Theory predicts that when a semimetal or narrow band-gap semiconductor is in a charge-neutral state, electron-hole pairs can form under the influence of Coulomb interaction, resulting in the formation of "electron-hole" pairs. These quasi-particles can undergo Bose-Einstein condensation below a critical temperature, and their quantum ground state is known as an exciton insulator [1-2].
Over the past half-century, exciton insulators have been observed in various experimental systems, predominantly through indirect spectroscopic studies [3-6]. However, there is a notable lack of research on the electrical transport and gate-tuning of this correlated insulator. The main reason for this limitation is the difficulty in controlling the strength of electron correlations in semi-metallic systems (or narrow bandgap semiconductors) near charge neutrality. Common approaches to enhance electron correlations include manipulating the dielectric environment and tuning the effective mass of electrons (such as through the construction of flat bands) to suppress carrier kinetic energy and amplify the Coulomb effect.
We used a dry transfer method to fabricate a vertical heterostructure consisting of a bilayer graphene (BLG) with Bernal stacking and a few-layer antiferromagnetic insulator, chromium oxychloride (CrOCl), equipped with top gate and bottom gate, as shown in Figure 1. CrOCl is an air-stable layered antiferromagnetic insulator, and the interface formed with BLG exhibits atomic-level cleanliness. When this device is in the low-temperature ground state (at 1.5 K), under a perpendicular electric field, BLG exhibits an anomalous dual-gate modulation behavior, with a significant bending of the charge neutrality point (CNP) as shown in Figure 2a. In the bent region of the CNP, a novel insulating state is achieved with a resistance up to 10 Gigaohms. This is in stark contrast to the behavior of BLG encapsulated in hexagonal boron nitride (hBN). While the latter also exhibits a gap opening near the CNP under a perpendicular electric field, it only shows insulating behavior in a narrow gate region around the CNP, and the resistance monotonically increases with the electric field, typically reaching values in the megaohm range, as shown in Figure 2b.
The obtained field-effect curves of CrOCl-interfaced BLG shows insulating state of Gigaohms over a wide range of gate voltages, as shown in Figure 2c. This indicates a breakthrough in addressing the long-standing challenge of achieving “gap opening” in graphene systems, which is also the reason why transition metal dichalcogenides have been considered as better candidates for two-dimensional logic devices in recent years. Our experiment and theory indicate that the novel insulating state of the BLG coupled with the CrOCl interface is attributed to the synergistic interplay between graphene and a long-wavelength charge order (presumably a Wigner crystal) in the surface state in the underneath insulator [7, 8]. The subtle electron-electron interactions thus drive the system into the formation of an excitonic insulator. The main pieces of evidence are as follows:
- In this insulating phase, the thermal excitation gap above the critical temperature is on the order of 100 meV, and the effective vertical electric field estimated from the electrostatic model is on the order of 1 V/nm. These results cannot be explained solely by the classical single-electron bandgap picture.
- The insulating phase exhibits nonlinear I-V curves and shows a gate-tunable critical behavior at zero bias voltage, where the system rapidly insulates below a certain threshold temperature, resulting in resistance values beyond the experimental measurement range.
- The insulating phase can be disrupted by a small in-plane electric field and reverts back to the normal (metallic) state.
- The relationship between the in-plane electric field that kills the insulating phase and the sample size aligns with the theoretical expectation of an excitonic pair-breaking picture .
- By intercalating with boron nitride, the insulating phase completely disappears when the distance from the CrOCl surface is 6 nm, which is consistent with the theoretical calculations of the interaction profile.
Our theoretical modelings suggest that, under a vertical electric field, the charge in graphene can transfer to the interface state of CrOCl due to the alignment of surface band of CrOCl and the Fermi level of BLG, leading to spontaneous symmetric breaking and the formation of a charge order in the CrOCl surface state, with a wavelength ranging from a few nanometers to tens of nanometers. This long-range periodicity charge order (a hypothesis to be further confirmed by experiments) acts as a superlattice Coulomb potential, further enhancing the electron correlation in the overlying bilayer graphene. As a result, the electron-hole excitonic pairing at the charge neutrality point is strengthened, leading to the opening of a correlated band-gap. This phenomenon manifests as a quantum insulator in transport, which can be controlled by in-plane electric fields, vertical electric fields, temperature, carrier density, and other parameters.
Our findings suggest that, based on this correlated insulating state, both N-type and P-type doped transistors can be achieved by maintaining a fixed top gate (or bottom gate) and scanning the appropriate bottom gate (or top gate). These transistors exhibit a switching ratio of above 107 and possess strong robustness (Figure 3). Furthermore, by using two of such CrOCl/BLG/hBN devices in a configuration shown in Figure 3c we can obtain a graphene logic inverter with a gain of approximately 1.2 (yet to be improved) at a temperature of 1.5 K at an input voltage of 0.2 V. This is a crucial step forward for future carbon computing.
Unlike the conventional approaches based on intrinsic band gaps and doping principles in silicon-based semiconductors and two-dimensional semiconductors, the route of quantum-origin correlated gapped state employed in this study breaks new ground. It constructs long-range charge order at the interface by utilizing interface coupling and then leverages the interface states to influence electronic correlations in graphene. This coupling mechanism represents a universal control method and holds the potential for discovering intriguing physical phenomena in a broader range of two-dimensional electron systems.
For more details, please see the original version of the manuscript in Nature Communications
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