density is in the 1020 cm−3 range, yet type conversion across the CNP by hydrogen is obtained (Supplementary Figs. 17 and 18). Hydrogenation can also deliver an essentially continuous EF tuning across the bulk gap of an intrinsic topological antiferromagnet, where the axion insulator behavior was very recently reported when the AFM ITM was made thin enough (~6 SLs or ~8 nm)32 to reduce the contribution from bulk conduction channels and to be able to deplete bulk carriers by electrostatic gating. Here we demonstrate in one exemplary AFM ITM that through hydrogen-tuning of EF we can turn its bulk into an insulating state sans voltage gating. Figure 4e shows how the longitudinal resistance Rxx(T) of a ten times thicker (80 nm) MnBi2−xSbxTe4 (x = 0.6) crystal continuously transforms under hydrogenation from a metallic-like into a strongly insulating-like—a feat not yet achieved by a step-wise Bi–Sb alloying13. Under hydrogen uptake the Néel temperature TN ~ 25K remains unchanged while the low-temperature Rxx(T) increases by about two orders of magnitude, reaching maximum value at the CNP (Fig. 4e, f and Supplementary Fig. 19). Once near the CNP, Rxx can be finetuned by gate voltage Vg (inset in Fig. 4f, g and Supplementary Fig. 20). The Hall resistance Rxy (Fig. 4g) at the CNP displays ambipolar behavior, akin to the one in Bi2Te3 (Fig. 1d). The field dependencies of Rxx(H) and Rxy(H) under hydrogenation are consistent with the results previously only obtained in a few SL thin layers under voltage gating12,32, also see Supplementary Fig. 19. Near the CNP the magnetoresistance Rxx(H) sharply changes at two characteristic fields: H1, above which the spin order is driven into a canted AFM state13,14, and H2 at which all spins align in a FM state (Fig. 4h). Below H1 Hall resistance Rxy(H) exhibits a distinct plateau (where some of the SLs align with field) and a ‘zero-plateau’ (Fig. 4i) ubiquitous to AFM. Such plateaus — previously seen only in ultrathin exfoliated flakes12,14 where net magnetization M is set by the odd (FM) or even (AFM) number of SLs — are a manifestation of sensitivity of surface states to M. This is also consistent with the observed nearly-null Rxy(H = 0) vs.Vg, see Supplementary Fig. 20. Our key finding here is that by depleting free bulk carriers by hydrogenation we can access surface currents in bulk samples without modifying the band structure. This is in contrast to Bi-Sb alloying where the band structure is altered by addition of Sb and a topological transformation from an ITM to Weyl semimetal may occur14. And while the optimal ITM band structure for achieving high-temperature QAH is yet to be realized33, the hydrogenation technique provides a remarkably effective tool for tuning EF into the Dirac gap.

Finally, we remark that a paucity of bulk-insulating TIs impedes the search for emergent quantum phenomena, with the prospect for real-world topological electronics still remaining far off. Hydrogen-tunability of high bulk carrier densities expands the availability of robust and easily accessible device platforms for harnessing topological phases with stunning macroscopic manifestations, such as dissipationless edge transport of charge, axion electrodynamics34 in topological magnets, and proximal topological superconductivity1 for quantum computing.

## Methods

### Crystal growth and structural characterization

The standard Bridgman-Stockbarger technique employing a vertical pull through the temperature gradient was used to grow single crystals of Bi2Te3, and Ca(0.09%)-doped Bi2Se3, and Bi2Te3Se27. X-ray diffraction of crystals was performed in a Panalytical diffractometer using Cu Ka (λ = 1.5405 Å) line from Philips high intensity ceramic sealed tube (3 kW) X-ray source with a Soller slit (0.04 rad) incident and diffracted beam optics. MnBi2Te4/Bi2Te3 crystals were grown by the vertical Bridgman method following the two-step technique15. In the first step, ground (20–100 mesh) high-purity (99.999%) bismuth (Bi), tellurium (Te) and manganese (Mn) were weighted according to the formula MnxBi2−xTe3 and loaded into the double-wall quartz ampules to avoid depressurization during the cooling process. The ampules were evacuated to 10−6 Torr. sealed, and loaded into a vertical furnace, and heated to 900 K, where they remained for 48 hr to achieve better homogenization. Afterwards, the furnace was cooled down to In the second step, the synthesized material was ground again, loaded into the ampules for the Bridgman growth, evacuated to 10−6 Torr, and sealed. To create the seed crystal, ampules with a small diameter (1.5–2.0 mm) along the tip in the lower end were used. Two ingots obtained from the first (synthesis) step were used to fill the Bridgman growth ampule. To obtain a homogenized solution, the material was heated to 1073 K and rotated along the ampule axis for 5 d in the hot part of the furnace. The samples were then moved down from the hot part at the speed of 2 mm/day. The temperature in the lower part of the furnace was kept at 873 K. This procedure resulted in n-type superlattice crystals with average sizes of 50-mm length and 14-mm diameter.

The samples for transmission electron microscopy (TEM) investigations (see Supplementary Figs. 12 and 13) were cut along the c-axis, in the [1120] orientation, using a focused ion beam (FIB) method. TEM characterization was carried out in a FEI Talos F200X microscope operated at 200 kV. Structural observations were performed in scanning transmission electron microscope (STEM) mode using a high-angle annular dark field (HAADF) imaging. Energy dispersive X-ray spectroscopy (EDX) using a Super-X system with four silicon drift detectors (SDDs) was applied to detection of differences in local chemical composition.

