Magnetic brightening and nanoscale imaging of spin-polarized helical edge modes in ZrTe₅

Abstract

Efficient charge transport remains a fundamental challenge for nanoelectronic devices, as their performance is constrained by high dissipation and the impedance mismatch between high-frequency signal sources and nanoscale circuit interfaces. Although topologically protected helical edge modes offer a dissipationless and backscattering-resilient alternative, achieving nanoscale control over these modes requires direct visualization of their spatial electrodynamics, especially under high-frequency operation. Here, by utilizing cryogenic magneto-infrared scattering-type scanning near-field optical microscopy (cm-IR-sSNOM), we image spin-polarized helical edge channels in ZrTe₅ at the nanoscale, revealing magnetic-field-induced brightening as a high-frequency electrodynamic signature of robust topological edge modes. Operating at 1.8 K and under a magnetic field of up to 5 T, we observe the emergence of edge-state polarizability at infrared frequencies that is notably resilient to the magnetic gaps that typically quench d.c. and microwave edge transport. Our results reveal a topological ‘two-lane’ spatial reorganization in which an external magnetic field induces a spin-population imbalance between counterpropagating edge modes. Favoured helical branches are confined against physical boundaries to activate a net infrared near-field contrast. This electrodynamic response scales linearly with the number of atomic layers, which confirms that individual layers in ZrTe₅ preserve their discrete quantum spin Hall identities. These findings may be useful for developing topological spintronic devices, as the magnetic infrared tunability of helical edge channels provides a pathway for low-loss nanoscale interconnects and high-speed information processing.

Infrared nanoscopy resolves helical edge states in ZrTe₅, revealing magnetic-field-induced high-frequency transport channels.

Main

A defining feature of quantum spin Hall (QSH) insulators is the presence of two counterpropagating edge modes with opposite spin orientations^1,2. The edge-state electrons exhibit dissipationless transport characterized by a density decay length ξ ≈ 6 nm (ref. ³). The intrinsic spin-momentum locking of a QSH insulator is protected by time-reversal symmetry, irrespective of inversion symmetry. This topological protection prevents backscattering and effectively eliminates impedance mismatches in nanoelectronic circuits. Topological edge signatures typically attenuate under high magnetic fields at d.c. and microwave frequencies. This suppression arises from magnetic-field-induced gap opening and interlayer hybridization, which—for layered materials—compromises the discrete QSH identity of the individual layers^4–6. A strategy for overcoming magnetic quenching is to drive the conduction current at infrared (IR) frequencies greater than the hybridization gap energy, where the high-frequency transport regime remains dominated by the intrinsic signatures of the helical edge manifold.

A primary candidate for exploring the helical edge manifold is the Van der waals material zirconium pentatelluride (ZrTe₅), because it occupies a unique position at the boundary between strong and weak topological insulating phases^7–9. Scanning tunnelling microscopy (STM) has previously probed the distinct, spin-polarized density of states localized along crystal step edges and domain boundaries in ZrTe₅ (refs. ^3,10). These states exhibit distinct tunability under external magnetic fields. For example, monolayer and few-stacking-layer ZrTe₅ host QSH characteristics, which confirms the proximity of the bulk bandgap to the conducting edges^3,10. These studies also show the evolution of topological edge states with field-induced spin splitting^{5,7,8,11–13}. Notably, it is expected that the high-energy states in ZrTe₅ will retain their topological robustness even under substantial magnetic fields, owing to the strong spin–orbit coupling that remains the dominant energy scale over the magnetic hybridization gap energy (~5–10 meV). Although STM provides a robust mapping of the equilibrium spin-split local density of states in ZrTe₅, it cannot excite the helical edge modes and resolve their high-frequency electrodynamic response or directional selectivity between counterpropagating channels. The lack of techniques that can directly image these helical electrodynamics—specifically under the simultaneous conditions of tesla-scale magnetic fields and cryogenic temperatures at the nanoscale—leaves a critical gap in the ability to resolve and manipulate topologically protected helical edge manifolds.

In this Article, we demonstrate IR nano-imaging of spin-polarized helical edge modes down to 1.8 K and show the emergence of magnetic brightening in ZrTe₅. External magnetic fields of up to 4 T act as a symmetry-breaking trigger. They induce a two-lane spatial reorganization of the helical edge manifold and activate a net IR near-field response that bypasses the low-energy magnetic gaps. By resolving the near-linear scaling of this edge signal with the number of atomic layers, we provide compelling evidence to show that individual layers in ZrTe₅ maintain their discrete two-dimensional QSH identities. All these electrodynamic signatures are encoded in the phase-sensitive, complex near-field response, because our technique directly probes the local IR polarizability and dynamic screening of the spin-polarized helical manifold.

