Quantum Corridor part in graphene engineered by interfacial cost coupling

In a variety of solid-state programs, the quantum Corridor impact (QHE) is discovered to exhibit topologically protected dissipation much less edge channels with their transversal conductance quantized by e2/h, the place e and h are the elementary cost and the Planck fixed, respectively1,2,3,4,5. This peculiar behaviour is essential, for instance, within the implementation of quantum-based-resistance requirements with an especially excessive precision and reproducibility6. Among the many few recognized programs that manifest QHE, graphene receives particular consideration for its distinct band construction and the ensuing Nth Landau degree (LL) on the vitality of (varepsilon _{rmLL}(N)=rmsgn(N)v_rmFsqrt2ehslash B) underneath magnetic area B, the place vF is the Fermi velocity7,8,9 and the Landau quantization of graphene within the parameter house of B and n is outlined because the famed Landau fan, with all LLs linearly extrapolated to the cost neutrality level (CNP)8,9,10.

Interfacial coupling is thought to have an effect on the QHE in graphene, often in two other ways: cost impurities that trigger a decreased mobility but a wider quantum Corridor (QH) plateaux in some circumstances6, and cost switch that, to some extent, shifts the efficient doping11,12,13,14,15,16. Theories predict that the interaction between an antiferromagnetic insulator and graphene can provide rise to topological quantum floor states, reminiscent of quantum anomalous Corridor phases17,18,19. Experimentally, RuCl3/graphene is, certainly, noticed with a robust cost switch, which is typically presumably coupled to the magnetism20 and generally not absolutely evidenced so21.

On this work, we examine the case of monolayer graphene interfaced with CrOCl, an antiferromagnetic insulator. By analyzing a number of configurations of graphene encapsulated with hexagonal boron nitride (h-BN) and/or CrOCl, we mapped out the peculiar interfacial coupling between the carbon honeycomb lattice and CrOCl within the parameter house of temperature T, complete gate doping ntot, magnetic area B and displacement area D. At low temperatures, at which the CrOCl bulk was completely insulating, a robust interfacial coupling (SIC) was present in sure gate ranges. At finite magnetic fields, this led to a gate-tunable crossover from fan-like to cascades-like Landau quantization. Within the SIC regime, a QHE part with parabolic dependence between B and D was obtained in a large efficient doping vary from 0 to 1013 cm−2, with a Landau quantization of a ν = ±2 plateau ranging from as little as sub-100 mT at 3 Ok, and remained quantized at ~350 mT at 80 Ok.

Monolayered graphene, skinny CrOCl flakes and encapsulating h-BN flakes have been exfoliated from high-quality bulk crystals and stacked in ambient circumstances utilizing a dry switch methodology22. The van der Waals heterostructures have been then patterned into Corridor bars with their electrodes edge contacted. As seen in Fig. 1a, the field-effect curve of h-BN–graphene–CrOCl samples (pink curve) differs from the traditional h-BN–graphene–h-BN ones (blue curve), with the resistive Dirac peak disappearing and a degraded gate tunability (the configurations are illustrated within the Fig. 1a insets). Determine 1b exhibits the crystal construction of CrOCl (ref. 23). We first began with single-gated units and located that an SIC befell and affected the precise doping in graphene, which exhibited a drastic discrepancy with the doping anticipated from a standard gate dielectric, as proven in Supplementary Figs. 16.

Fig. 1: Characterization of CrOCl-supported graphene.
figure 1

a, Discipline impact curves of graphene encapsulated with h-BN and/or CrOCl. Insets: schematic configurations. b, Schematics of the crystallographic construction of CrOCl. c,d, Optical micrograph picture of a typical h-BN–graphene–CrOCl pattern (c), illustrated in d. Scale bar, 5 μm. e, Color map of a twin gate scan of the sphere impact in a typical pattern, measured at a temperature of T = 3 Ok and a magnetic area of B = 0.

