## Introduction

Quantum matter with non-trivial topologies of electronic bands holds great potential in advancing next-generation information, computing, and storage technologies1,2,3. Surface and edge modes in gapped topological systems1 are exciting venues for exploring how information can be transmitted with minimal dissipation4,5 and in a non-reciprocal way6,7. For example, two-dimensional magnetic topological insulators (also known as Chern insulators8,9) possess one-dimensional chiral edge states, in which electrons travel strictly in only one direction and backscattering is topologically forbidden, as in the quantum Hall effect. The direction of propagation of such edge state is controlled by magnetization of the material. The number of chiral edge states is equal to the Chern number C and determines the quantized Hall resistance, Ryx = h/Ce2 (ref. 10), where h is Planck’s constant and e is the elementary charge.

When two materials with different Chern numbers are put in contact with each other, due to bulk-boundary correspondence chiral edge states can emerge at the interface1. This was demonstrated in experiments on two-dimensional electron gas11 and graphene12,13,14 where regions with different C can be created by means of locally changing carrier densities in quantum Hall regime. The Chern insulator networks15,16,17 comprised of domains with distinct Chern numbers may lead to complex device architectures, where C of individual domains will control topological current properties, such as current amplitude and propagation direction. Previous attempts to construct such networks which went beyond quantum Hall state relied on chiral edge states existing at domain walls in magnetic topological insulators, since domains of opposite magnetization have opposite Chern number (ref. 18,19,20). One-dimensional edge modes can also exist on the crystal step edges of topological materials21,22,23,24,25,26, but domain-wall and step-edge states are nearly impossible to harness in an electronic device. As a result15,16,17,27, achieving robust and tunable topological circuit elements, such as a topological current divider27, has remained a challenge.

In this work, we intentionally create a “Chern junction” in MnBi2Te4 (MBT) between domains with C = 1 and C = 2 and exploit it to demonstrate the basic operations of a topological circuit, including splitting, redirection, and switching of chiral edge currents. MBT is a van der Waals topological antiferromagnet28 in which each covalently bonded layer (comprising seven atomic planes in the sequence Te-Bi-Te-Mn-Te-Bi-Te) is ferromagnetic with out-of-plane magnetization, while the coupling across the van der Waals gap between layers is antiferromagnetic (AFM)28. In few-layer MBT the intertwined magnetic and Chern insulator states are tuneable29,30,31,32,33,34,35 by a combination of factors: magnetic field, which modifies the magnetic state29,35,36; electrostatic gating, which tunes the chemical potential relative to the exchange gap9,29; and thickness32. The corresponding chiral edge states also persist to relatively high temperatures (up to T ≈ 30 K, ref. 29, 32), another helpful feature for prototyping topological circuits.

## Results

### Chern insulator junction formation

Our Chern junction design is shown in Fig. 1a, b. In addition to the C = 1 state in a thin flake29,30,31,32 (labeled Domain I), MBT can host higher Chern number states in a thicker flake30,32,35 (Domain II). Chern number C = 2 state in MnBi2Te4 was recently identified as a combination of C = 1, which originates from non-trivial band topology and ν = 1 quantum Hall state35. Within our experimental parameter space32,35, we observe C = 2 only in flakes which are $$\ge$$6 layers thick (see Methods). In flakes with thickness 4 and 5 layers only C = 1 state appears. As a result, in a single flake containing a step in thickness, the thinner (Domain I) and thicker (Domain II) parts can simultaneously be tuned to have C = 1 and C = 2, respectively, creating a Chern junction at the boundary (Fig. 1b). There are two possible scenarios for the chiral edge states at the Chern junction: either one of them travels along the boundary and one crosses it (Fig. 1c), or three travel along the boundary and none crosses it (Fig. 1d). We intentionally selected exfoliated MBT flakes with a 1–2 layer step edge because self-standing 1–2 layer flakes have no edge states, and thus any edge states at the boundary must be associated with the Chern junction.