IR nano-imaging of the helical manifold

Cryogenic magneto-IR/terahertz scattering-type scanning near-field optical microscopy (cm-IR/THz-sSNOM) has recently been demonstrated at sub-2-K temperatures and tesla magnetic fields^14–16. As illustrated in Fig. 1a, the cm-IR-sSNOM approach enables the measurement of phase-sensitive scattered electric fields governed by the local complex optical conductivity. It provides the nanometre spatial resolution required to resolve transport-capable helical edges (Fig. 1b) via the near-field IR responses of the field-induced spin-split states (Methods). Figure 1c,d illustrates the magnetic brightening proximal to step edges and domain walls in ZrTe₅. This phenomenon arises from an asymmetric electrodynamic response driven by the spin-population imbalance within the helical edge manifold.

Fig. 1. Cryogenic magneto-IR nano-imaging of spin-polarized edge states at crystal strip domains in ZrTe₅.

a, Representative schematic of an AFM probe scattering IR near-field signals above a ZrTe₅ sample, operated at 1.8 K and up to 5 T. When a finite magnetic field is applied, the spin degeneracy of the edge Dirac bands is lifted, resulting in a small magnetic gap and a spin imbalance at the Fermi energy E_F, as illustrated on the right. b, A magnetic field (B, blue arrow) is applied perpendicular to the ZrTe₅ sample surface along the crystallographic b axis, shown here for a single step edge. c, Schematic of step edges formed by stacking a few single layers. d, Schematics of domain walls resulting from variations in the structural stacking or from crystalline facets. The helical edge manifold manifests as a localized electrodynamic response whose directionality is governed by the boundary geometry. Although step edges (c) exhibit a unidirectional response, domain walls (d) host counterpropagating helical modes on opposite sides of the boundary. e–g, Illustration of the real-space distribution of spin-polarized, counterpropagating edge modes at magnetic fields B = 0 (e), an intermediate field (f) and a high field (g), which highlights the evolution of edge-state configurations with the magnetic field. As the field increases, the spin-up helical edge state (orange solid line) becomes increasingly confined to the step-edge boundary, whereas the spin-down counterpart (red dashed line) progressively spreads towards the inner bulk region³.

At zero magnetic field, the helical edge manifold consists of spatially overlapping, counterpropagating modes with opposite momenta (k and −k) and spins (Fig. 1e). Under the driving laser field and induced tip dipole, these degenerate helical branches exhibit out-of-phase electrodynamic responses (π phase difference), leading to near-complete destructive interference of the local polarizable responses. The application of an external magnetic field (B) along the crystallographic b axis (Fig. 1b) triggers symmetry breaking within the helical edge manifold. Although an applied field of a few teslas is perturbative relative to the topological field of tens of teslas in the QSH system (Methods), it is sufficient to lift the spin degeneracy near E_F (Fig. 1a), which triggers a two-lane spatial reorganization of the edge modes¹⁷. As shown for intermediate (Fig. 1f) and high (Fig. 1g) field strengths, this field-induced imbalance in the spin population of the counterpropagating branches establishes a ‘favoured’ branch (orange solid line) that is tightly confined against the boundary and an ‘unfavoured’ branch (red dashed line) that smears towards the bulk, effectively breaking the spatial degeneracy of the edge states. This disruption of the zero-field helical balance suppresses the destructive interference that otherwise masks the edge electrodynamic response, thereby activating the net IR near-field contrast at both step edges (Fig. 1c) and domain walls (Fig. 1d), thus providing a robust high-frequency signature of the underlying topologically protected helical channels. Notably, the domain walls (Fig. 1d) promote the coupling of the tip to counterpropagating helical edge channels on both sides of the wedge, which reverses the near-field electrodynamic response owing to an inherent asymmetric tip–sample interaction. This characteristic reversal, alongside the magnetic brightening and the spatial narrowing of the helical modes, can be captured by the cm-IR-sSNOM signal.

Our cm-IR-sSNOM operates at 1.8 K and in magnetic fields up to 5 T (Methods)^14,15. In this study, we shine mid-IR fields (~110–116 meV) onto a metallic-coated atomic force microscope (AFM) tip, which serves as an antenna to focus the incident light and amplify the near-field scattering^{13,14,18–32}. Phase-sensitive signals (S_nΩ) are extracted via quasi-heterodyne detection by interfering the complex scattered near-field $E_{\mathrm{NF}}^{\left(n\right)}$ with a reference beam (Methods). The complex scattered field at frequency Ω is demodulated at the nth harmonic of the tip-tapping frequency (n = 3 in our study, or S₃) to suppress background far-field effects. The inherent ~30° tilt of the probe—complemented by the directional asymmetry of the probe–cantilever assembly—breaks the C₂ rotational symmetry of the near-field interaction and, thus, achieves directional selectivity.