Determine 1c exhibits the optical picture of a typical h-BN–graphene–CrOCl system, with its construction illustrated in Fig. 1d. A dual-gate mapping of the resistance obtained at T =3 Ok is given in Fig. 1e. Three notable areas are seen, every separated by a resistive peak and marked as both gap or electron doping, as decided by measurements at excessive magnetic fields mentioned under. To additional elucidate the SIC within the present system, we outline the efficient displacement area as Deff = (CtgVtg − CbgVbg)/2ϵ0 − D0, and the induced complete service of the 2 gates as ntot = (CtgVtg + CbgVbg)/e − n0, as generally utilized in dual-gated graphene units24,25. Right here, Ctg and Cbg are the highest and backside gate capacitances per space, respectively, and Vtg and Vbg are the highest and backside gate voltages, respectively. n0 and D0 are the residual doping and residual displacement area, respectively. Discover that the actual doping in graphene ngraphene might be affected by the interfacial states of CrOCl, whose service density is outlined as n2 (Supplementary Be aware 1), and due to this fact completely different from ntot within the SIC part, as is mentioned later. Examples of dual-gated maps of channel resistance within the Deffntot house are given in Supplementary Figs. 712.

Determine 2a exhibits a magnetic area scan of Rxy alongside a hard and fast service density on the gap aspect with ntot ≈ −3.8 × 1012 cm−2 (pink dashed line in Fig. 2b, a mapping of the channel resistance of device-S16 within the Deffntot house). Little Deff dependence of the filling fraction (that’s, LLs) is seen. That is the usual behaviour of monolayer graphene, as there isn’t a z dimension and thus the displacement area performs no function within the LLs. Strikingly, as proven in Fig. 2c, a magnetic area scan of transverse resistance Rxy alongside ntot ≈ + 1.8 × 1012 cm−2 (inexperienced dashed line in Fig. 2b) reveals drastically completely different patterns as in contrast with that in Fig. 2a. Extra particulars of the service sorts within the dual-gated units are given in Supplementary Fig. 13. This, as in Fig. 2c, permits one to succeed in the electron aspect at Deff ≈ 0.8 V nm–1, as indicated by the road profiles of each Rxx and Rxy at 12 T in Fig. second. On this regime (we name it the SIC–QHE part), Rxy is quantized in an especially broad parameter house. For instance, at B = 14 T, a filling fraction of ν = ±2 is discovered within the efficient doping of ntot from 0 to 1013 cm−2 with a displacement area distinction δD of over ~2 V nm–1, which converts into a really giant vary of gate voltages.

Fig. 2: Gate tunable SIC within the QH regime.
figure 2

a,c, Color maps of Rxy as a operate of B, recorded alongside the pink (a) and inexperienced (c) dashed strains in b. b, Rxx within the parameter house of Deff and ntot, measured at 14 T and three Ok. d, Line profiles of Rxx and Rxy at B = 12 T in c. e,f, Line profiles alongside the yellow dashed strains in b of Rxx and Rxy at Deff = 0.35 V nm–1 (e), with the zoomed-in σxy proven in f. g, Gate-tunable crossover from fan-like to cascade-like Landau quantization at Deff = 0.35 V nm–1.

Determine 2e exhibits the road profiles of Rxx and Rxy at Deff = 0.35 V nm–1 (alongside the yellow dashed line in Fig. 2b) at B = 14 T and T = 3 Ok. It’s seen that on the opening aspect (famous as the traditional QHE part), Landau quantizations are in settlement with these noticed in standard monolayered graphene8,9. Full degeneracy lifting with every integer filling fractions from ν = –2 to –10 is seen within the zoomed-in window in Fig. 2f. By becoming the hole-side impact curve at a zero magnetic area (Supplementary Fig. 14), the opening service mobility was estimated to be about 104 cm2 V−1 s−1. On the constructive aspect of ntot in Fig. 2e, the SIC–QHE part dominated, because the QH plateau of ν = –2 prolonged all through the entire gate vary. By various the magnetic fields at D = 0.35 V nm−1, we obtained a color map within the parameter house of B and ntot, proven in Fig. 2g. It’s seen that the SIC led to a change in Landau quantization from the well-known fan-like behaviour to a cascade-like one. To confirm ngraphene as in contrast with ntot within the pattern, we extracted neff from the Corridor resistance at low fields (that’s, B < 0.5 T earlier than the quantum oscillation began)—Fig. 2g exhibits a slope of ~1 with ntot on the standard part, however a robust departure at a constructive ntot, as proven in Supplementary Fig. 15. Furthermore, to have a worldwide image of the most important options described above, the color maps proven in Fig. 2 have been replotted in a three-dimensional presentation, as proven in Supplementary Fig. 16. All these observations have been reproducible in a number of samples (Supplementary Figs. 17 and 18), and likewise confirmed in samples fabricated in a glove field, which dominated out defects in graphene–CrOCl heterostructures (Supplementary Fig. 19).

