Coulomb Blockade Spectroscopy of a MoS2 Nanotube

Low‐temperature transport spectroscopy measurements on a quantum dot lithographically defined in a multiwall MoS2 nanotube are demonstrated. At T = 300 mK, clear Coulomb blockade is observed, with charging energies in the range of 1 meV. In single‐electron tunneling, discrete conductance resonances are visible at finite bias. Additionally, a magnetic field perpendicular to the nanotube axis reveals clear indications of quantum state transitions, with effective g factors consistent with published theoretical predictions.

When constraining two-dimensional electronic systems further to obtain quantum dots, zero-dimensional electronic systems with discrete quantum states, both generating welldefined boundary conditions and reaching a discrete density of states are significant challenges. Recently, semiconducting two dimensional transition metal dichalcogenides (TMDCs) have attracted interest as a potential material system for quantum dots. Based on the strong spin-orbit coupling, leading to a spin-split bandstructure, multiple types of electronic qubits, utilizing spin and valley degrees of freedom have been proposed [1][2][3][4]. Unlike III-V semiconductors, TMDCs in principle allow zero nuclear spin materials, avoiding hyperfine interactions with the electron spin.
From the experimental side, quantum dots have been defined in layers of MoS 2 [5][6][7][8][9][10], but also WSe 2 [11] and WS 2 [12]. The large electron effective mass, recently found to be m * ∼ 0.7m e for MoS 2 [13] and significantly exceeding previous density functional theory (DFT) results [2,14], leads to a small level spacing. Consequently, so far it has been a challenge to reach the regime of single quantum level transport in nanofabricated TMDC quantum dots. Discrete level spectroscopy would allow a detailed analysis of the coupled spin/valley physics in the TMDC conduction band.
Here, we present first transport spectroscopy data on a quantum dot defined in a semiconducting multiwall MoS 2 nanotube. Similar to carbon nanotubes [15,16] and semiconducting nanowires [17,18], the geometry creates a quasi one-dimensional confinement, with intrinsically larger singleparticle energy scales. Low temperature measurements performed at 300 mK are dominated by Coulomb blockade, with regular Coulomb oscillations and features of quantum confinement. In a perpendicular magnetic field, we observe clear indications of quantum state transitions, with effective g-factors consistent with published theoretical predictions.
MoS 2 nanotubes are grown by a chemical transport reaction in a two-zone furnace, using iodine as transport agent [19,20]. The slow, near-equilibrium growth from the vapour phase leads to clean multiwall nanotubes with lengths up to hundreds of micrometers, and relatively small density of defects in comparison with other types of growth. As shown in Figures 1(a)-(b), the tubes grow individually without forming ropes or bundles. Typical diameters range from ∼ 10 nm up to several micrometers. The nanotubes are hollow with a wall thickness from 25 % to 30 % of their diameter. The wall of the MoS 2 nanotube presented in Figure 1(c) is composed of 25 to 26 molecular layers. Its diameter is 52 ± 0.2 nm. The electron diffraction pattern of Figure 1(c) reveals that the nanotube has grown in a chiral mode. All walls share a similar angle of chirality α ∼ 16 • [21,22]. From the growth ampule, the nanotubes are transfered to a highly p-doped silicon wafer with a 500 nm thick thermally grown surface oxide. The transfer is performed using wafer dicing tape with low adhesion. This way, a large number of individual nanotubes can be spread over the chip surface and can subsequently be detected using optical microscopy. SEM imaging of the nanotubes or the finished devices is not performed to avoid charging of traps in the SiO 2 surface and contamination with hydrocarbons. Figure 1(d) shows an optical micrograph of the nanotube used for device 1. Based on previous comparisons of optical and SEM micrographs, we estimate a diameter of 20 nm-50 nm. The device design is sketched in Figure 1(e). Contacts with a separation of ∼ 450 nm are defined using standard electron beam lithography, followed by deposition of 30 nm of scandium and 80 nm of gold. To avoid formation of high Schottky tunnel barriers at the contacts, we use scandium as contact metal because of its low work-function [23,24]. Tensile strain in the tube potentially leads to an increase of the MoS 2 affinity energy and thus contributes to a further reduction of the Schottky barrier [25].
At room temperature, the fabricated devices show linear I(V SD ) characteristics with typical resistances on the order of ∼ 1 MΩ. When cooled to 300 mK, all studied devices display nonlinear I(V SD ) behavior, with a suppression of current around zero bias voltage. Figure 2(a) shows a resulting stability diagram. We observe a sequence of Coulomb oscillations with high regularity, indicating the formation of a quantum dot on the contacted tube segment.
