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Tuesday, April 16, 2024

Electrical detection of the flat-band dispersion in van der Waals field-effect buildings


Machine construction and band diagrams of few-layer InSe

To acquire high-quality samples, we encapsulate γ-phase InSe flakes in hBN and use few-layer graphite (FLG) flakes as electrodes. We use a FLG backside gate to modulate the service density within the semiconductor. The entire gadget schematic is reported in Fig. 1b, representing an optically excited heterostructure based mostly on InSe. In Fig. 1a, an instance of a 3L InSe gadget is proven in false color to focus on the stacked layers. The band construction for 3 layers of InSe was obtained by density purposeful concept (DFT) calculations accounting for the presence of selenium vacancies (VSe), the commonest kind of defects in few-layer InSe as a result of their low formation power19,20 (Supplementary Notice 1). These defects produce two peaks within the DOS near the conduction band and a peak at roughly 150 meV from the valence band, as proven in Fig. 1c,d. In few-layer InSe, a pointy DOS enhance characterizes the VBM place (Fig. 1e) because of the look of a van Hove singularity.

Fig. 1: Schematic and band construction of an encapsulated InSe gadget.
figure 1

a, Optical microscope image of the 3L gadget with layers highlighted in false color. FLG, InSe and hBN layers are depicted in gray, violet and blue, respectively. Scale bar, 20 μm. b, Three-dimensional schematic representing an hBN-encapsulated InSe layer with graphene contacts and a large again gate. The pattern is optically excited utilizing a pink laser and excitonic species are fashioned throughout the semiconductor. When a gate voltage is utilized, holes in InSe can tunnel by means of the underside hBN giving rise to a tunnelling photocurrent. {The electrical} measurement scheme is proven on the correct. c, Band alignment of the supplies of curiosity within the gadget of Fig. 1b. Two electron donor (pink) and one acceptor (blue) states are induced by the presence of selenium vacancies. d, Band construction of the 3L slab of InSe with a selenium emptiness. A van Hove singularity arises because of the band flattening on the Γ level. e, The DOS in a 3L-InSe reveals a pointy peak on the VBM, in addition to the donor (pink) and acceptor (blue) states. The inset reveals in logarithmic scale the area between the best donor state and the start of the conduction band, with its minimal positioned at 1.54 eV with respect to the acceptor state.

By taking defect states under consideration, we clarify the character of lateral gap transport in InSe gadgets and the change in tunnelling behaviour on the level comparable to the flat-band place. Furthermore, our calculations reveal valence-band offsets on the order of tons of of meVs in heterostructures with FLG-contacted few-layer InSe on prime of hBN (Fig. 1c and Supplementary Fig. 1), unveiling a notably asymmetrical alignment when in comparison with the band offsets on the conduction band (roughly 3.8 eV). This asymmetry is essential for {the electrical} detection of the DOS on the van Hove singularity on the VBM.

We notice that band alignments obtained by DFT calculations are identified to be vulnerable to variabilities21. Right here, we use hybrid and meta-GGA functionals in DFT calculations to achieve semiquantitative insights into the highly-asymmetrical band alignment between few-layer InSe and hBN. The calculated values of the band alignment are within the vary of tons of of meV for holes, which additional confirms our findings concerning the order of magnitude of the obstacles extracted experimentally from tunnelling photocurrent measurements, as offered within the following sections.

Lateral transport and tunnelling photocurrent

On Fig. 2a we current the gate dependence of the lateral present in our 3L and 6L gadgets. We observe ambipolar transport with dominant n-type transport5,6 whereas p-type conduction is strongly suppressed as a result of comparatively excessive gap efficient plenty in comparison with the electron ones (Supplementary Desk 1). The profitable remark of subthreshold p-type lateral currents in our gadgets is attributed to the mixture of utilizing a high-purity InSe crystal supply (HQ Graphene) and full hBN-encapsulation with lateral graphene electrodes. This ensures that the InSe flakes are by no means uncovered to air at any level throughout gadget dealing with (Strategies). A visual lower within the p-type subthreshold slope is seen within the 3L with respect to the 6L gadget, in line with the discount of the outlet efficient mass with an rising variety of InSe layers, as mentioned in Supplementary Notes 1 and 2.