We focus here on a device (Device 1) which has a 4-layer part (Domain I) and a 6-layer part (Domain II) (Supplementary Fig. 1). We first establish the phase diagrams of the two domains as a function of magnetic field μ0H and back gate voltage Vbg by measuring Ryx to determine their respective Chern numbers, CI and CII (see Supplementary Note and Methods). Figure 1e is a 2D color map of Ryx as a function of μ0H and Vbg at T = 50 mK (the longitudinal resistance Rxx is shown in Supplementary Fig. 2). Within the blue dashed contour 0.98 h/e2 ≤ Ryx ≤ 1.002 h/e2, implying CI = 1. Figure 1f is a similar plot for Domain II. Here, within the black dashed contour 0.98 h/e2 ≤ Ryx ≤ 1.002 h/e2, implying CII = 1, and within the green dashed contour 0.49 h/e2 ≤ Ryx ≤ 0.51 h/e2 implying CII = 2 (ref. 35). Figure 1g shows an overlay of these parameter regions for both domains. The region where CI = 1 and CII = 2, i.e., where a Chern junction forms, is shaded orange. The Chern junction can be reconfigured (eliminated) by changing the parameters to lie in the blue shaded region where CI = CII = 1.

### Topological current divider

We next establish the existence of chiral edge states at the junction interface. We can probe the configuration of chiral edge states using various contact configurations. To start with, we inject a bias current I (2 nA) at contact 1 and measure the currents flowing to ground through contacts 8 (I8) and 9 (I9 = I—I8) with all other contact floating. The magnetic field is first set to μ0H = −12 T, such that the edge states propagate clockwise around the sample (Fig. 2a). The resulting variation of I8 and I9 with Vbg is shown in Fig. 2b. When Vbg is well outside the range for which CI = 1 and CII = 2, which is roughly 85 V < Vbg < 95 V (yellow shaded area in Fig. 2b), I9 is several times larger than I8. This is naturally explained by the presence of bulk conductivity (when Vbg < 80 V or Vbg > 95 V), the path through the bulk from 1 to 9 being shorter than that from 1 to 8. In contrast, when 85 V < Vbg < 95 V, where CI = 1 and CII = 2, we observe I9 = I8. This measurement unambiguously identifies that Fig. 1c depicts the correct interfacial chiral edge conduction channel configuration. In case the physical picture depicted in Fig. 1d would be a valid one, all current should flow from contact 1 to 9 and give vanishing I8. The configuration in Fig. 1c leads to the current flow pattern sketched using white lines in Fig. 2a, which leads to I9 = I8 (see Methods and Supplementary Fig. 3 for measurement details).

When the magnetic field is reversed to +12 T (Fig. 2c), the behavior is quite different and now I9 dominates I8 when 85 V < Vbg < 95 V. This is because the sample magnetization is now reversed, switching the Chern numbers to CI = −1 and CII = −2 and causing the chiral edge states to reverse direction so that they now both directly convey current from contact 1 to contact 9, as sketched in Fig. 2d. Using other contact configurations we can confirm that this picture is correct. For example, when we inject the current at contact 9 and measure the currents to ground through contacts 8 and 10 at μ0H = −12 T, when 85 V < Vbg < 95 V most of the current is delivered directly to contact 10 via both chiral edge states (Fig. 2e, f). However, when the field is reversed to +12 T, equal currents flow out of contacts 8 and 9 (Fig. 2g) because the junction then acts as a 1:1 current divider (Fig. 2h). Results for a third configuration are shown in Supplementary Fig. 4.

The above results demonstrate that a chiral edge state can exist at a crystalline step edge in MBT. Unlike the topological edge states that have been detected in other systems using scanning probe techniques21,22,23,24,25,26, this chiral edge state can be switched, detected by transport, and harnessed for multi-terminal devices. The results presented in Fig. 2 demonstrate that the Chern junction can function as a simple circuit element: a current signal can be either split equally between two outputs or routed to a single output by flipping the direction of the chiral edge mode. The existence of chiral edge states in this device makes the use of different contacts within a single topological domain equivalent6,7. To demonstrate this explicitly, in Fig. 3a we show that in the appropriate gate range (85 V < Vbg < 95 V), the current splitting obtained using any of contacts 4, 5, 6 or 7 to Domain I is identical to that using contact 8 as in Fig. 2a, b, i.e., the current injected at contact 1 in Domain II is always divided 1:1 at the Chern junction (see also Supplementary Fig. 5). Note that small changes in the gate range for current divider operation in Fig. 3a might be related to small Fermi level variations across the device, which has a large lateral size of 100 μm.

