Multi-Valley Superconductivity in Ion-Gated MoS2 Layers

Ultrafast Charge Transfer and Recombination Dynamics in Monolayer-Multilayer WSe2 Junctions Revealed by Time-Resolved Photoemission Electron Microscopy

The ultrafast carrier dynamics of junctions between two chemically identical, but electronically distinct, transition metal dichalcogenides (TMDs) remains largely unknown. Here, we employ time-resolved photoemission electron microscopy (TR-PEEM) to probe the ultrafast carrier dynamics of a monolayer-to-multilayer (1L-ML) WSe2 junction. The TR-PEEM signals recorded for the individual components of the junction reveal the sub-ps carrier cooling dynamics of 1L- and 7L-WSe2, as well as few-ps exciton-exciton annihilation occurring on 1L-WSe2. We observe ultrafast interfacial hole (h) transfer from 1L- to 7L-WSe2 on an ∼0.2 ps time scale. The resultant excess h density in 7L-WSe2 decays by carrier recombination across the junction interface on an ∼100 ps time scale. Reminiscent of the behavior at a depletion region, the TR-PEEM image reveals the h density accumulation on the 7L-WSe2 interface, with a decay length ∼0.60 ± 0.17 μm. These charge transfer and recombination dynamics are in agreement with ab initio quantum dynamics. The computed orbital densities reveal that charge transfer occurs from the basal plane, which extends over both 1L and ML regions, to the upper plane localized on the ML region. This mode of charge transfer is distinctive to chemically homogeneous junctions of layered materials and constitutes an additional carrier deactivation pathway that should be considered in studies of 1L-TMDs found alongside their ML, a common occurrence in exfoliated samples.

Formation of Highly Conductive Interfaces in Crystalline Ionic Liquid-Gated Unipolar MoTe2/h-BN Field-Effect Transistor

2H MoTe2 (molybdenum ditelluride) has generated significant interest because of its superconducting, nonvolatile memory, and semiconducting of new materials, and it has a large range of electrical properties. The combination of transition metal dichalcogenides (TMDCs) and two dimensional (2D) materials like hexagonal boron nitride (h-BN) in lateral heterostructures offers a unique platform for designing and engineering novel electronic devices. We report the fabrication of highly conductive interfaces in crystalline ionic liquid-gated (ILG) field-effect transistors (FETs) consisting of a few layers of MoTe2/h-BN heterojunctions. In our initial exploration of tellurium-based semiconducting TMDs, we directed our attention to MoTe2 crystals with thicknesses exceeding 12 nm. Our primary focus centered on investigating the transport characteristics and quantitatively assessing the surface interface heterostructure. Our transconductance (gm) measurements indicate that the very efficient carrier modulation with an ILG FET is two times larger than standard back gating, and it demonstrates unipolarity of the device. The ILG FET exhibited highly unipolar p-type behavior with a high on/off ratio, and it significantly increased the mobility in MoTe2/h-BN heterochannels, achieving improvement as one of the highest recorded mobility increments. Specifically, we observed hole and electron mobility values ranging from 345 cm2 V-1 s-1 to 285 cm2 V-1 s-1 at 80 K. We predict that our ability to observe the intrinsic, heterointerface conduction in the channels was due to a drastic reduction of the Schottky barriers, and electrostatic gating is suggested as a method for controlling the phase transitions in the few layers of TMDC FETs. Moreover, the simultaneous structural phase transitions throughout the sample, achieved through electrostatic doping control, presents new opportunities for developing phase change devices using atomically thin membranes.

Spin-Valley Locking for In-Gap Quantum Dots in a MoS2 Transistor

Spins confined to atomically thin semiconductors are being actively explored as quantum information carriers. In transition metal dichalcogenides (TMDCs), the hexagonal crystal lattice gives rise to an additional valley degree of freedom with spin-valley locking and potentially enhanced spin life and coherence times. However, realizing well-separated single-particle levels and achieving transparent electrical contact to address them has remained challenging. Here, we report well-defined spin states in a few-layer MoS₂ transistor, characterized with a spectral resolution of ∼50 μeV at T_el = 150 mK. Ground state magnetospectroscopy confirms a finite Berry-curvature induced coupling of spin and valley, reflected in a pronounced Zeeman anisotropy, with a large out-of-plane g-factor of g_⊥ ≃ 8. A finite in-plane g-factor (g_∥ ≃ 0.55-0.8) allows us to quantify spin-valley locking and estimate the spin-orbit splitting 2Δ_SO ∼ 100 μeV. The demonstration of spin-valley locking is an important milestone toward realizing spin-valley quantum bits.