Fig. 2: Area-effect transport and tunnelling photocurrent with few-layer InSe.
figure 2

a, Area-effect lateral transport within the 3L (measured at 80 mK) and 6L gadgets in logarithmic scale. Subthreshold p-type conduction was achieved in each samples. Notice a decrease subthreshold slope within the 3L with respect to the 6L gadget (Supplementary Notice 2). The inset highlights the onset of p-type conduction within the 3L gadget (({V}_{mathrm{ON}}^{3{mathrm{L}}}simeq-6.4,{mathrm{V}})). b, The gate-dependent lateral present between the FLG contacts in a 6L gadget (black) reveals predominantly n-type conduction in linear scale. The dashed gray line signifies the onset of n-type conduction. A gate-dependent tunnelling photocurrent is induced when the pattern is illuminated utilizing a 633 nm laser at 50 µW of energy (yellow). The behaviour of the tunnelling present could be divided into two predominant areas, that are separated by a yellow dashed line with respect to the gate voltage. c, The gate-dependent tunnelling photocurrent knowledge for 3L, 5L and 6L gadgets are reported in blue, pink and yellow circles, respectively, utilizing the (mathrm{ln}left(|{I}_{mathrm{G}}textual content/{V}_{mathrm{G}}^{2}proper)) scale with respect to −1/VG for VG < −1 V. The tunnelling behaviour is modelled utilizing Simmons’ approximation, with direct tunneling (DT) and FNT regimes separated by a pointy onset. FNT fittings reveal efficient obstacles for tunnelling holes of 237, 340 and 292 meV for 3L, 5L and 6L samples, respectively. d, Ratio between the differential conductance and the tunnelling conductance at low temperature for 5L and 6L gadgets. The weaker 3L sign doesn’t permit us to look at adjustments within the normalized conductance at cryogenic temperature. Additional dialogue on the temperature dependence of the dIG/dVG indicators is supplied in Supplementary Notice 3.

Illumination of the gadget with a laser beam (λ = 633 nm) ends in the looks of an out-of-plane tunnelling present between the InSe layers and the FLG gate, proven on Fig. 2b for the 6L gadget along with the lateral present as a operate of gate voltage. The tunnelling present reveals a speedy enhance at VG = −3.5 V, carefully matching the outlet conduction onset voltage VON6L= −3.6 V. Photocurrents for gadgets with various thicknesses (3L, 5 layers (5L) and 6L) are proven in Fig. 2c on a logarithmic scale, revealing two predominant areas with linear and logarithmic developments, respectively. This behaviour is paying homage to the separation between direct tunnelling (DT) and Fowler–Nordheim tunnelling (FNT) mechanisms in digital gadgets resembling metal-insulator-metal diodes22,23 and could be modelled utilizing Simmons’ approximation22,24 (Supplementary Notice 3). To carry out the becoming underneath Simmons’ approximation, we’ve got used the measured backside hBN thicknesses of 20, 25 and 18 nm for the 3L, 5L and 6L gadgets, respectively (Strategies). The FNT half permits us to extract the tunnel barrier heights. We confer with the place of fixing developments because the transition voltage VTRAN, which for the 6L gadget happens at −3.5 V whereas for the 3L pattern, ({V}_{mathrm{TRAN}}^{3{mathrm{L}}},)= (-5.8,{mathrm{V}}), near the onset of p-type conductivity ({V}_{mathrm{ON}}^{3{mathrm{L}}}simeq-6.4,{mathrm{V}}).

To rule out the chance that the drastic change within the tunnelling transition is because of change within the transmission likelihood, we contemplate the differential tunnelling conductance dIG/dVG normalized over the full conductance IG/VG (Fig. second). As beforehand reported25, the looks of a peak within the (dIG/dVG)/(IG/VG) curve signifies that the rise of the tunnelling sign is because of a sudden change within the materials DOS (Supplementary Notice 3).

Relationship between tunnelling mechanisms and excitons

To know the sharp transition within the tunnelling photocurrent within the presence of a van Hove singularity on the VBM, we examine tunnelling photocurrent measurements with gate-dependent photoluminescence spectroscopy (Fig. 3a), permitting us to establish completely different excitonic species and defect-bound states8. We focus our consideration on the redshift of the primary excitonic species within the p-type area X+, along with its sturdy suppression of emission for ({V}_{mathrm{G}}^{6{mathrm{L}}} < -3.5,{mathrm{V}}). This corresponds to the Fermi degree crossing into the valence band and the accompanying BGR on the flat band. This voltage additionally coincides with the onset of the tunnelling photocurrent within the 6L gadget (Fig. 3b) and gap accumulation within the semiconductor. Related behaviour is proven in Supplementary Notice 5 for the 5L gadget.