Magnetic brightening in layered step edges

Figure 2 presents typical near-field images acquired at various magnetic fields. The cm-IR-sSNOM set-up was cooled to a base temperature of 1.8 K. We focus on a two-step ‘staircase’ structure consisting of the typical stacking edges of ZrTe₅ layers. The AFM topography (Fig. 2a) reveals step heights of approximately 9 nm and 5 nm, from left to right, corresponding to stacking of 11 and 6 atomic layers, respectively. The Sobel gradient in the scanning direction of the region of interest (Fig. 2b) highlights the two distinct step-edge boundaries. Interestingly, the IR near-field images reveal a pronounced magnetic-field-induced edge-brightening effect, as illustrated in Fig. 1c, which was consistently observed at two probe wavelengths. Figure 2c–e shows the S₃ cm-IR-sSNOM images at 0 T, 3 T and 4 T, respectively, acquired at an excitation wavelength of 10.652 μm (116.39 meV). Figure 2f–h presents the corresponding cm-IR-sSNOM images at a different excitation wavelength of 11.262 μm (110.09 meV), which exhibits the same magnetic-field dependence. The emergence of the sharply localized near-field signal is correlated with the stacking-layer boundaries shown in Fig. 2a,b. In particular, increasing the magnetic field markedly enhanced the edge signals to form well-defined conducting edge channels visible in the near-field images. From left to right, two distinct edge enhancements are observed, with the higher step edge (left) showing a stronger response than the lower step edge (right). The magnetic brightening of the edge channels is further detailed in Fig. 2i–k as line cuts of the cm-IR-sSNOM images, taken along the grey dashed line in Fig. 2c, at 116.39 meV (red) and 110.09 meV (blue) for 0 T, 3 T and 4 T, respectively. At 0 T (Fig. 2i), the line cut shows only a slight contrast at positions corresponding to the two step-edge features in the AFM topography line cut (grey). With increasing magnetic field (Fig. 2j,k), sharp peaks clearly emerged, indicating the tip-coupling with the helical edge modes with strong near-field contrast. These results are consistent with the B-field-induced spin-population imbalance that manifests as a net IR electrodynamic response at the step edges (Fig. 1c).

Fig. 2. Magnetic brightening revealed by near-field signals acquired at 1.8 K under various magnetic fields in a representative layered region of ZrTe₅.

a, AFM topography featuring two step edges. b, Horizontal Sobel gradient in the AFM image showing the sharp sloping boundaries. c–e, cm-IR-sSNOM images taken at 10.652 μm (116.39 meV) for 0 T (c), 3 T (d) and 4 T (e). f–h, cm-IR-sSNOM images taken at 11.262 μm (110.09 meV) for 0 T (f), 3 T (g) and 4 T (h). i–k, Line cuts of AFM topography (grey) and SNOM images at 116.39 meV (red) and 110.09 mev (blue) across the two step edges with heights of approximately 5 nm and 9 nm for 0 T (i), 3 T (j) and 4 T (k), at the grey dashed line shown in c. Max, maximum; Min, minimum.

Contrast reversal in ZrTe₅ topological domain walls

Another feature of the field-driven spin-population imbalance is the emergence of spatially separated, counterpropagating helical edge modes on each side of the domain wall (Fig. 1d). To observe this behaviour, we identified two distinct layers of ZrTe₅ separated by a domain boundary using the AFM topography (Fig. 3a) and the Sobel gradient (Fig. 3b). A three-dimensional topographic view of this location (Fig. 3c) highlights three distinct structures, marked by red dashed lines across the ‘hill’. IR near-field images acquired under various magnetic fields at 60 K show a strong contrast at these topographic edges with distinct magnetic-field dependence. Figure 3d–g presents the S₃ cm-IR-sSNOM images at 0 T, 2 T, 3 T and 4 T, respectively. These exhibit magnetic brightening with opposite signal change. Like the step edges in Fig. 2c,f,i, the 0-T sSNOM image in Fig. 3d shows only a slight contrast at positions corresponding to topographic features. As the magnetic field was increased (Fig. 3e–g), the sharp near-field edge signals clearly emerged and became increasingly pronounced as the magnetic field rose, with opposite changes on the left (dark) and right (bright) sides of the hill. This asymmetric near-field scattering is fully consistent with counterpropagating IR edge modes on opposite sides of the domain walls, as illustrated in Fig. 1d, which arise from the field-induced net a.c. polarizability. The phase-sensitive near-field signal resolves the directional coupling between our asymmetric tip dipole and the magnetically polarized helical manifold, which manifests as a field-induced enhancement or suppression of the signal on opposing sides.

Fig. 3. Near-field images acquired across a sharp domain boundary in ZrTe₅ at 60 K under various magnetic fields.

a, AFM topography of the sample surface. b, Horizontal Sobel gradient in the AFM image highlighting two flat plateaux separated by sloped regions that converge at a sharp domain boundary. c, Three-dimensional representation of the AFM topography. Red dashed lines indicate regions of interest and mark the height variations of key surface features. d–g, S₃ SNOM images acquired at 10.652 μm (116.39 meV) under magnetic fields of 0 T (d), 2 T (e), 3 T (f) and 4 T (g). h–k, Line profiles of AFM topography (black) and SNOM signal (red) corresponding to 0 T (h), 2 T (i), 3 T (j) and 4 T (k), taken along the black dashed line in d.

