Flat band detection by tunneling currents in van der Waals field effect structures

Flat band energy detection via tunneling currents in a field-effect structure. Such a method is potentially applicable to any flat band system. Furthermore, the landmark ambipolar transport in few-layer InSe is achieved, pivotal for emergent phenomena exploration in this material.
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Flat band detection by tunneling currents in van der Waals field effect structures

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Flat-bands and 2D semiconductors

Materials with flat band dispersions have recently captivated the broad attention of scientists and researchers due to their potential to unlock exotic properties and phenomena. In fact, flat dispersions allow a high density of states and can show the so-called van Hove singularities (Figure 1), leading to intriguing physics such as unconventional superconductivity, emergent magnetic states, and fascinating topological phenomena1–3. However, the electrical detection of the flat-band energy position in field-effect structures has been a longstanding challenge, hindering comprehensive investigations into the unique properties of such systems.

Figure 1. (a) Band structure of 3-layer InSe with a selenium vacancy. A van Hove singularity arises due to the band flattening at the point. (b) Density of states in a 3L-InSe which shows a sharp peak at the valence band maximum, as well as the donor (red) and acceptor (blue) states. The inset shows in logarithmic scale the region between the highest donor state and the beginning of the conduction band, with its minimum located at 1.54 eV with respect to the acceptor state.

Singularities – but how to find them?

Our story begins with the choice of InSe as our flat-band system of interest. InSe is a two-dimensional (2D) semiconductor belonging to the III-VI metal mono-chalcogenide family, characterized by remarkable electrical and optical properties that make it an attractive platform for optoelectronic devices4. The intriguing feature of InSe is its direct-to-indirect bandgap transition, which occurs as the number of layers decreases. This transition results in the formation of a flat-band dispersion and a van Hove singularity at the valence band edge, making it an ideal candidate for our explorative interests.

Pinpointing the energy position of the flat valence band of InSe has been an ongoing challenge for years. After the first seminal works4,5 and the theoretical predictions motivating strong research efforts6, several groups have attempted to observe hole transport in monolayer and few-layer InSe to locate the flat-band energy position in this material by electrical means. However, since the effective mass of carriers becomes higher as the band flatness increases, no successful report of hole transport has been reported to date. Until now, the van Hove singularity in InSe has been observed only with highly invasive and expensive techniques (ARPES, STS)7,8, with no reports on transport in few-layers field-effect structures.

To tackle this challenge, we devised a device geometry that allows us to circumvent the problems of lateral hole transport. We encapsulated InSe flakes in hexagonal boron nitride (hBN) and used few-layer graphite (FLG) flakes as electrodes. A FLG bottom gate allowed us to modulate the carrier density in the InSe layers. This geometry enabled us to study tunneling photo-currents, which would hold the key to detecting the elusive flat band.

What we observed

With such a device geometry and improved materials quality, we managed to observe for the first time ambipolar transport in a few-layer InSe device. However, we recorded a very weak hole transport with vanishing signals for very few layers of InSe - where the flatness is more pronounced. This observation finally convinced us that lateral transport in flat-band semiconductors is not well suited as an accurate probe to study the energy dispersions in such systems.

Therefore, we focused our attention on another type of transport that occurs in such devices: out-of-plane tunneling of carriers from the 2D semiconductor to the bottom gate. In fact, our experiments revealed that an out-of-plane tunneling photo-current emerges when the device is illuminated by a laser even at very low temperatures (80 mK). Most importantly, such tunneling currents exhibit a sharp exponential increase at specific gate voltages, precisely matching the hole conduction onset of lateral transport for different devices and different numbers of InSe layers (Figure 2). Indeed, high availability of states at the singularity position can induce a dominant transition in the tunneling current mechanism, thus explaining the exponential onset. By studying the optical response of InSe, we further excluded excitonic effects as the explanation for such a tunneling behavior, and we confirmed that our electrical signal effectively probes the entrance of the Fermi level in a flat dispersion.

This finding provided the first electrical detection of the flat-band position in a field effect structure. The tunneling mechanisms we observed shed light on the intricate interplay of carrier transport and excitonic properties, further enhancing our understanding of flat-band physics.

One significant advantage of our approach is that we only needed two electrodes to detect the flat band, making it a highly reproducible and practical method for future investigations. The high signal-to-noise ratios we achieved with tunneling photocurrents, even in thin InSe samples, showcased the versatility of our approach.

To take our investigation one step further, we extended the temperature range from 80mK up to room temperature without laser illumination. To our delight, we observed that the sharp transition in tunneling mechanisms remained largely unaffected by temperature changes. This reaffirmed the reliability of tunneling currents as a marker for the flat band position, even at higher temperatures and without laser illumination.

Figure 2. (a) The gate-dependent tunneling photocurrent data for 3L, 5L and 6L devices are reported blue, red and yellow dots, respectively, using a  scale. The direct (DT) and Fowler-Nordheim tunneling (FNT) regimes are separated by a sharp onset. (b) The ratio between the differential conductance and the tunneling conductance at low temperature for 5L and 6L devices, which follows the trend of the density of states.

Future outlook

We believe that our findings hold exciting implications for the exploration of flat-band physics in 2D materials. Few-layer InSe emerges as a promising and accessible platform to study emergent phenomena and correlated electronic states in van der Waals heterostructures by both optical and electrical means. Moreover, we infer that such a simple and reproducible device functioning principle can be employed for flat-band systems beyond InSe, and we are looking forward to other applications with other materials.

Thank you for joining us on this journey, and stay tuned for more exciting discoveries ahead!

For more details, please check out our paper titled “Electrical detection of the flat band dispersion in van der Waals field effect structures” in Nature Nanotechnology.


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