1 Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator Canxun Zhang123 6 Tiancong Zhu126 Tomohiro Soejima16 Salman Kahn126 Kenji Watanabe4

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Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator

Canxun Zhang1,2,3,6, Tiancong Zhu1,2,6*, Tomohiro Soejima1,6, Salman Kahn1,2,6, Kenji Watanabe4,

Takashi Taniguchi5, Alex Zettl1,2,3, Feng Wang1,2,3, Michael P. Zaletel1,2*, Michael F. Crommie1,2,3*

1Department of Physics, University of California, Berkeley, CA 94720, USA.

2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

3Kavli Energy NanoScience Institute at the University of California, Berkeley and the

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

4Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1

Namiki, Tsukuba 305-0044, Japan.

5Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1

Namiki, Tsukuba 305-0044, Japan.

6These authors contributed equally: Canxun Zhang, Tiancong Zhu, Tomohiro Soejima, Salman Kahn.

*Email: tiancongzhu@berkeley.edu; mikezaletel@berkeley.edu; crommie@berkeley.edu.

Abstract

In recent years, correlated insulating states, unconventional superconductivity, and

topologically non-trivial phases have all been observed in several moiré heterostructures. However,

understanding of the physical mechanisms behind these phenomena is hampered by the lack of local

electronic structure data. Here, we use scanning tunnelling microscopy and spectroscopy to

demonstrate how the interplay between correlation, topology, and local atomic structure determines

the behaviour of electron-doped twisted monolayer-bilayer graphene. Through gate- and magnetic

field-dependent measurements, we observe local spectroscopic signatures indicating a quantum

anomalous Hall insulating state with a total Chern number of ±2 at a doping level of three electrons

per moiré unit cell. We show that the sign of the Chern number and associated magnetism can be

electrostatically switched only over a limited range of twist angle and sample hetero-strain values.

This results from a competition between the orbital magnetization of filled bulk bands and chiral

edge states, which is sensitive to strain-induced distortions in the moiré superlattice.

Introduction

Van der Waals stacking of twisted two-dimensional (2D) atomic sheets provides a versatile

platform for engineering exotic electronic states through rotational misalignment that folds

dispersive electronic bands into flat mini-bands within a moiré Brillouin zone.1,2 The resulting

suppression of kinetic energy relative to electron-electron interactions can lead to correlated

insulating states as well as unconventional superconductivity.3,4 Moiré flat bands also inherit the

large Berry curvature of the individual atomic layers which can result in topologically non-trivial

phases.5-7 Electron-doped twisted monolayer-bilayer graphene (tMBLG)—a graphene monolayer

rotationally misaligned with a Bernal-stacked bilayer—stands out among these since it exhibits the

quantum anomalous Hall (QAH) effect (i.e., quantized Hall conductance in the absence of external

magnetic field) accompanied by doping-controlled switching of its Chern number, an effect not

observed in other moiré QAH systems.8 Such behaviour is expected to be sensitive to local structural

parameters such as twist angle and hetero-strain (i.e., the relative strain between adjacent layers). For

example, twist angle directly affects the moiré mini-band structure while even small hetero-strains (<

0.5%) can be magnified by the moiré superlattice to induce large moiré distortions, thus altering the

energetics of mini-bands and the behaviour of emergent correlated and topological phases.9,10

Understanding the rich physics of moiré systems requires understanding the relationship between

exotic electronic phases and local structure, something difficult to achieve using macroscopic probes

that only explore spatially-averaged behaviour.

Here we show how scanning tunnelling microscopy and spectroscopy (STM/STS) enables

determination of how changes in local structure alter correlated and topological electronic behaviour

in tMBLG field-effect transistor devices. We find that tuning the electron doping concentration of

tMBLG results in the emergence of charge gaps observable to STS at filling levels ν = 2 and ν = 3

(i.e., two and three electrons per moiré unit cell), indicating the formation of correlated insulating

states. STS performed in an out-of-plane magnetic field allows us to detect non-trivial topology in

the ν = 3 QAH insulating state which has total Chern number Ctot = ±2, and to demonstrate its

dependence on local twist angle and hetero-strain. In addition to observing strong variation of

correlation and topological properties at different twist angles, we find that regions having nearly

identical twist angle but different hetero-strain values exhibit very different behaviour. In the small-

strain regime, the correlation gap evolves into two separate gaps at different gate voltages that

correspond to Ctot = +2 and Ctot = –2, indicating doping-controlled switching of valley polarization

consistent with previous electrical transport results.8 Such behaviour is absent, however, when large

hetero-strain is present, in which case only a single correlation gap with Ctot = +2 is observed. This

behaviour can be understood using a continuum model for tMBLG that reveals how Chern number

switching results from a competition between the bulk and edge contributions to orbital

magnetization that is highly sensitive to local hetero-strain. These results demonstrate the crucial role

that local structural parameters play in shaping correlation and topological effects in twisted moiré

systems.