To highlight the magnetic-field-induced edge signals, Fig. 3h–k present line cuts across the domain boundary, which were taken along the black dashed line in Fig. 3d. The near-field signal line cuts (red) exhibit an ‘inductive’ line shape, with both negative and positive peaks. These are overlaid on the AFM topography line cuts (black). Each trace was normalized by dividing by its overall mean, so the plotted values represent deviations from this mean. The primary peak (strongest response) increased by 6%, 25%, 35% and 48% from the mean for 0 T, 2 T, 3 T and 4 T, respectively. A secondary, less-bright peak followed the jagged boundary between the intermediate step and the lower plateau, increasing by 3%, 10%, 15% and 20% for the same fields. On the opposite (left) side of the boundary, the contrast was inverted, with decreases of −5%, −10%, −22% and −28% for 0 T, 2 T, 3 T and 4 T, respectively.

Figure 4a summarizes these average positive (negative) deviations along the edge boundaries. Near-field amplitudes from the right (red) and left (blue) sides of the boundary are qualitatively consistent with the trends for average QSH edge-state spin-dependent energy splitting previously resolved in STM measurements³. The good agreement indicates that the energy splitting associated with the one-dimensional QSH effect has a common origin in both datasets. Note that the near-field signal contrast was minimal at low fields but rose sharply above ~1.5–2 T, which coincides with the system entering the three-dimensional quantum Hall effect regime, where bulk transport is quenched and edge-dominated transport becomes the primary contribution to the local dielectric response.

Fig. 4. Magnetic-field and layer-number dependence of near-field edge-mode signals in ZrTe₅ and reference gold films.

a, Near-field amplitudes from the right (red) and left (blue) sides of the boundary are plotted as the maximum deviation from the local mean. These results are qualitatively consistent with the trends of spin splitting previously resolved in STM measurements³. b,c, AFM topography (b) and sSNOM s₃ measurements acquired at 0 T and 3 T (c) on a 160-nm gold film deposited over ZrTe₅ for comparison. d, sSNOM (s₃) line scans at 3 T and 4 T, shown alongside the AFM topography line scan (black dashed line) across two step edges. Inset: three-dimensional rendering of the AFM topography illustrating the measured region. Note that red dashed lines indicate step heights of 11 and 6 layers and highlight the height variations of key surface features. 6L, six layers; 11L, 11 layers.

We performed cm-IR-sSNOM scans of a 160-nm gold film as a control experiment. The gold film was deposited on a ZrTe₅ substrate cut from the same crystal used in this study. The gold topography, shown in Fig. 4b, closely follows the step structure of the underlying ZrTe₅. Magnetic field scans at 0 T and 3 T (Fig. 4c) revealed little to no meaningful change across the topographic steps like those seen in bare ZrTe₅.

Two-lane edge reorganization and layer-additive conductivity

In the weak topological insulator phase, ZrTe₅ acts as a stack of nearly decoupled QSH layers, each contributing a pair of spin-momentum-locked edge channels. To confirm this physical picture, we analysed the magnetic brightening across step edges of various thicknesses (Fig. 4d). By measuring the AFM topographic heights (Fig. 4d, inset), we identified two distinct boundaries of ~9 nm and ~5 nm, corresponding to approximately 11 and 6 atomic layers, respectively. At high magnetic fields (3–4 T), for which the degeneracy of counterpropagating modes was mostly lifted, the near-field signal amplitude scaled linearly with the layer count. That is, the ratio $S_3^{6\mathrm{L}}/S_3^{11\mathrm{L}}$ closely matched the ratio of the numbers of layers, 6/11, indicating that each individual layer contributed additively to the total edge conductivity. This linear scaling provides evidence that individual layers preserve their discrete QSH identities despite being stacked in a bulk crystal. These results corroborate previous STM observations¹⁰ and our own simulations (Fig. 5) and confirm that the edge states remain robust and additive along the out-of-plane direction. The linear scaling is facilitated by the low carrier concentration and the resulting long screening length of ~50 nm (Methods).

Fig. 5. Theoretical understanding of the band structure of ZrTe₅ in the context of a QSH insulator for different edge terminations and numbers of layers.

a,b, Illustration of a single step edge for one layer (a) and two layers (b). The schematics highlight the different edge terminations: telluride-terminated T-Te₂-zigzag (left) and zirconium-terminated T-ZrTe₃ (right). The Zr and Te atoms are shown in green and gold, respectively. c,d, Band-structure calculations for semi-infinite edge terminations for one layer (c) and two layers (d) of ZrTe₅. The left (right) panels are for the T-Te₂-zigzag (T-ZrTe₃) and show the edge Dirac crossings. e,f, Calculated band structure for ribbon configurations with both types of terminations as colour-coded for T-Te₂-zigzag (blue) and T-ZrTe₃ (red) for one layer (e) and two (f) layers. The calculations use thicker ribbons (6 and 11 layers) to match the experimental configuration shown in Fig. 4. The grey bands are the projected bulk bands.