Fig. 3: Excitonic emission and tunnelling mechanisms with few-layer InSe.
figure 3

a, Gate-dependent photoluminescence (PL) spectra for the 6L gadget. The change in the primary excitonic peaks with respect to gate voltage is said to completely different cost configurations (Supplementary Notice 4). When the Fermi degree within the semiconductor enters the valence band (gray dashed line), the best power peak shifts linearly with respect to the gate voltage as a result of BGR within the presence of a dense gap Fermi sea. b, Peak place of the best power excitonic species (pink) and tunnelling photocurrent (yellow) within the neighborhood of the VBM. The direct tunnelling (DT)-to-FNT transition (({V}_{mathrm{TRAN}}^{5{mathrm{L}}})) and the BGR begin (({V}_{mathrm{BGR}}^{5{mathrm{L}}}) are highlighted by dashed yellow and pink strains, respectively. c, Energy-dependent tunnelling photocurrent for the 5L gadget (Supplementary Notice 5) when the Fermi degree lies throughout the bandgap (blue) or has entered the valence band (pink). The superlinear behaviour of the previous case signifies that second-order excitonic results play a task, which is excluded throughout the valence band. d, Auger and exciton–exciton recombination mechanisms can radiatively switch their power to resident carriers and induce hot-hole tunnelling by means of a thick hBN barrier within the presence of a vertical electrical discipline (EV<EF<ED). When the Fermi degree lies throughout the valence band (EF<EV), excitonic species are topic to interactions with the Fermi sea induced by the excessive DOS and straight photo-excited holes are answerable for the photocurrent by FNT by means of the hBN barrier (proper). e, Transition voltage (VTRAN), BGR crossover (VBGR) and p-type onset (VON) for the 3L, 5L and 6L gadgets. The 5L pattern was not geared up with two FLG contacts for lateral transport measurements, and the depth of photoluminescence emission within the 3L pattern was too low to be analysed as a operate of gate voltage. f, Layer-dependent efficient tunnelling barrier extracted from FNT fittings (Fig. 2b) and valence-band offsets obtained from DFT calculations (Supplementary Fig. 1). The efficient barrier values are offered as imply values (dots) and corresponding customary deviations (error bars).

In Fig. 3c, we present the excitation energy (P) dependence of the tunnelling photocurrent (I) within the p-type area (VG = −7 V) and throughout the bandgap (VG=3 V), displaying a linear and a superlinear behaviour, respectively. IPα dependence with ɑ 2 is often attributed to second-order mechanisms resembling exciton–exciton annihilation26. For 1 < α < 2, first-order recombination pathways additionally play a task, primarily represented by Auger processes27. Right here, non-radiative exciton recombination ends in power switch to cost carriers, which develop into sufficiently excited to tunnel by means of the hBN barrier within the presence of a vertical electrical discipline. The efficient tunnelling barrier extracted for the Fowler–Nordheim area lies within the vary of a number of hundred meV for 3L, 5L and 6L gadgets, with values which can be comparable with the calculated valence-band offsets for the respective buildings (Supplementary Fig. 1).

Earlier stories have proven the excitation of cost carriers by means of Auger recombination and vertical photocurrent as a result of hot-carrier tunnelling for different 2D supplies24,27,28. Nonetheless, no DOS-dependent sharp transition between direct tunnelling and FNT areas could be recognized in both our TMDC-based samples (Supplementary Notice 6) or within the literature, the place the rise in photocurrent is attributed to the bending of the hBN bands by an rising electrical discipline. A distinct mechanism is due to this fact wanted to clarify the sharp transition between direct tunnelling and FNT areas in InSe. In our case, the aforementioned suppression of photoluminescence from X+, along with the discount of the ability coefficient α with the onset of gap conduction, each point out that exciton densities are lowered when the Fermi degree enters the valence band. Because the technology issue is fastened solely by the enter optical energy (Supplementary Notice 4), we infer that, within the p-type area, Auger recombination performs a minor position within the tunnelling pathways from InSe by means of the hBN barrier.

Even when hot-carrier excitonic-assisted tunnelling have been allowed in our system, it could not be a probable origin of the sharp onset in photocurrent for the reason that efficient barrier seen by holes is corresponding to the one predicted by DFT (Fig. 3f). Instantly photo-excited carriers have additionally been beforehand reported as a contribution to out-of-plane currents26,29. Nonetheless, in our case, the magnitude of the extracted efficient barrier signifies that tunnelling carriers are probed within the neighborhood of the VBM and never from power ranges deep throughout the valence band (Fig. 3d). On the idea of our understanding of the power-dependent photocurrent and the BGR, we attribute the sharp onset of the photo-assisted course of to a change of the primary tunnelling species from scorching carriers assisted by recombining defect-bound excitons (VTRAN<VG< 0 V) to straight photo-excited holes positioned on the VBM (VG<VTRAN).