Full Control of Solid-State Electrolytes for Electrostatic Gating

Ionic gating is a powerful technique to realize field-effect transistors (FETs) enabling experiments not possible otherwise. So far, ionic gating has relied on the use of top electrolyte gates, which pose experimental constraints and make device fabrication complex. Promising results obtained recently in FETs based on solid-state electrolytes remain plagued by spurious phenomena of unknown origin, preventing proper transistor operation, and causing limited control and reproducibility. Here, a class of solid-state electrolytes for gating (Lithium-ion conducting glass-ceramics, LICGCs) is explored, the processes responsible for the spurious phenomena and irreproducible behavior are identified, and properly functioning transistors exhibiting high density ambipolar operation with gate capacitance of ≈ 20   -   50   µ F c m - 2 \[20{\bm{ - }}50\;\mu F c{m^{{\bm{ - }}2}}\] (depending on the polarity of the accumulated charges) are demonstrated. Using 2D semiconducting transition-metal dichalcogenides, the ability to implement ionic-gate spectroscopy to determine the semiconducting bandgap, and to accumulate electron densities above 10¹⁴ cm^-2 are demostrated, resulting in gate-induced superconductivity in MoS₂ multilayers. As LICGCs are implemented in a back-gate configuration, they leave the surface of the material exposed, enabling the use of surface-sensitive techniques (such as scanning tunneling microscopy and photoemission spectroscopy) impossible so far in ionic-gated devices. They also allow double ionic gated devices providing independent control of charge density and electric field.

Impact of Large Gate Voltages and Ultrathin Polymer Electrolytes on Carrier Density in Electric-Double-Layer-Gated Two-Dimensional Crystal Transistors

Electric-double-layer (EDL) gating can induce large capacitance densities (∼1-10 μF cm^-2) in two-dimensional (2D) semiconductors; however, several properties of the electrolyte limit performance. One property is the electrochemical activity which limits the gate voltage (V_G) that can be applied and therefore the maximum extent to which carriers can be modulated. A second property is electrolyte thickness, which sets the response speed of the EDL gate and therefore the time scale over which the channel can be doped. Typical thicknesses are on the order of micrometers, but thinner electrolytes (nanometers) are needed for very-large-scale-integration (VLSI) in terms of both physical thickness and the speed that accompanies scaling. In this study, finite element modeling of an EDL-gated field-effect transistor (FET) is used to self-consistently couple ion transport in the electrolyte to carrier transport in the semiconductor, in which density of states, and therefore quantum capacitance, is included. The model reveals that 50 to 65% of the applied potential drops across the semiconductor, leaving 35 to 50% to drop across the two EDLs. Accounting for the potential drop in the channel suggests that higher carrier densities can be achieved at larger applied V_G without concern for inducing electrochemical reactions. This insight is tested experimentally via Hall measurements of graphene FETs for which V_G is extended from ±3 to ±6 V. Doubling the gate voltage increases the sheet carrier density by an additional 2.3 × 10¹³ cm^-2 for electrons and 1.4 × 10¹³ cm^-2 for holes without inducing electrochemistry. To address the need for thickness scaling, the thickness of the solid polymer electrolyte, poly(ethylene oxide) (PEO):CsClO₄, is decreased from 1 μm to 10 nm and used to EDL gate graphene FETs. Sheet carrier density measurements on graphene Hall bars prove that the carrier densities remain constant throughout the measured thickness range (10 nm-1 μm). The results indicate promise for overcoming the physical and electrical limitations to VLSI while taking advantage of the ultrahigh carrier densities induced by EDL gating.

Multivalley Superconductivity in Monolayer Transition Metal Dichalcogenides

In transition metal dichalcogenides (TMDs), Ising superconductivity with an antisymmetric spin texture on the Fermi surface has attracted wide interest due to the exotic pairing and topological properties. However, it is not clear whether the Q valley with a giant spin splitting is involved in the superconductivity of heavily doped semiconducting 2H-TMDs. Here by taking advantage of a high-quality monolayer WS₂ on hexagonal boron nitride flakes, we report an ionic-gating induced superconducting dome with a record high critical temperature of ∼6 K, accompanied by an emergent nonlinear Hall effect. The nonlinearity indicates the development of an additional high-mobility channel, which (corroborated by first principle calculations) can be ascribed to the population of Q valleys. Thus, multivalley population at K and Q is suggested to be a prerequisite for developing superconductivity. The involvement of Q valleys also provides insights to the spin textured Fermi surface of Ising superconductivity in the large family of transition metal dichalcogenides.