The line profiles in Fig. 4d provide a direct spatial visualization of the magnetically separated and topologically confined edge modes. The apparent confinement width of ~100 nm is governed by the combined effects of topological localization and instrumental convolution. Although STM measurements near monolayer steps in ZrTe₅ reveal an electronic ‘core’ width of only ~6 nm (ref. ¹⁰), which reflects the effective topological confinement, the S₃ cm-IR-sSNOM response is sensitive to the longer-range decay of the edge electromagnetic fields, which are characterized by a decay length of ~70–100 nm, as well as to the tip convolution of ~60–90 nm (Methods). Because these two length scales are comparable, they jointly determine the observed edge-mode width of ~100 nm. In addition, although alternative mechanisms, such as magnetic-field-induced trivial carrier redistribution, could, in principle, contribute, the observed emergence of magnetic brightening, near-linear layer scaling and magnetic contrast reversal, together with the established Berry-curvature-related anomalous magneto-transport³³ and optical⁸ responses in ZrTe₅, collectively provide a body of evidence that is more naturally consistent with the topological two-lane picture, elaborated in Fig. 4d.

The external magnetic field modulates the spin-split edge modes through two primary mechanisms: the activation of magnetic brightening via the spin-population imbalance and the spatial confinement of the edge wavefunctions. To further understand the magnetic influence, we considered both the semiclassical cyclotron radius, r_c = E_F/(eBv_F), and the quantum magnetic length, $l_{\mathrm{B}}=\sqrt{\hslash /eB}$, where ℏ is the reduced Planck constant and ν_F is the Fermi velocity. For our sample parameters, both scales are of the order of 10 nm at 3–4 T. That is, they are notably smaller than the near-field width observed. Therefore, the resulting near-field profiles in Fig. 4d exhibit a modest ~10% narrowing when the field was increased from 3 T (blue) to 4 T (green). In addition, the two-lane reorganization dictates that the favoured chiral mode is compressed tightly against the hard vacuum boundary of the step riser. Consequently, the S₃ cm-IR-sSNOM signal peaks in Fig. 4d represent the maximal coupling to the magnetically compressed topological mode residing along the hard vacuum boundary of the step riser, which was broadened and spatially convolved by the edge electromagnetic-field decay and the tip geometry: (1) The peak sSNOM signal was centred on the step riser, rather than the upper plateau in Fig. 1e–g, and it was shifted towards the lower terrace. (2) The mode exhibited a pronounced spatial squeezing asymmetry, being tightly compressed against the hard vacuum boundary (right) while maintaining an evanescent tail that extended into the bulk crystal (left).

To understand why magnetic-field-induced gaps do not substantially hybridize individual-layer edge states at the IR energy scale, we calculated the band structure of ZrTe₅ in the context of QSH edge states. Conventional discussions of topological insulators typically focus on a single, isolated layer, which on its own exhibits the QSH effect. However, in realistic experiments of step edges in the samples studied, a few layers can stack to produce atomically sharp edges spanning ~10 nm in height, like the step edges (Fig. 2). Such stacked layers may interact, such that they modify the single-layer band structure and give rise to a more complex system. Figure 5a illustrates a single layer of ZrTe₅ with a truncated lattice. It has a sharp edge along the (001) direction where the crystal would most probably cleave, namely, at the telluride atom. This is shown for monolayer ZrTe₅ for two distinct edge terminations: telluride-terminated T-Te₂-zigzag (left) and zirconium-terminated T-ZrTe₃ (right). In this simple single-layer case, our band-structure calculations (Fig. 5c) revealed the emergence of the characteristic conical dispersion with a Dirac point at both edges, which hosts a pair of counterpropagating helical edge states^3,10,11.

We then extend the single-layer case to several layers terminating at the same lattice plane, which gives rise to the experimentally observed atomically sharp, multi-layer edges. Figure 5b,d shows a two-layer edge of ZrTe₅ that is analogous to the single-layer configuration. Interestingly, at this two-layer edge, the conical band of the first layer remains largely intact. A second conical band that is slightly shifted in energy emerged and contributed its own pair of helical edge states. This behaviour can be attributed to the weak van der Waals coupling between adjacent layers, which distorted the individual band structures and produced overlapping but shifted conical edge dispersions. Such weak interlayer coupling supports the notion of a robust edge state persisting across the ZrTe₅ terrace, as reported in previous STM studies^3,10,11.

A key feature of the ZrTe₅ system is the preservation of spin-momentum-locked helical edge states, whose number doubles in the two-layer case, thereby increasing the available spin channels within the step-edge region. For a step edge with more layers, as observed in Fig. 4, we used the ribbon configuration with both Te₂-zigzag and ZrTe₃ terminations present in the large supercell¹¹, such that the same calculation gives the edge-state dispersion of both terminations, as plotted in Fig. 5e,f for 6 and 11 layers, respectively, with Te₂-zigzag edge states shown in blue and ZrTe₃ in red (Methods). These two types of edge-state calculations are complementary to each other, as shown by the good agreement between Fig. 5c,d and Fig. 5e,f. Importantly, the number of edge states in Fig. 5e,f increased proportionally with the increase in the number of layers from 6 to 11. The increased number of spin-momentum-locked conducting channels explains our experimentally observed scaling behaviour of the near-field signals in Fig. 4d.