Results

Correlated insulating behaviour at integer fillings. Figure 1a shows a schematic of our

experiment, which incorporates a gate-tunable graphene device into an STM measurement geometry.

A Bernal-stacked bilayer graphene is placed on top of a graphene monolayer with a twist angle θ

between them, and the stack is supported by a hexagonal boron nitride (hBN) substrate placed on a

SiO2/Si wafer (Methods, Supplementary Fig. 1). The carrier density n of the graphene stack can be

tuned continuously via voltage VG applied to the Si back-gate. Our devices were annealed in ultra-

high vacuum before being loaded into the STM system at T = 4.6 K for measurement (Methods).

Figure 1b shows a representative topographic image of the monolayer-bilayer moiré pattern which

exhibits an average wavelength of lM = 11.2 nm, from which we extracted a local twist angle of θ =

1.25° (Methods). Within each moiré unit cell (dashed box) we observe three representative regions

with different apparent heights that correspond to the three local tMBLG stacking orders: BAB, ABC,

and AAB (Supplementary Note 1).

We access correlated electronic states of tMBLG by tuning the carrier concentration via VG

and performing dI/dV spectroscopy. Figure 1c shows a density plot of gate-dependent dI/dV spectra

obtained in the BAB region. Estimation of the device capacitance allows us to convert VG to the

filling factor ν, defined as the average number of electrons/holes per moiré unit cell referenced to

charge neutrality (Methods). At ν = 0 (VG = 0 V) we observe two narrow peaks in the dI/dV spectrum

that are centred at VBias = 6 mV and VBias = –14 mV (Fig. 1d) that we identify as originating from van

Hove singularities of the four-fold degenerate conduction flat band (CFB) and valence flat band

(VFB). Increasing VG leads to partial occupation of the CFB and shifts both peaks toward lower

energy. As the filling level approaches ν = 2 the CFB peak gradually splits into two branches, CFB–

and CFB+, that are located below and above the Fermi energy EF (VBias = 0 mV). At ν = 2 (VG = 31.5

V) these two branches have roughly the same spectral weight and a clear charge gap can be observed

across EF (Fig. 1e). As the doping level is further increased from ν = 2 to ν = 2.5 (VG = 39 V), the

energy splitting between CFB– and CFB+ becomes smaller and the gap feature evolves into a

shallow dip (Fig. 1f). At ν = 3 (VG = 47 V) an insulating gap reappears at EF with CFB– having

significantly greater weight compared to CFB+ (Fig. 1g). Finally, at ν = 4 (VG = 62.5 V, full filling

of the CFB) the CFB– and CFB+ branches merge into a single peak that lies completely below EF

(Fig. 1h). The presence of charge gaps at ν = 2 and ν = 3 demonstrates the formation of correlated

insulating states at these filling factors, corroborating results from previous electrical transport

studies8,11-13 (Supplementary Note 2, Supplementary Figs. 2, 3).

Gate-switchable QAH insulating state. To discern the nature of the ν = 2, 3 correlated

insulating states in tMBLG, we applied an out-of-plane magnetic field B = (0, 0, B) to our sample

and performed gate-dependent dI/dV spectroscopy. Figure 2a-c shows density plots of gate-

dependent dI/dV spectra measured near ν = 2 for B = 0, 1, 2 T, respectively. The insulating gap

feature, marked by vanishing dI/dV at EF and maximum CFB peak splitting, always appears at the

same filling level (white arrows) regardless of the B value. dI/dV spectra measured near ν = 3 (Fig.

2d-i), however, exhibit very different field-dependent behaviour. The charge gap (white arrows) is

seen to remain constant in energy splitting (Supplementary Note 3) but to evolve into two separate

gaps for B > 0 T. These two gaps bracket ν = 3 and split away from it as B increases.

We can better visualize the magnetic field evolution of the ν = 3 correlated insulating state by

plotting normalized dI/dV at VBias = 0 mV (EF) as a function of both ν (VG) and B (Fig. 2j). The dark

region in the plot indicates vanishing dI/dV due to the emergence of a charge gap, which forms a V-

shape (white dashed lines) that is roughly symmetric about the ν = 3 horizontal line. This linear

scaling of the correlation gap position with magnetic field is reminiscent of correlated Chern

insulating states reported previously in magic-angle twisted bilayer graphene (MA-tBLG)14-16 where

the change in carrier concentration n of a Chern insulating state is related to the out-of-plane field B

through the Středa formula Δ𝑛

Δ𝐵 =𝐶tot

𝛷0 (Ctot is the total Chern number and Φ0 = h/e is the magnetic flux

quantum).17 Our observations thus imply that the ν = 3 insulating state in tMBLG has Chern number