We notice that the profitable detection of the flat-band place by tunnelling mechanisms depends on the beneficial band alignment between the van Hove singularity place and the dielectric barrier, in addition to the thickness and out-of-plane service efficient mass of the dielectric itself (Supplementary Notice 8). Specifically, we need to stress that additional research on the band alignment between dielectric supplies and 2D flat-band programs are wanted to use tunnelling mechanisms for investigating their properties. Therefore, the tactic proposed on this examine could be efficiently generalized to different programs, supplied that the gadgets are engineered to acquire a sizeable exponential tunnelling present following the optimization of the aforementioned parameters.

Room-temperature tunnelling present

The low exciton binding power in InSe (roughly 10 meV)12, along with the will to research emergent physics on the flat band1,2, motivated preliminary measurements carried out at low temperatures. Extending the temperature vary can additional improve our understanding of the tunnelling mechanisms in few-layer InSe. In Fig. 4a we present the tunnelling present measured with out laser illumination at 80 mK (black) and 295 Ok (pink). At 80 mK, the darkish present displays a linear relationship with respect to VG, with no observable change in tunnelling mechanisms within the gate voltage vary of curiosity. Nonetheless, at room temperature we observe a pointy transition in tunnelling mechanisms from direct tunnelling to FNT. In actual fact, larger temperatures are associated to a rise in tunnelling possibilities and in photocurrent sign magnitudes30. Furthermore, the room-temperature transition voltage is in line with that obtained at low temperatures underneath laser illumination (({V}_{mathrm{TRAN}}^{,mathrm{RT}}simeq 5,{mathrm{V}})), as highlighted within the inset of Fig. 4a. This means that gap tunnelling from the VBM is dominating each at room temperature at the hours of darkness, the place thermally enhanced out-of-plane transport of holes on the van Hove singularity is straight detectable, and at low temperatures with gentle, the place straight photo-excited carriers close to the VBM are extracted because of excessive electrical fields. The temperature change solely impacts the magnitude of the detectable sign with out influencing the origin of the tunnelling present. This confirms that the change in tunnelling mechanisms of out-of-plane currents is because of the Fermi degree reaching the van Hove singularity within the DOS on the InSe VBM, and guidelines out excitonic results.

Fig. 4: Temperature-dependent lateral transport and tunnelling present.
figure 4

a, Tunnelling present within the 3L gadget with out laser illumination at 100 mK (black) and 295 Ok (pink). The logarithmic dependence within the (mathrm{ln}left(|{I}_{mathrm{G}}textual content/{V}_{mathrm{G}}^{2}proper)) scale with respect to −1/VG for VG < −1 V reveals no transition at the hours of darkness at low temperatures and a pointy transition at room temperature. Within the inset, the tunnelling photocurrent at 100 mK (blue) is in contrast with the darkish tunnelling present at room temperature, revealing a comparable development within the Fowler–Nordheim regime (1/VG < −0.2 V and a transition voltage of round 5 V for each instances. b, Lateral p-type transport for the 3L gadget at 100 mK (blue) and 295 Ok (violet). The thermal broadening as a result of Fermi–Dirac scaling with temperature induces a shift within the first-detectable subthreshold p-type sign33, as additional mentioned in Supplementary Notice 2. Nonetheless, no substantial change within the subthreshold slope is detected. Within the inset, the p-type subthreshold slopes (SSp) of the 3L (blue) and 6L (yellow) gadgets are proven. The sizeable distinction in magnitude of ({mathrm{SS}}_{mathrm{p}}^{3{mathrm{L}}}) and ({mathrm{SS}}_{mathrm{p}}^{6{mathrm{L}}}) each at room and cryogenic temperatures is said to the rise in gap efficient mass in InSe for a lowering variety of layers.

We additional observe a change within the lateral transport of holes at high and low temperatures (Fig. 4b). In actual fact, the presence of in-gap defect states influences the transport traits, as mentioned in Supplementary Notice 2. As a result of excessive gap efficient mass (Supplementary Notice 1), it’s tough to establish the valence-band edge from the onset of gap conduction in thinner InSe samples (n ≤ 3L). This explains the upper discrepancy within the portions of curiosity proven in Fig. 3e between 3L and thicker samples. We are able to conclude that, whereas the onset of p-type conduction in our InSe gadgets is affected by the presence of defect states at room temperature, the tunnelling present transition voltage stays unaffected. Such a end result helps using tunnelling currents as a dependable mechanism to electrically detect van Hove singularities of flat-band programs in field-effect gadgets.

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