Conclusions

We have demonstrated the robustness of helical edge transport in ZrTe₅ and shown that it can be magnetically ‘switched on’ at IR frequencies. This activation occurs because a spin-population imbalance is induced. This imbalance yields a net IR polarizability, which is absent in the compensated zero-field state, while preserving the discrete QSH identities of the individual layers. Finally, together with recent advances in ultrafast field-driven transport³⁴ and supercurrent acceleration^35,36, our tunable, scattering-resilient edge signatures establish a potential pathway towards high-speed topological devices at petahertz rates.

Methods

Sample preparation and characterizations

ZrTe₅ single crystal was grown by flux growth method using Te as flux³³ (Supplementary Information). The basic properties of ZrTe₅ single crystals have been extensively studied using both THz spectroscopy^7,8 and magneto-IR spectroscopy⁹. The samples studied have a Fermi energy of E_F ≈ 10 meV, a band gap of  ≈ 10 meV, and a Fermi velocity v_F ~ 5 × 10⁵ m s⁻¹. The absorption spectra exhibit a linear dependence in the energy range of 20–130 meV, encompassing the probe energies of cm-IR-sSNOMs.

The ZrTe₅ crystal resides in a critical state near the phase boundary between strong and weak topological insulators (TIs)^37–39, rendering it highly sensitive to minute external stimuli such as strain and magnetic fields^13,40. This material with van der Waals layers stacked along the b-axis manifests notably anisotropic strip features, characterized largely by step edges (Fig. 1a) and domain walls (Fig. 1b) aligned along the a-axis. A scanning electron microscopy (SEM) image of locations representative of the AFM and SNOM images shown in the main text is included in Supplementary Information. Previous scanning tunneling microscopy (STM) studies have unveiled the proximity of the bulk band gap to step edges, alongside the ubiquitous presence of 1D topological edge states^3,10. These distinctive traits facilitate the formation of looped electron pathways that encircle the outer edges of ZrTe₅ strips, enabling the realization of QSH effect phenomena.

Experimental method: cm-IR-sSNOMs

Our broadband cm-IR-sSNOM (supplementary Fig. 1) is based on a tapping-mode atomic force microscope (AFM) inside a top-loading 5-Tesla split-pair magnet cryostat with a base temperature of 1.8 K through a helium exchange gas system. The AFM is a fiber-based cantilever system designed for applications at low temperatures and in high magnetic fields. In operation, we focus electromagnetic fields to an AFM metallic coated probe that acts as an antenna to receive the far-field incident electric fields and amplifies the near-field interaction through field enhancement of the tip resonances. This interaction scatters near-field encoded signals to the far field for detection^{13,14,18,20,22–28,30–33}.

In this measurement, we operate the cm-sSNOM system at mid-IR frequencies by use of a CW CO₂ laser capable of outputting wavelengths between 10.652-11.300 μm (~ 116.39−109.72 meV respectively). The sSNOM probe used to accept and scatter the electromagnetic waves containing the near-field information is a nominally 25 μm long Pt-coated Si AFM probe with a tip apex radius of curvature of  ~ 20 nm and a tapping frequency of 158 kHz. Once the AFM probe is in contact with the sample, near-field signals are extracted from the scattered electromagnetic waves by demodulating from the tip–sample system at the n-th harmonics of the tip-tapping frequency of the AFM. It is generally considered that higher order harmonics of the tip tapping frequency provide a cleaner near-field response, limiting the contributions of far-field interactions. All images are demodulated to the third harmonic, S₃, and averaged over their respective forward and backward scans, denoted by $S_3^{\mathrm{fwd+bwd}}$ which is plotted in Figs. 2–4. In our tapping-mode geometry, the oscillating AFM tip functions as an asymmetric optical antenna that couples to the local high-frequency complex conductivity without charge exchange. In applicable situations, we can average the forward and backward scanning images to reduce noise⁴¹.

To resolve the complex conductivity of the edge channels, we employ quasi-heterodyne detection. The scattered field ($E_{NF}^{\left(n\right)}$) is interfered with a reference beam, yielding a signal $S_{n\mathrm{\Omega }}\propto E_{\mathrm{ref}}\mid E_{\mathrm{NF}}^{\left(n\right)}\mid e^{i{\varphi }_{\mathrm{NF}}^{\left(n\mathrm{\Omega }\right)}}$. By demodulating the signal at the third harmonic (S₃), we suppress unwanted far-field contributions while preserving high-frequency information.

We further validate AFM performance through a Sobel-gradient alignment procedure⁴¹, enabling quantitative characterization via spatial Fourier transforms and the root-mean-square deviation from the mean AFM scan (Supplementary Information). These results confirm fully consistent AFM operation across all magnetic fields and temperatures with the Si-based cantilevers used here. Notably, the magnetic brightening of edge modes observed in ZrTe₅ is absent in the overlaid Au control film.