In addition, in Figure 2(a) a clear threshold bias voltage of V SD ∼ 4 mV is visible. This indicates that the electronic system consists of a chain of several quantum dots [26]. Unlike the typical shard-like features in a disordered system of quantum dots, here the onset of neighbouring single electron tunneling (SET) regions is at similar bias voltage; also, only a single set of slopes of the SET region edges is observed, see Figure 2 the potential of the back gate is mostly screened. The deposition of reactive metals as, e.g., scandium, leads to interfacial reactions with MoS 2 as likely cause of such additional trap states [27,28].
The overall conducance data quality is reminiscent of early works on carbon nanotubes, where the macromolecule was (as it is here) in direct contact with a SiO 2 substrate surface, its dangling bonds and disorder. Either suspending the nanotube or encapsulating it into hexagonal BN is thus likely to lead to significantly cleaner and more stable transport spectra.
Analysing the sequence of Coulomb diamonds highlighted in Figure 2(a), we extract an average gate conversion factor α G = 0.048 and an average gate voltage spacing ∆V G = 23 mV. From this we calculate a charging energy E C = e α G ∆V G = 1.1 meV and a gate capacitance C G = e/∆V G = 7 aF. The expected value of the geometric gate capacitance is C G,th = 2πLε 0 ε r / ln(2h/r) with the channel length L, the tube radius r, the thickness of the dielectric layer h, and an empirical effective dielectric constant ε r = 2.2 [29]. Choosing L = 450 nm, r = 10 nm, and h = 500 nm yields a value C G,th = 12 aF, in good agreement with the measurement, indicating that the size of the quantum dot is defined by the metal electrodes [30][31][32].  Figure 2(b) with a dashed rectangle. Within the single electron tunneling region, pronounced discrete conductance resonances corresponding to an excitation energy ∆E ∼ 500 µeV are visible. Such a large single-particle excitation energy is a strong indication that we have reached the limit of one-dimensional confinement, where the level spacing is proportional to the number of charges on the quantum dot, similar to measurements on semiconducting nanowires [30].
Finally, we have collected first data on the influence of a perpendicular magnetic field on the current through the quantum dot. Figure 3 shows a measurement of I(V G , B) over a sequence of four Coulomb oscillations at a fixed finite bias voltage V SD = −3.5 mV, tracing across the "tips" of the SET regions, as indicated in the insert of Figure 3. The conductance maxima shift gate voltage position, with slopes comparable to Zeeman phenomena at g 2, and multiple apparent quantum state transitions. This is in good agreement with DFT-based results on circular quantum dots in two-dimensional MoS 2 , predicting both spin and valley effective g-factors on this order of magnitude [2]. For the case of MoS 2 nanotubes, or generally TMDC nanotubes, further theoretical modeling is needed to uncover the precise electronic structure in strong magnetic fields.
In conclusion, we have performed first low-temperature transport experiments on a transition metal dichalcogenide multiwall nanotube quantum dot. A chemical vapour transport reaction with slow, near equilibrium growth conditions leads to clean MoS 2 nanotubes with very low intrinsic disorder. By using scandium contacts, we avoid the formation of Schottky barriers at the contacts. Current measurements at 300 mK are dominated by Coulomb blockade, with regular Coulomb oscillations and clear resonant features in nonlinear transport overlaid on a low-bias region of suppressed conductance. In a perpendicular magnetic field, we observe clear indications of quantum state transitions, with effective g-factors consistent with published calculations [2].
The low-bias suppression of conductance is a typical feature of an array of multiple quantum dots, however, the measurement shows that this disorder is limited to the contact regions. Future work shall improve the contact properties, towards detailed single quantum dot level spectroscopy in aligned magnetic fields and exploration of the confinement spectrum in the band structure of the material. An obvious next step is also to encapsulate or suspend the nanotubes, to suppress substrate charge influences. Furthermore, WS 2 nanotubes have already been shown to exhibit intrinsic superconductivity at strong doping [33,34], pointing towards the possibility of intrinsic one-dimensional semiconductor-superconductor heterostructures within a single macromolecule.
The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft via SFB 1277, by the DAAD via the PPP Slovenia program, grant no. 57401796, and by the Slovenian Research Agency. We would like to thank Ch. Strunk and D. Weiss for the use of experimental facilities. The data has been recorded using the Lab::Measurement software package [35].