The nearly free electron states and the conductivity limited by electron-phonon scattering of an OH-terminated MXene material, a case study of the Hf2C(OH)2 monolayer

Reducing the electron-phonon scattering is always desirable for realizing high conductivity of actual materials at room temperature. It is seemingly feasible in some OH-terminated MXenes such as the Hf₂C(OH)₂ monolayer, which hosts the so-called nearly free electron states (NFESs) near the Fermi energy. The NFESs are characterized by a large separation between the major electronic probability distribution and the atomic layer of MXenes. This implies that the NFESs suffer from a very weak electron-phonon scattering, hence the high conductivity at room temperature of these materials. We perform first principles calculations on the conductivity limited by the electron-phonon (e-ph) scattering of the Hf₂C(OH)₂ monolayer. Our results indicate that the conductivity of the Hf₂C(OH)₂ monolayer at room temperature is indeed higher than those of most of the MXene materials. However, such a high conductivity cannot be attributed to the existence of the NFESs because of their relatively low electronic band velocity. This conclusion is applicable to other OH-terminated MXene materials such as Zr₂C(OH)₂ since their band structures around the Fermi energy are highly analogous. Our study suggests that both large band velocity and weak e-ph coupling are important for realizing ultrahigh conductivity facilitated by the NFESs in materials.

Exciton Manifolds in Highly Ambipolar Doped WS2

The disentanglement of single and many particle properties in 2D semiconductors and their dependencies on high carrier concentration is challenging to experimentally study by pure optical means. We establish an electrolyte gated WS2 monolayer field-effect structure capable of shifting the Fermi level from the valence into the conduction band that is suitable to optically trace exciton binding as well as the single-particle band gap energies in the weakly doped regime. Combined spectroscopic imaging ellipsometry and photoluminescence spectroscopies spanning large n- and p-type doping with charge carrier densities up to 1014 cm-2 enable to study screening phenomena and doping dependent evolution of the rich exciton manifold whose origin is controversially discussed in literature. We show that the two most prominent emission bands in photoluminescence experiments are due to the recombination of spin-forbidden and momentum-forbidden charge neutral excitons activated by phonons. The observed interband transitions are redshifted and drastically weakened under electron or hole doping. This field-effect platform is not only suitable for studying exciton manifold but is also suitable for combined optical and transport measurements on degenerately doped atomically thin quantum materials at cryogenic temperatures.

Directly Visualizing Photoinduced Renormalized Momentum-Forbidden Electronic Quantum States in an Atomically Thin Semiconductor

Resolving the momentum degree of freedom of photoexcited charge carriers and exploring the excited-state physics in the hexagonal Brillouin zone of atomically thin semiconductors have recently attracted great interest for optoelectronic technologies. We demonstrate a combination of light-modulated scanning tunneling microscopy and the quasiparticle interference (QPI) technique to offer a directly accessible approach to reveal and quantify the unexplored momentum-forbidden electronic quantum states in transition metal dichalcogenide (TMD) monolayers. Our QPI results affirm the large spin-splitting energy at the spin-valley-coupled Q valleys in the conduction band (CB) of a tungsten disulfide monolayer. Furthermore, we also quantify the photoexcited carrier density-dependent band renormalization at the Q valleys. Our findings directly highlight the importance of the excited-state distribution at the Q valley in the band renormalization in TMDs and support the critical role of the CB Q valley in engineering the quantum electronic valley degree of freedom in TMD devices.