Origin of the near-field observable

To clarify the physical meaning of the measured observable, we emphasize that the cm-IR-sSNOM signal is a phase-sensitive finite-frequency near-field electromagnetic response, rather than a direct map of the local current density itself. The signal is generated by the local electrodynamic coupling between the tip field and the edge states, and is governed by the dynamic screening and infrared polarizability of the edge-state manifold at the  ~ 28 THz probe frequency. In our tapping-mode geometry, the oscillating AFM tip acts as an asymmetric optical antenna that couples to the local high-frequency complex conductivity without charge exchange. This interaction manifests as a dynamic screening contrast between the metallic edge and the insulating bulk, where ‘magnetic brightening’ signifies the high-frequency signature of B field-induced, transport-capable helical edge modes. By capturing the local infrared polarizability and dynamic screening at 116meV, our sSNOM probe resolves a robust metallic dispersion that persists even when low-energy DC transport is suppressed by magnetic gaps.

The robust observation of directional selectivity suggests that any departure from perfect C₂ symmetry–whether from the  ~30^∘ tip tilt or the directional tip-cantilever assembly–sufficiently disrupts the interference cancellation between counter-propagating helical modes, that is this introduces a longitudinal field component that facilitates asymmetric interference between them (Supplementary Information). This symmetry-breaking is further enhanced by the strong dynamic screening of the edge manifold, which amplifies small coupling imbalances into a detectable near-field contrast. This asymmetric tip dipole provides the directional selectivity required to resolve the “two-lane" spatial reorganization of the helical edge manifold under magnetic modulation (Fig. 1c,d).

The electromagnetic edge modes decay exponentially from the physical boundary into the massive bulk inversion band, with a characteristic length scale set by the Dirac mass gap Δ according to the decay length ${\lambda }_{\mathrm{\Delta }}=\frac{2\hslash v_{\mathrm{F}}}{\mathrm{\Delta }}$. Using Δ ≈ 7–10meV and v_F ≈ 5 × 10⁵m/s, we estimate an intrinsic topological decay length of  ~ 70–100 nm. At the same time, the spatial resolution of sSNOM is limited by the effective optical confinement length due to the tip convolution L_opt, typically 2–3 times the tip radius, corresponding to  ~ 60–90 nm in our experiments.

Estimation of the topological magnetic field scale and spin population imbalance

The form of the complex conductivity used in our analysis is based on a minimal intraband (free-electron) transport model in the presence of magnetic fields, extended to include both applied external and effective ‘topological’ field contributions. Specifically, we model the conductivity using a Drude-type framework with a finite transport lifetime, which naturally yields a longitudinal (dissipative) response and a transverse (Hall/cyclotron) component under a magnetic field. In tensor form, this corresponds to the standard magneto-Drude conductivity, where the off-diagonal terms arise from cyclotron motion.

To capture the physics relevant to our system, we include two contributions to the effective field: (i) the externally applied magnetic field B_ext, and (ii) an effective intrinsic field B_topo that reflects spin-dependent transport associated with the underlying topological band structure. At a phenomenological level, B_topo is incorporated through a spin imbalance, Δn = n_↑ − n_↓, which modifies the relative weights of the two spin channels while keeping the total carrier density approximately constant.

The resulting complex conductivity tensor therefore represents a superposition of longitudinal Drude response and transverse cyclotron response, with the effective field determining the magnitude and sign of the off-diagonal components. Let Δn = n_↑ − n_↓ as a function of B_ext, where n = n_↑ + n_↓ ≈ const. The conductivity tensor σ_TI is approximated as:

$${\sigma }_{TI}\approx \frac{{ϵ}_0{\omega }_p^2}{\left({\omega }_{CT}^2+{\tau }^{-2}\right)-{\omega }^2-i\omega \left(2{\tau }^{-1}\right)}\left(\begin{array}{cc}\hfill {\tau }^{-1}-i\omega \hfill & \hfill -\left({\omega }_{CB}+\frac{\mathrm{\Delta }n}{n}{\omega }_{CT}\right)\hfill \\ \hfill +\left({\omega }_{CB}+\frac{\mathrm{\Delta }n}{n}{\omega }_{CT}\right)\hfill & \hfill {\tau }^{-1}-i\omega \hfill \end{array}\right)$$ 1

Where B_T ≫ ∣B_ext∣ as discussed below. We define

$${\omega }_{CB}=\frac{\mid e\mid B_{\mathrm{ext}}}{m^{*}}\mathrm{and}{\omega }_{CT}=\frac{\mid e\mid B_{\mathrm{topo}}}{m^{*}}$$ 2

If B_ext = 0, then Δn = 0 and ω_CB = 0.