Crystals of MnBi2−xSbxTe4 (x = 0.6) were grown out of a Bi(Sb)–Te flux13,35. Mixtures of Mn (Alfa Aesar, 99.99%), Bi and Sb pieces (Alfa Aesar, 99.999%), and Te shot (Alfa Aesar, 99.9999%) in the molar ratio of 1:10:16 (MnTe:Mn2Te3 = 1:5) were placed in a 2 ml alumina growth crucible and heated to 900 °C and held for 12 h. After slowly cooling across a ≈10 degree window below 600 °C in two weeks, the excess flux was removed by centrifugation above the melting temperature of (Bi,Sb)2Te3 (>585 °C). Crystals produced by this flux method were typically few mm on a side and often grew in thick, block-like forms with thicknesses up to 2 mm, but are easily delaminated.

### Hydrogenation and hydrogen detection

Hydrogenation of already-fabricated devices and single crystals was performed by submerging them in a dilute (0.5M) HCl + H2O = H+(H2O) + Cl solution at room temperature for a predetermined periods of time, then submerged and rinsed with deionized water and dried with N2. The diffusion of hydrogen H+ from the solution was controlled by the submerging time. Hydrogen was removed from within the samples by vacuum anneals in the 60–100 °C range. The rate of this process is prescribed by the annealing temperature and the thickness of the crystal—at higher temperature and/or for thinner crystals the diffusion rate of hydrogen to the surfaces is faster (see Supplementary Note 1).

### Time-of-flight secondary ion mass spectrometry (ToF-SIMS) and X-ray photoelectron spectroscopy (XPS)

The samples before and after hydrogenation were characterized with TOF-SIMS and XPS. Our hydrogenated samples are stable in air during the routine 30–40 min air exposure during sample handling during the process. In the TOF-SIMS sample preparation and loading steps, after hydrogenation samples were DI water rinsed, dried, but kept in air for 1–2 h before they were loaded into the vacuum chamber. The HCl does remove the oxide (as shown in Supplementary Fig. 8) but the surface may oxidize again after hours of exposure to air. The Physical Electronics nano-TOF TOF-SIMS was configured with a 20 kV Ar2500+ gas cluster ion gun for sputtering and 30 kV LMIG Bi+ analysis ion gun. In mass spectrum acquisition mode, the TOF-SIMS analysis ion gun was set in high-current bunched mode (Bi at 25 keV ion energy and 100 ns pulse duration). The TOF-SIMS data were acquired at a base pressure of ~10−10 Torr. XPS measurements were performed in Physical Electronics VersaProbe II XPS with a Kα Al x-ray source (energy 1486.6 eV) and a hemispherical electron energy analyzer (pass energy 20 eV). The XPS energy-scale calibration was made with Bi 4f5/2 (162.5 eV), 4f7/2 (157.1 eV), Ag 3d5/2 (368.2 eV) and C 1s (284.8 eV) when available. PHI MutiPak software is used for XPS data reduction.

### Transport measurements

Transport measurements were performed in a 14 Tesla Quantum Design Physical property measurement system (PPMS) in 1 Torr (at low temperature) of He gas on many samples, each subjected to the same annealing protocol. The samples were annealed in situ starting from 330 K to 400 K. The annealing temperature ramp rate was 7 K per minute with the annealing time typically ~1 h. For Ta > 400 K, samples were annealed ex situ in a vacuum furnace. Crystals were mechanically exfoliated onto 300 nm SiO2/Si+++ wafers, typically resulting in micron-size crystals with thicknesses less than ~400nm, as determined by the atomic force microscope (AFM). Electrical contacts in the van der Pauw (vdP) configuration36 were photo-lithographically patterned and a sputtered Au metallurgy was used (Fig. 2c). Conformal Au coating amply covered side surfaces in order to make good contacts to top and bottom surfaces. The VdP dc measurements were carried out using a custom-configured electronic system in which four measurement configurations are switched by a Keithley scanner, with the current direction reversal employed for each measurement to minimize thermal emf. Sheet resistances in data analysis were calculated using the vdP formulae.

## Data availability

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

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## Acknowledgements

We wish to thank Tai-De Li for the technical assistance with the surface analytical tools at the Surface Science Facility of CUNY Advanced Science Research Center (ASRC). Jim Hone’s comments are much appreciated. This work was supported by the NSF grants DMR-2011738 and HRD-2112550. Computational support was provided by Virginia Tech ARC and San Diego Supercomputer Center (SDSC) under DMR-060009N.

## Author information

Authors

### Contributions

Experiments were designed by H.D. and L.K.-E. Materials were grown by H.D. and J.Y., and their modification and characterization, device fabrication and transport measurements were performed by H.D., A.L., E.B., and L.Z. HAADF-STEM and EDX elemental imaging was performed by K.S. DFT band structures and electronic density of states (DOS) under hydrogenation were calculated by K.P.. Data analysis was done by H.D. and L.K.-E. L.K.-E. wrote the manuscript with the input from H.D.

### Corresponding author

Correspondence to Lia Krusin-Elbaum.

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### Competing interests

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Deng, H., Zhao, L., Park, K. et al. Topological surface currents accessed through reversible hydrogenation of the three-dimensional bulk. Nat Commun 13, 2308 (2022). https://doi.org/10.1038/s41467-022-29957-3

• Accepted:

• Published:

• DOI: https://doi.org/10.1038/s41467-022-29957-3