Topological nature of higher-order hinge states revealed by spin transport

One-dimensional (1D) gapless hinge states are predicated in the three-dimensional (3D) higher-order topological insulators and topological semimetals, because of the higher-order bulk-boundary correspondence. Nevertheless, the topologically protected property of the hinge states is still not demonstrated so far, because it is not accessible by conventional methods, such as spectroscopy experiments and quantum oscillations. Here, we reveal the topological nature of hinge states in the higher-order topological semimetal Cd3As2 nanoplate through spin potentiometric measurements. The results of current induced spin polarization indicate that the spin-momentum locking of the higher-order hinge state is similar to that of the quantum spin Hall state, showing the helical characteristics. The spin-polarized hinge states are robust up to room temperature and can nonlocally diffuse a long distance larger than 5 {\mu}m, further indicating their immunity protected by topology. Our work deepens the understanding of transport properties of the higher-order topological materials and should be valuable for future electronic and spintronic applications.

Despite extensive studies on its spatial identification, the topological nature of higher-order hinge state has still not been revealed so far. Moreover, the bulk and surface states are often in parallel conduction, rendering the 1D hinge modes elusive through conventional transport experiments. Here we reveal the topological nature and spin helicity of hinge states in the higher-order topological semimetal Cd3As2 nanoplate via spin potentiometric measurements.

Materials and methods
For higher-order Dirac semimetals, the quadruple-invariant protected hinge states span the projection of bulk 3D Dirac points along the 1D hinges [25,26,29], as sketched in Fig. 1a. For usually synthesized Cd3As2 nanoplates with (112) surface orientation, 3 the 1D helical hinge states (Fig. 1b) are also expected due to the existence of projection along the (001) direction. The hinge states feature Kramers pairs of counterpropagating modes on opposite edges. In the presence of a current bias, the orientation of induced spin polarization is contrary on opposite edges of sample surface (Fig. 1c). When the current bias is reversed, the induced spin polarization of each edge would also be reversed.   Figure 2 shows the spin transport results measured on the device A. As sketched in Fig. 2a, a direct current (dc) was injected into the nanoplate via the outmost two Ti/Au electrodes, and the voltage was measured between the inner Co and Ti/Au electrodes.

Spin-momentum locking of the hinge states
An external magnetic field was applied along the long axis of the cobalt strip, in-plane perpendicular to the current direction, to modulate the Co magnetization M for probing the spin signals. The As shown in Fig. 2b  (c) (e) (f) 6 the high and low voltage states, respectively [46,52]. A dc bias generally gives rise to a net momentum e in the electronic system. With the determined orientation S and e , we can obtain the right-handed and left-handed spin-momentum locking on the upper and lower edges, respectively, as seen in the insets of Fig. 2b, c. For each edge, upon reversing the current direction, the spin polarization also reverses its direction (Fig. 2d which is greatly underestimated due to the edge current accounting for only a small part of the total current. The ∆ S is also found linearly proportional to I (Fig. 3d), indicating that the spin polarization ratio is independent of bias current [47,52]. Spin related potential difference between the two opposite Co electrodes is also measured     The |∆ S | from the two sides demonstrates opposite tendency with varying gate 9 voltage g . For the contributions from surface states, it decreases as tuning g away from the Dirac point due to the decrease of surface-bulk conduction ratio [41, 42,52].
The opposite spin signals of the two hinges are combined with the contribution of surface states, so that the total measurement signal is strengthened on one side and weakened on the other. As the g is tuned to a large positive value, the surface spin contribution can be ignored, and nearly identical |∆ S | are observed on two sides for g = 50 V (Fig. 3h). Furthermore, the edge spin signals are robust against temperature.
As presented in Fig. 3i, the spin signals on the two edges can both exist steadily at 290 K, holding promise for the practical spintronic devices in the future.

Nonlocal spin transport on the hinges
Driven by the dc bias, the electrons of edge states acquire net spin polarization in the local region. The spin diffusion process allows us to detect the spin-related hysteretic loops in the region away from the local source electrode. As sketched in Fig. 4a, the dc bias is applied to the nanoplate via the rightmost two Ti/Au electrodes, while the voltage is measured nonlocally between the Co electrode and the leftmost Ti/Au electrode. We here fabricate several pairs of Hall-bar-like Co electrodes, denoted by the Roman number 1 to 6, serving as nonlocal spin detectors. When applying a bias current = 2 mA , hysteretic loops are clearly observed on the upper and lower edges of the nanoplate (Fig. 4b, c). Similar to the local measurement results, these two edges still demonstrate opposite spin-polarized signals in the nonlocal regime. Upon changing the polarity of the bias current, the spin polarization of the nonlocal transport also experiences a reversal (Fig. 4d, e), showing consistent spin-momentum locking with the local channel. To suppress the charge-current-spreading effect, the nearest nonlocal spin probe is set beyond 2 μm from the local electrode, where the distance is larger than the mean free path of electrons [54][55][56], facilitating the detection of spin diffusion process (Supplementary materials, Fig. S6). Figure 4f shows the |∆ S | as a function of , where is the distance between the nonlocal spin detector Co and the its nearest

Conclusions
In summary, we have identified the helical hinge states in the higher-order topological semimetal by employing spin potentiometric measurements. Benefiting from topological protection and the strict prohibition of backscattering of non-magnetic impurities in the 1D hinge channel, the current induced spin polarization is still observable at room temperature and the nonlocal spin diffusion length is longer than 5 μm. Our work should be valuable for understanding the transport properties of higherorder topological states. The topological edge transport channels are easy to replicate, integrate and scale up, paving the way for low-dissipation electronic and spintronic devices.