To contextualize the role of the external magnetic field (B_ext), we estimate two key physical scales: the intrinsic topological field (B_topo) and the resulting spin population imbalance (Δn/n). The intrinsic magnetic field scale associated with the topological confinement of the edge states is estimated using the relationship:

$$B_{\mathrm{topo}}~\frac{\hslash }{e{\xi }^2}$$ 3

where ξ is the edge-state confinement width. Prior STM measurements of ZrTe₅ have reported a confinement width of ξ of few nm. We adopt the 100 T scale as a representative upper limit required to fully reconstruct the underlying topological manifold. Crucially, this demonstrates that our experimental field of 4 T is largely perturbative relative to the massive intrinsic topological energy scale, serving as a symmetry-breaking trigger rather than a total reconfiguration of the topological state.

The “activation" of the infrared near-field contrast is driven by a population imbalance between the counter-propagating helical branches. This imbalance, Δn/n, can be estimated by the ratio of the Zeeman energy (E_Z) to the Fermi energy (E_F):

$$\frac{\mathrm{\Delta }n}{n}\approx \frac{E_Z}{E_F}=\frac{g{\mu }_{B}B}{E_F}$$ 4

In ZrTe₅, the g-factor is exceptionally large, with reported values of g ≈ 20–30. At an applied field of B = 4 T, the Zeeman splitting is  ≈ 5.8meV. Given the low Fermi energy of our samples (E_F ≈ 10–15 meV), the resulting population imbalance is approximately 30%. We estimate that such a spin populatoin imbalance at 4 T will lead to an effective confinement field B_topo*Δn/n ~ 30T.

Weak screening and the linear additivity of edge channels

ZrTe₅ at low temperature exhbit a low Fermi energy (E_F ≈ 10 − 15 meV). In such dilute systems, the Thomas-Fermi screening length (λ_TF) is quite long. Here λ_TF can be estimated to be $\sqrt{\frac{ϵ{ϵ}_0}{e^{2}g\left(E_F\right)}}$. Given the small density of state g(E_F) and small fermi energy in ZrTe₅, we have λ_TF ≈ 50 nm. This ensures that the infrared near-field probe can access the full depth of the step edge, capturing the cumulative polarizability of the discrete layers. First, since our step heights (5-9 nm) are significantly smaller than the bulk screening length λ_TF, the tip’s electric field penetrates through the entire stack of layers effectively. Each layer’s edge mode contributes nearly equally to the scattered field, leading to the observed linear scaling. Second, we expect significant deviations from linearity when the total step height H becomes comparable to the screening length (H ≈ λ_TF ≈ 50 nm). At that scale, the deeper layers would be increasingly shielded by the surface layers, causing the signal to saturate. Our observations on 6-layer and 11-layer steps remain well within the linear, weakly-screened regime.

The near-linear scaling observed across the studied thickness range (up to 11 layers) and within the 3–4 T field window is consistent with the additive nature of finite-frequency edge electrodynamics. This behavior corroborates our picture of stacked, quasi-independent 1D edge channels–a hallmark of a weak topological insulator–rather than a single, strongly coupled 3D side-surface state. While interlayer hybridization or side-surface transport may induce deviations from this additivity deeper in the quantum-limit or 3D-QHE regimes of ZrTe₅, our results establish a robust, layer-independent regime for these helical modes.

Computational method

The electronic band structures of ZrTe₅ layers were calculated within density functional theory (DFT) (Supplementary Information). To evaluate the topological edge states along the [100] direction, we constructed a tight-binding (TB) model based on maximally localized Wannier functions (MLWFs), which accurately reproduced the DFT band structure including SOC within  ± 1 eV of E_F, using Zr sd and Te p orbitals. The edge-state spectral functions were obtained via both surface Green’s function techniques^42,43 for semi-infinite edge state and supercell ribbon configurations for edge states of thicker layers as implemented in WANNIERTOOLS⁴⁴.

Our first-principles calculations in Fig. 5, based on relaxed lattice parameters, show that ZrTe₅ in the weak topological insulator regime does not host a surface Dirac cone on the terrace of the (010) surface imaged in the experimental configuration. This again agrees with earlier STM experiments^3,10. Consequently, a Chern-insulating edge state is not expected to emerge under an external magnetic field on this surface. Instead, the weak topological insulator feature of ZrTe₅ produces nanometer-scale step edges that can be viewed as stacks of QSH layers, each contributing a robust helical edge state. Each of these contributes one quantum of conductance, $\frac{e^2}{h}$, consistent with the well-established QSH state. When a finite magnetic field is applied, the spin degeneracy of these edge states is lifted, producing a spin imbalance. This imbalance generates a spin-polarized infrared polarizability and conductivity, which in turn manifests as the observed infrared near-field scattering signals.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41565-026-02193-2.

Author contributions

J.W. conceived and supervised the project. S.H., R.H.J.K., R.K.C. and J.M.P. performed the IR nano-imaging measurements. G.G., P.M.L. and Q.L. produced the samples and performed the transport characterizations. T.K. and L.L.W. developed the near-field model with the input from J.W., S.H. and M.M. L.-L.W. performed the density functional theory calculations. J.W. and S.H. analysed the data with input from all authors. The paper was written by J.W., S.H. and L.-L.W. after discussions with all authors.

Peer review

Peer review information

Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41565-026-02193-2.