Anomalous Metallic Phase in Molybdenum Disulphide Induced via Gate-Driven Organic Ion Intercalation

Transition metal dichalcogenides exhibit rich phase diagrams dominated by the interplay of superconductivity and charge density waves, which often result in anomalies in the electric transport properties. Here, we employ the ionic gating technique to realize a tunable, non-volatile organic ion intercalation in bulk single crystals of molybdenum disulphide (MoS2). We demonstrate that this gate-driven organic ion intercalation induces a strong electron doping in the system without changing the pristine 2H crystal symmetry and triggers the emergence of a re-entrant insulator-to-metal transition. We show that the gate-induced metallic state exhibits clear anomalies in the temperature dependence of the resistivity with a natural explanation as signatures of the development of a charge-density wave phase which was previously observed in alkali-intercalated MoS2. The relatively large temperature at which the anomalies are observed (∼150 K), combined with the absence of any sign of doping-induced superconductivity down to ∼3 K, suggests that the two phases might be competing with each other to determine the electronic ground state of electron-doped MoS2.

Electronic Band Tuning and Multivalley Raman Scattering in Monolayer Transition Metal Dichalcogenides at High Pressures

Transition metal dichalcogenides (TMDs) possess spin-valley locking and spin-split K/K' valleys, which have led to many fascinating physical phenomena. However, the electronic structure of TMDs also exhibits other conduction band minima with similar properties, the Q/Q' valleys. The intervalley K-Q scattering enables interesting physical phenomena, including multivalley superconductivity, but those effects are typically hindered in monolayer TMDs due to the large K-Q energy difference (ΔE_KQ). To unlock elusive multivalley phenomena in monolayer TMDs, it is desirable to reduce ΔE_KQ, while being able to sensitively probe the valley shifts and the multivalley scattering processes. Here, we use high pressure to tune the electronic properties of monolayer MoS₂ and WSe₂ and probe K-Q crossing and multivalley scattering via double-resonance Raman (DRR) scattering. In both systems, we observed a pressure-induced enhancement of the double-resonance LA and 2LA Raman bands, which can be attributed to a band gap opening and ΔE_KQ decrease. First-principles calculations and photoluminescence measurements corroborate this scenario. In our analysis, we also addressed the multivalley nature of the DRR bands for WSe₂. Our work establishes the DRR 2LA and LA bands as sensitive probes of strain-induced modifications to the electronic structure of TMDs. Conversely, their intensity could potentially be used to monitor the presence of compressive or tensile strain in TMDs. Furthermore, the ability to probe K-K' and K-Q scattering as a function of strain shall advance our understanding of different multivalley phenomena in TMDs such as superconductivity, valley coherence, and valley transport.

Inducing chiral superconductivity on honeycomb lattice systems

Superconductivity in graphene-based systems has recently attracted much attention, as either intrinsic behavior or induced by proximity to a superconductor may lead to interesting topological phases and symmetries of the pairing function. A prominent system considers the pairing to have chiral symmetry. The question arises as to the effect of possible spin-orbit coupling on the resulting superconducting quasiparticle (QP) spectrum. Utilizing a Bogolyubov-de Gennes (BdG) Hamiltonian, we explore the interplay of different interaction terms in the system, and their role in generating complex Berry curvatures in the QP spectrum, as well as non-trivial topological behavior. We demonstrate that the topology of the BdG Hamiltonian in these systems may result in the appearance of edge states along the zigzag edges of nanoribbons in the appropriate regime. For suitable chemical potential and superconducting pairing strength, we find the appearance of robust midgap states at zigzag edges, well protected by large excitation gaps and momentum transfer.

Ionic-Liquid Gating in Two-Dimensional TMDs: The Operation Principles and Spectroscopic Capabilities

Ionic-liquid gating (ILG) is able to enhance carrier densities well above the achievable values in traditional field-effect transistors (FETs), revealing it to be a promising technique for exploring the electronic phases of materials in extreme doping regimes. Due to their chemical stability, transition metal dichalcogenides (TMDs) are ideal candidates to produce ionic-liquid-gated FETs. Furthermore, as recently discovered, ILG can be used to obtain the band gap of two-dimensional semiconductors directly from the simple transfer characteristics. In this work, we present an overview of the operation principles of ionic liquid gating in TMD-based transistors, establishing the importance of the reference voltage to obtain hysteresis-free transfer characteristics, and hence, precisely determine the band gap. We produced ILG-based bilayer WSe₂ FETs and demonstrated their ambipolar behavior. We estimated the band gap directly from the transfer characteristics, demonstrating the potential of ILG as a spectroscopy technique.