The central results of this text is the commentary of an SIC–QHE part, through which Landau quantizations appear to be ‘pinned’, reminiscent of proven in Fig. 2g. A trivial clarification for this might be that the cost accumulation on the interface of graphene–CrOCl screened the constructive gate voltages utilized, which ends up in a failure of electron injection. Nonetheless, as proven in Fig. 2c, Deff completely shuffles the LLs (therefore the ngraphene), which guidelines out the ‘cost pinning’ image, as it might then be D unbiased, as within the standard QHE part (reminiscent of in Fig. 2a). Furthermore, the Landau quantization appeared to method the B = 0 restrict within the SIC–QHE part, as proven in Fig. 2c.

To additional make clear this perplexing situation, we carried out a zoomed-in scan of the low magnetic area a part of Fig. 2c. We outlined the displacement area through which the service kind switches from holes to electrons as Dimpartial, and thus the D axis was renormalized as δD = D − Dimpartial. As proven in Fig. 3a,b (Rxx and Rxy, respectively), broad Landau plateaux are seen. The quantized areas contact the B = 0 T line, and a tiny width nonetheless exists within the neighborhood of a zero magnetic area. The DB relation of LLs noticed right here is distinct from these present in different multilayered graphene programs26,27,28. We took the δD = –0.08 V nm–1 right here (indicated by the white dashed line in Fig. 3b), and plotted each Rxx and Rxy (Fig. 3c). The curves present a well-quantized plateaux of Rxy= ± 0.5h/e2 ranging from B as little as sub-100 mT, at which Rxx exhibits near-zero reminiscent values at every plateau. Though a quantum anomalous Corridor impact (QAHE) or Chern insulator is claimed in graphene programs29,30,31,32, our system with a h-BN–monolayer-graphene–CrOCl heterostructure appears to be topologically trivial when a magnetic area is totally absent, and the noticed Rxy quantization at a really low B continues to be within the regime of QH states, because the quantization of ν = ± 2 is inherited from the Dirac electrons, and no magnetic hysteresis (that’s, the coercive area) is seen within the hint–retrace loop of a magnetic scan in our system (indicated by arrows in Fig. 3c, and see Supplementary Fig. 20). Extra dialogue might be seen in Supplementary Be aware 2. A trivial impact of gate leakage was dominated out, and a number of samples have been examined to a most temperature earlier than gate leakage befell, proven in Supplementary Figs. 2123. Notably, this strong SIC–QHE part within the graphene/CrOCl heterostructure prevails at a lot increased temperatures (Fig. 3c inset).

Fig. 3: Traits of the SIC–QHE part in graphene–CrOCl heterostructures.
figure 3

a,b, Rxx (a) and Rxy (b) of device-S16 plotted within the parameter house of δD and B. c, Line profiles of Rxx and Rxy at δD = –0.08 V nm–1. Inset: temperature dependence of one other typical pattern (device-S40) at δD = –0.15 V nm–1. d, Line profile of Rxx in a at B = –1 T (indicated by the vertical white dashed line). Pink dots are resistive peaks picked by every most. e, Dependence of δD and (sqrtN). The black strong line is a linear match. f, Parabolic dependence of (updelta D=alpha sqrtN), plotted with α = 0.513 and N < 200.