Ctot = ±2 as derived from the slope of the lines in Fig. 2j. Two significant differences, however,

distinguish our results from those reported in MA-tBLG. First, Δn/ΔB linear scaling is observed in

MA-tBLG only under high external fields (B > 3 T) that break time-reversal symmetry and stabilize

the Chern insulating states, whereas such behaviour in tMBLG can be resolved in fields as low as B

= 0.2 T (Supplementary Fig. 4) and can be traced back to B = 0 T. Combined with the robust charge

gap at ν = 3, this indicates that the zero-field ground state of tMBLG is a topologically non-trivial

QAH insulator with spontaneous time-reversal symmetry breaking (Supplementary Note 4). Second,

each non-zero integer filling of MA-tBLG features only a single correlation gap that shifts

monotonically with increasing B, while in tMBLG we observe two separate gaps corresponding to

Ctot = +2 and Ctot = –2. This indicates that the total Chern number for the tMBLG QAH state is

switchable between +2 and –2 by simply tuning the carrier concentration across ν = 3.8

Tuning Chern number switching with twist angle and strain. Simultaneous structural

measurement via STM and local electronic characterization via STS provide a unique opportunity to

investigate how correlation and topological effects in tMBLG are affected by local structural

variations at the moiré scale. Figure 3a summarizes our experimental results as a function of local

twist angle and local hetero-strain obtained through analysis of moiré anisotropy in our STM

topographs (Methods). While the emergence of an insulating gap at ν = 2 is robust in all of our data,

the behaviour at ν = 3 depends strongly on both local twist angle and local hetero-strain. Gate-

tunability of the Chern number is only observed when the twist angle is between 1.25° and 1.28°, as

indicated by the green data points in Fig. 3a. When the twist angle increases slightly above this range

(orange data points) the charge gap at ν = 3 persists but Chern number switching is suppressed. Fig.

3b-d shows representative data from this regime in which the gap feature (white arrows) evolves

monotonically toward higher filling factors as the magnetic field is increased instead of developing

into two separate gaps. When the twist angle deviates even further the correlation gap at ν = 3

disappears (red data points in Fig. 3a; see Supplementary Fig. 5).

To reveal the effect of hetero-strain, we directly compare two regions with almost identical

twist angle (~1.26°) but different hetero-strain values (0.10% versus 0.24%) for the same device,

thus allowing other variables such as carrier concentration, electric field, and correlation strength to

be kept mostly constant. In the region with a smaller hetero-strain (Fig. 3e), the ν = 3 insulating gap

develops into two branches under application of an out-of-plane magnetic field (Fig. 3f), indicating

gate-induced switching between Ctot = +2 and Ctot = –2 QAH insulating states. In contrast, the region

with a larger hetero-strain (Fig. 3g) exhibits only one branch of the ν = 3 insulating gap (Fig. 3h; see

Supplementary Fig. 6), corresponding to Ctot = +2 with no gate-controlled switching.

Discussion

The emergence of correlated QAH insulating states in electron-doped tMBLG can be

understood as resulting from spontaneous symmetry breaking driven by electron-electron Coulomb

interactions. The CFB of tMBLG is four-fold degenerate due to spin and valley degrees of freedom.

Each CFB sub-band in the graphene K+ (K–) valley hosts a non-zero Chern number of C = +2 (–2)

due to the large Berry curvature inherited from constituent graphene layers.18,19 At integer fillings

(e.g., ν = 2 and ν = 3) strong correlation can drive spontaneous polarization along a certain axis in the

spin-valley space, splitting the CFB into occupied lower sub-bands (CFB–) and unoccupied upper

sub-bands (CFB+) separated by a charge gap as observed in the experimental dI/dV (Fig. 1e,g). At ν

= 3 the spin-valley polarization leads to breaking of time-reversal symmetry and topologically non-

trivial states with Ctot ≠ 0. Figure 4a shows one possible filling configuration with double occupancy

of CFB sub-bands in the K+ valley, resulting in a QAH insulating state with Ctot = +2. Similarly,

double occupancy of K– valley sub-bands can result in a Ctot = –2 state that is energetically

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1Localspectroscopyofagate-switchablemoiréquantumanomalousHallinsulatorCanxunZhang1,2,3,6,TiancongZhu1,2,6*,TomohiroSoejima1,6,SalmanKahn1,2,6,KenjiWatanabe4,TakashiTaniguchi5,AlexZettl1,2,3,FengWang1,2,3,MichaelP.Zaletel1,2*,MichaelF.Crommie1,2,3*1DepartmentofPhysics,UniversityofCalifornia,Berkeley,...

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1 Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator Canxun Zhang123 6 Tiancong Zhu126 Tomohiro Soejima16 Salman Kahn126 Kenji Watanabe4

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