Ionic gating in metallic superconductors: A brief review

Ionic gating is a very popular tool to investigate and control the electric charge transport and electronic ground state in a wide variety of different materials. This is due to its capability to induce large modulations of the surface charge density by means of the electric-double-layer field-effect transistor (EDL-FET) architecture, and has been proven to be capable of tuning even the properties of metallic systems. In this short review, I summarize the main results which have been achieved so far in controlling the superconducting (SC) properties of thin films of conventional metallic superconductors by means of the ionic gating technique. I discuss how the gate-induced charge doping, despite being confined to a thin surface layer by electrostatic screening, results in a long-range ‘bulk’ modulation of the SC properties by the coherent nature of the SC condensate, as evidenced by the observation of suppressions in the critical temperature of films much thicker than the electrostatic screening length, and by the pronounced thickness-dependence of their magnitude. I review how this behavior can be modelled in terms of proximity effect between the charge-doped surface layer and the unperturbed bulk with different degrees of approximation, and how first-principles calculations have been employed to determine the origin of an anomalous increase in the electrostatic screening length at ultrahigh electric fields, thus fully confirming the validity of the proximity effect model. Finally, I discuss a general framework—based on the combination of ab-initio Density Functional Theory and the Migdal-Eliashberg theory of superconductivity—by which the properties of any gated thin film of a conventional metallic superconductor can be determined purely from first principles.

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

Metal-Insulator Transition and Emergent Gapped Phase in the Surface-Doped 2D Semiconductor 2H-MoTe_{2}

Artificially created two-dimensional (2D) interfaces or structures are ideal for seeking exotic phase transitions due to their highly tunable carrier density and interfacially enhanced many-body interactions. Here, we report the discovery of a metal-insulator transition (MIT) and an emergent gapped phase in the metal-semiconductor interface that is created in 2H-MoTe_{2} via alkali-metal deposition. Using angle-resolved photoemission spectroscopy, we found that the electron-phonon coupling is strong at the interface as characterized by a clear observation of replica shake-off bands. Such strong electron-phonon coupling interplays with disorder scattering, leading to an Anderson localization of polarons which could explain the MIT. The domelike emergent gapped phase could then be attributed to a polaron extended state or phonon-mediated superconductivity. Our results demonstrate the capability of alkali-metal deposition as an effective method to enhance the many-body interactions in 2D semiconductors. The surface-doped 2H-MoTe_{2} is a promising candidate for realizing polaronic insulator and high-T_{c} superconductivity.

Weak Distance Dependence of Hot-Electron-Transfer Rates at the Interface between Monolayer MoS2 and Gold

Electron transport across the transition-metal dichalcogenide (TMD)/metal interface plays an important role in determining the performance of TMD-based optoelectronic devices. However, the robustness of this process against structural heterogeneities remains unexplored, to the best of our knowledge. Here, we employ a combination of time-resolved photoemission electron microscopy (TR-PEEM) and atomic force microscopy to investigate the spatially resolved hot-electron-transfer dynamics at the monolayer (1L) MoS₂/Au interface. A spatially heterogeneous distribution of 1L-MoS₂/Au gap distances, along with the sub-80 nm spatial- and sub-60 fs temporal resolution of TR-PEEM, permits the simultaneous measurement of electron-transfer rates across a range of 1L-MoS₂/Au distances. These decay exponentially as a function of distance, with an attenuation coefficient β ∼ 0.06 ± 0.01 Å^-1, comparable to molecular wires. Ab initio simulations suggest that surface plasmon-like states mediate hot-electron-transfer, hence accounting for its weak distance dependence. The weak distance dependence of the interfacial hot-electron-transfer rate indicates that this process is insensitive to distance fluctuations at the TMD/metal interface, thus motivating further exploration of optoelectronic devices based on hot carriers.

Evolution of high-frequency Raman modes and their doping dependence in twisted bilayer MoS2

Twisted van der Waals heterostructures provide a new platform for studying strongly correlated quantum phases. The interlayer coupling in these heterostructures is sensitive to the twist angle (θ) and key to controllably tuning several interesting properties. Here, we demonstrate the systematic evolution of the interlayer coupling strength with twist angle in bilayer MoS₂ using a combination of Raman spectroscopy and classical simulations. At zero doping, we observe a monotonic increase in the separation between the A_1g and E_2g¹ mode frequencies as θ decreases from 10°→ 1°, and the separation approaches that of a bilayer at small twist angles. Furthermore, using doping dependent Raman spectroscopy, we reveal the θ dependent softening and broadening of the A_1g mode, whereas the E_2g¹ mode remains unaffected. Using first principles based simulations, we demonstrate large (weak) electron-phonon coupling for the A_1g (E_2g¹) mode, which explains the experimentally observed trends. Our study provides a non-destructive way to characterize the twist angle and the interlayer coupling and establishes the manipulation of phonons in twisted bilayer MoS₂ (twistnonics).