By extracting a line profile of Rxx in Fig. 3a at B = –1 T (indicated by the vertical white dashed line), resistive peaks have been discovered at every LL, as indicated by the pink dots in Fig. 3d. It was discovered that the δD values at every resistive peak have been in linear dependence with (sqrtN), with N the Nth LL, proven in Fig. 3e. This can be a typical Landau quantization vitality dependence in standard monolayered graphene. Certainly, the δDB relation might be fitted utilizing a parabolic curve as (updelta D=alpha sqrt ). The peaks of Rxx of the primary LL in Fig. 3a (pink circles) have been fitted with a white strong parabolic curve, with α = 0.513. The primary 200 LLs have been then plotted (Fig. 3f), and properly simulated the experimental δD knowledge. This means that δD linearly tunes the chemical potential of the LLs of graphene, which stimulated us to suggest a attainable mechanism to clarify the SIC–QHE as outlined within the following part. Curiously, the noticed SIC–QHE part appears to haven’t any connection to the antiferromagnetic nature of CrOCl, as its Néel temperature is ~13 Ok (ref. 23), a lot decrease than the higher sure temperature for the SIC–QHE part. As well as, we seen {that a} sister compound of CrOCl, FeOCl, is much much less steady, and couldn’t be used to verify the universality of the findings on this work (Supplementary Fig. 24).

We then replotted (Fig. 4a) the Rxx of device-S16 within the Deffntot house at 14 T with false color that separates the boundary between the traditional and SIC phases, and the LLs naturally denote iso-doping strains, as outlined by ν = hngraphene/eB. Two key options are seen in Fig. 4a. First, the CNP is bent because the system enters from standard part into the SIC part. Second, every spacing between the iso-doping strains will increase because the system enters deeper into the SIC part. We suggest an electrostatic mannequin in Supplementary Be aware 1. An interfacial band with appreciable cost density of n2 is launched on the floor of CrOCl with a distance d2 under the graphene layer, and the highest and backside gates are situated at distances d1 and d3, respectively, as illustrated in Supplementary Fig. 25a,b. By evaluating the mannequin, we discovered that these two main options might be properly reproduced, as proven within the part diagram in Fig. 4b. However, within the simplified mannequin we needed to introduce two assumptions—a band construction reconstruction with an enhanced Fermi velocity as soon as the Fermi degree of graphene turns into aligned with the interfacial band in CrOCl, and likewise that the interfacial band reveals no contribution to move, as mentioned in Supplementary Figs. 2528.

Fig. 4: QH part diagram within the Deffntot house and the transition processes between phases.
figure 4

a,b, Experimental (a) and calculated (b) part diagram within the Deffntot house, with the part boundary highlighted. Iso-doping strains with the calculated ngraphene are indicated by strong strains in b. c, Schematic of a typical part diagram with two paths of transition processes famous by arrows. dj, Schematics of the band diagrams (steps (1)–(4)) for path a (dg, respectively) and people (steps (1′)–(3′) for path b (hj, respectively) illustrated in c.

We additional carried out density useful concept calculations (Supplementary Figs. 2931 in Supplementary Be aware 2). It’s seen that, within the bilayered CrOCl mannequin and at sure vertical electrical fields, the interfacial band from the highest layer of CrOCl (Supplementary Figs. 3234) begins to overlap with the Fermi degree of graphene. The cost switch from graphene to the interfacial band is thus allowed through tunnelling. Our calculations counsel {that a} long-wavelength localized cost order (a Wigner crystal, on this case, because the dimensionless Wigner–Seitz radii are estimated to exceed the vital worth of 31 for two-dimensional electrons,33 proven in Supplementary Desk 1) is prone to kind within the interfacial band of the Cr 3d orbitals within the prime layer of CrOCl. This self-consistently explains that, as soon as full of electrons, the interfacial band could bear a Wigner instability and doesn’t contribute to move, however offers a superlattice of Coulomb potential for the graphene resting on prime. When systematically contemplating the interaction between generic long-range Coulomb superlattice potentials in a variety of supplies coupled with graphene, our separate theoretical work means that such e−e interplay in graphene certainly enhances the Fermi velocity dramatically and within the meantime opens a niche on the CNP34. It got here to our discover that comparable phenomena have been additionally not too long ago seen, reminiscent of in graphene–CrI3 system35.