### Control of Chern junction

The gate voltage and magnetic field provide additional control of the Chern junction by altering CI and CII. Figure 3c shows the division of current injected at contact 1 between contacts 8 and 9 as a function of Vbg and μ0H. The black dashed line outlines the region where CI = 1, CII = 2 and the device works as a 1:1 chiral edge current divider, as depicted in Fig. 3b. The white dashed line outlines the region with CI = CII = 1, where there is no edge state along the boundary and the current is not divided but is all conveyed to contact 8 via a single edge state on the perimeter of the flake (Fig. 3d). In the low-field limit (|μ0H | < 4 T) and close to charge neutrality (85 V < Vbg < 95 V), most of the current flows from contact 1 to the nearest contact 9 via bulk conduction, because the chiral edge states do not exist in the AFM phase29,31,32,35.

An asset of MBT devices is the persistence of the chiral edge states to elevated temperature29,32. Figure 4 shows the efficiency of topological current division as a function of temperature in another device (Device 2) in which Domains I and II differ in thickness by only 1 layer (Supplementary Fig. 6). Figure 4a shows the divider configuration (similar to that shown in Fig. 2a), and Fig. 4b shows how the current is actually divided between contacts 6 (I6) and 10 (I10) at T = 10 K. For 30 V < Vbg < 33 V (shaded yellow region) and μ0H = −9 T, when the required Chern junction condition (CI = 1, CII = 2) is met, the deviation from ideal 1:1 current division (blue dashed line) is <5% (black dashed lines). The evolution of I6 with temperature and gate voltage is plotted in Fig. 4c. Even at 30 K, the deviation under optimal conditions is only 10% (Supplementary Fig. 7).

## Discussion

In conclusion, we have shown the creation and manipulation of chiral edge states at crystal step edges in the topological magnet MnBi2Te4 and used them to demonstrate proof-of-concept topological circuit elements which can divide and redirect dissipationless current. Both C = 1 (ref. 29, 32) and C = 2 (ref. 32) states persist to high temperatures, which is important for practical applications. In the future, additional degrees of freedom such as multiple top gates can be introduced for further control of Chern numbers locally, while recent developments in controllable molecular beam epitaxy of MBT (ref. 37,38,39,40) offer scalability. Finally, although our results are in the low-frequency limit, the device architecture offers a promising route to higher frequency non-reciprocal switches6,7 based on van der Waals topological magnets.

## Methods

### Device fabrication

Bulk crystals of MnBi2Te4 were grown out of a Bi-Te flux as previously reported41. Scotch tape exfoliation was used to obtain flakes with thicknesses between 4 and 8 layers on 285 nm SiO2 grown on degenerately p-doped Si wafer. The thickness was determined by combination of optical contrast, RMCD measurements and atomic force microscopy29. We identified suitable stepped flakes and cleaned away surrounding bulk flakes with a sharp needle. The flakes were incorporated into back-gated devices by electron beam lithography using polymethyl methacrylate (PMMA) resist, thermal evaporation of Cr (5 nm) and Au (60 nm) and lift off in anhydrous solvents. All fabrication was carried inside an argon-filled glovebox and additional layer of spin coated PMMA was added before the device was taken out to perform measurements.

### Hall bar transport measurements

Transport measurements reported in Main Text Figs. 13 and Supplementary Figs. 2 and 6 were conducted in a dilution refrigerator (Bluefors) with low-temperature electronic filters and 13 T superconducting magnet. Four-terminal longitudinal resistance Rxx and Hall resistance Ryx were measured using standard lock-in technique with an AC excitation between 0.5 and 10 nA at around 13 Hz. Supplementary Note discusses simultaneous measurement of Rxx and Ryx in both domains, with measurement configuration depicted in Supplementary Fig. 1e. We present raw Ryx and Rxx data in Fig. 1e, f and Supplementary Fig. 2. Large Ryx signals in both domains at low magnetic field are related to mixing with Rxx signal due to non-ideal device geometry. This mixing does not affect topological signals at fields above 4 T which we focus on in this work. For transport measurements reported in Main Text Fig. 4 and Supplementary Fig. 7, we used physical property measurement system (PPMS, Quantum Design).

### Topological circuits measurements

To perform directional current measurements in Main Text Figs. 24 and Supplementary Figs. 4, 5, 7, using schematic of Fig. 2a as an example, constant current with the magnitude of 2–4 nA was injected at contact 1 and current to ground was detected with virtual-earth current preamplifiers at contacts 8 and 9. All other electrodes were floating. Supplementary Fig. 3 provides measurement details in these types of devices.