Recent progress of TMD nanomaterials: phase transitions and applications

Transition metal dichalcogenides (TMDs) show wide ranges of electronic properties ranging from semiconducting, semi-metallic to metallic due to their remarkable structural differences. To obtain 2D TMDs with specific properties, it is extremely important to develop particular strategies to obtain specific phase structures. Phase engineering is a traditional method to achieve transformation from one phase to another controllably. Control of such transformations enables the control of properties and access to a range of properties, otherwise inaccessible. Then extraordinary structural, electronic and optical properties lead to a broad range of potential applications. In this review, we introduce the various electronic properties of 2D TMDs and their polymorphs, and strategies and mechanisms for phase transitions, and phase transition kinetics. Moreover, the potential applications of 2D TMDs in energy storage and conversion, including electro/photocatalysts, batteries/supercapacitors and electronic devices, are also discussed. Finally, opportunities and challenges are highlighted. This review may further promote the development of TMD phase engineering and shed light on other two-dimensional materials of fundamental interest and with potential ranges of applications.

Band Filling and Cross Quantum Capacitance in Ion-Gated Semiconducting Transition Metal Dichalcogenide Monolayers

Ionic liquid gated field-effect transistors (FETs) based on semiconducting transition metal dichalcogenides (TMDs) are used to study a rich variety of extremely interesting physical phenomena, but important aspects of how charge carriers are accumulated in these systems are not understood. We address these issues by means of a systematic experimental study of transport in monolayer MoSe₂ and WSe₂ as a function of magnetic field and gate voltage, exploring accumulated densities of carriers ranging from approximately 10¹⁴ cm^-2 holes in the valence band to 4 × 10¹⁴ cm^-2 electrons in the conduction band. We identify the conditions when the chemical potential enters different valleys in the monolayer band structure (the K and Q valley in the conduction band and the two spin-split K-valleys in the valence band) and find that an independent electron picture describes the occupation of states well. Unexpectedly, however, the experiments show very large changes in the device capacitance when multiple valleys are occupied that are not at all compatible with the commonly expected quantum capacitance contribution of these systems, C_Q = e²/ (dμ/dn). A theoretical analysis of all terms responsible for the total capacitance shows that under general conditions a term is present besides the usual quantum capacitance, which becomes important for very small distances between the capacitor plates. This term, which we call cross quantum capacitance, originates from screening of the electric field generated by charges on one plate from charges sitting on the other plate. The effect is negligible in normal capacitors but large in ionic liquid FETs because of the atomic proximity between the ions in the gate and the accumulated charges on the TMD, and it accounts for all our experimental observations. Our findings therefore reveal an important contribution to the capacitance of physical systems that had been virtually entirely neglected until now.

Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS2 nanolayers

Gate-induced superconductivity at the surface of nanolayers of semiconducting transition metal dichalcogenides (TMDs) has attracted a lot of attention in recent years, thanks to the sizeable transition temperature, robustness against in-plane magnetic fields beyond the Pauli limit, and hints to a non-conventional nature of the pairing. A key information necessary to unveil its microscopic origin is the geometry of the Fermi surface hosting the Cooper pairs as a function of field-effect doping, which is dictated by the filling of the inequivalent valleys at the K/K[Formula: see text] and Q/Q[Formula: see text] points of the Brillouin zone. Here, we achieve this by combining density functional theory calculations of the bandstructure with transport measurements on ion-gated 2H-MoS₂ nanolayers. We show that, when the number of layers and the amount of strain are set to their experimental values, the Fermi level crosses the bottom of the high-energy valleys at Q/Q[Formula: see text] at doping levels where characteristic kinks in the transconductance are experimentally detected. We also develop a simple 2D model which is able to quantitatively describe the broadening of the kinks observed upon increasing temperature. We demonstrate that this combined approach can be employed to map the dependence of the Fermi surface of TMD nanolayers on field-effect doping, detect Lifshitz transitions, and provide a method to determine the amount of strain and spin-orbit splitting between sub-bands from electric transport measurements in real devices.