Primarily based on the above evaluation, we plotted a schematic part diagram (Fig. 4c), through which the traditional and SIC phases have been denoted as part (i) and part (ii) for simplicity. Two completely different paths are used as an instance the doping processes in our system. In path a, graphene begins in a hole-doped state (state (1) in Fig. 4d). It crosses the CNP, turns into electron doped and approaches the part boundary at which the Fermi degree of graphene touches the bottom vitality of the interfacial band in CrOCl (state (2) in Fig. 4e), which thus triggers the electron-filling occasion within the interfacial band and varieties a cost order. The latter exerts a long-wavelength Coulomb superlattice potential to the Dirac electrons in graphene. Consequently, the Fermi velocity is notably enhanced (sharpening of the Dirac cone within the illustration) pushed by e–e interactions in graphene (state (3) in Fig. 4f). Moreover, when Deff is decreased from state (3) to state (4), the Fermi degree in graphene reaches its CNP, at which an interaction-driven hole is seen (as supported by the extraction of thermal activation hole; Supplementary Fig. 35). On an additional lower in Deff, the system turns into hole-doped once more. An identical course of might be interpreted for path b (Fig. 4h–j).

Experimentally, by becoming the Shubnikov–de Haas oscillations from numerous temperatures at dopings in part (i) and part (ii) (Supplementary Fig. 36), the cyclotron mass m* in part (i) was estimated to be akin to that in ‘extraordinary’ monolayer graphene, however 3–5 occasions bigger than that in part (ii). It therefore yields a Fermi velocity a number of occasions bigger than that of graphene in part (ii), in settlement with the conjectures in our theoretical mannequin. Thus, on this regime the cyclotron hole of the primary LL, (Delta =v_rmFsqrt2hslash eB), is within the order of about 50 meV at 0.1 T, which qualitatively explains the quantization at a really low B. We emphasize that additional probes, reminiscent of infrared transmission, would assist to straight confirm the cyclotron hole estimated within the present system on this regard. A strong QH state with ultralow magnetic fields at relaxed experimental circumstances might be essential for future constructions of topological superconductivity in addition to quantum-information processing, which has lengthy regarded as solely attainable in QAHE programs. The above outcomes unambiguously present that the interfacial cost coupling, when it comes to engineering the quantum digital states, is a robust approach that we could have neglected so far. For comparability, Fig. 5 summarizes the magnetic fields and temperatures required to comprehend quantized Corridor conductance in typical completely different QHEs or QAHE programs reported not too long ago6,12,30,36,37,38,39,40,41.

Fig. 5: Views for the SIC–QHE part.
figure 5

The diagram summarizes magnetic fields (under 10 T) and temperatures that notice quantized Corridor conductance in a number of typical programs reported not too long ago. Information from three samples (units S16, S36 and S40) on this work are included.

In conclusion, we now have demonstrated a hybrid system of graphene–CrOCl, through which an unique QHE part was noticed because of the peculiar gate tunable interfacial coupling. At finite magnetic fields and fixed Deff, a crossover from fan-like to cascade-like Landau quantization is seen. Additionally, within the DB house, in contrast to in standard D-independent ones, the LLs within the SIC–QHE part reveals a parabolic dependence between B and Deff in a large efficient doping vary from 0 to 1013 cm−2, with a Landau quantization of a ν = ±2 plateau ranging from as little as sub-100 mT under 10 Ok, and stays quantized at ~350 mT at liquid nitrogen temperature. Our theoretical evaluation self-consistently attributes the bodily origin of this noticed phenomenon to the formation of a long-wavelength cost order within the interfacial states in CrOCl and a subsequent band reconstruction in graphene. Our findings appear to open a brand new door to engineering the QH part, and should make clear the longer term manipulation of quantum digital states through interfacial cost coupling, reminiscent of to assemble novel topological superconductors, and to construct quantum metrology requirements.

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