Conflict of interest
The authors declare that they have no conflict of interest.

Sample growth and transport measurements
Cd3As2 nanoplates were grown by chemical vapor deposition with (112) surface orientation. Cd3As2 powders with high purity (> 99.99%) were placed in the center of horizontal quartz tube. Silicon wafers with 5 nm gold thin film were placed downstream as substrates to collect the products. The quartz tube was first flushed three times with Argon gas to get rid of oxygen, then gradually heated from room temperature to 700 0 C within 15 minutes, and kept for 10 minutes at 700 0 C along with an Argon gas flow of 20 s.c.c.m. The system was then cooled down naturally. Cd3As2 nanoplates were collected on the silicon wafer substrates. Figure S1a shows the scanning electron microscopy (SEM) image of the as-grown nanoplates. The selected area electron diffraction (SAED) pattern is shown in Fig. S1b. According to the crystallography calculation and hexagonal lattice symmetry, (112) surface orientation can be determined for the nanoplate.
Individual Cd3As2 nanoplates were then transferred onto a silicon substrate with a 285-nm-thick oxide layer. The thickness of selected nanoplate is about 100 nm. Ti/Au and Co/Au electrodes were fabricated after two rounds of e-beam lithography and ebeam evaporation process. A gold layer above was used as a capping layer to protect Co from oxidization. To establish the Ohmic contact between Cd3As2 and Ti/Au electrode, an in-situ Ar + etching process was performed to remove the native oxide layer of the nanoplate before metal deposition. A 3-nm-thick Al2O3 layer was inserted between Cd3As2 and Co electrode using e-beam evaporation system. Figure S1c presents the optical image of a finished nanoplate device.
Transport measurements were performed in a commercial Oxford cryostat system with a base temperature ~ 1.4 K. The magnetic field was aligned along the easy axis of  A total of 22 devices have been investigated in our work. In all of these devices, opposite spin-polarized signals are observed on the two sides of nanoplate. Figure S2 gives the counting results of these devices in terms of the spin resistance ∆ S = ∆ S / , which can be employed to characterize the charge-to-spin conversion efficiency. The positive and negative ∆ S correspond to the clockwise and counterclockwise magnetic loops, respectively. Limited by the process of Ar + milling and Al2O3 deposition, the Co/Cd3As2 interface would greatly affect the spin detection efficiency.
Moreover, carrier density varies for different nanoplates. Both effects together lead to the device-to-device variations in the spin resistance.  Figure S3 shows the raw data of spin transport measured on device A, where the linear magnetoresistance background is clearly observed (marked by dashed lines). The linear background has been previously investigated [1,2], which may originate from the vertical charge transport between the bulk and surface conduction channels. After subtracting the linear background, we can obtain the spin-dependent voltage S versus magnetic field .   distances from the current electrode (Fig. S6a). Contrary to the condition of local spin detection, the nonlocal voltage is detected on the Co electrode away from the source and drain electrodes.
In the nonlocal transport regime, both the spin diffusion process and charge-currentspreading (CCS) effect could produce notable nonlocal spin signals, as shown by nonlocal I-V curves also confirms the dominance of CCS effect (Fig. S6i). When the distance L is gradually increased beyond the MFP scale (~1 μm), the CCS effect is 11 greatly quenched, rendering the quick decrease of nonlocal voltage signals (Fig. S6j,   k). Instead, spin diffusion process gradually comes into prominence, where the reversal of spin voltage loop is observed for each edge (Fig. S6g, h).

Discussions of possible mechanisms for the opposite spin polarizations
Several other mechanisms for the observed opposite spin-polarized signals on the two sides of a single nanoplate can be ruled out. First, the topological or Rashba surface states cannot be the origination, because the current-induced surface spin polarization signal should be spatially independent (Fig. S7) and almost the same through the same surface [1,2]. In our work, the 3-nm-thick Al2O3 layer, inserted between the Cd3As2 surface and the Co electrode, plays a significant role in manifesting the hinge state spin transport.
The oxide layer not only enhances the spin detection efficiency, but also protects the surface and hinge states from the poisoning of ferromagnetic Co electrode. Despite this, the 2D surface states are still inevitably suffering from the degradation of spin polarization due to the finite-angle scattering process [6,7], which could not happen in the 1D hinge channels. Furthermore, the surface Fermi arc states are resulted from fragile topology [8,9], while the 1D hinge states are viewed as topological consequence of bulk Dirac points [8], generally featured with a much higher spin polarization ratio.
Therefore, the contrary spin polarizations on opposite edges of nanoplate are observable as a consequence of the dominant contribution of spin-polarized hinge state transport.