Impact of Spin-Entropy on the Thermoelectric Properties of a 2D Magnet.

Heat-to-charge conversion efficiency of thermoelectric materials is closely linked to the entropy per charge carrier. Thus, magnetic materials are promising building blocks for highly efficient energy harvesters as their carrier entropy is boosted by a spin degree of freedom. In this work, we investigate how this spin-entropy impacts heat-to-charge conversion in the A-type antiferromagnet CrSBr. We perform simultaneous measurements of electrical conductance and thermocurrent while changing magnetic order using the temperature and magnetic field as tuning parameters. We find a strong enhancement of the thermoelectric power factor at around the Néel temperature. We further reveal that the power factor at low temperatures can be increased by up to 600% upon applying a magnetic field. Our results demonstrate that the thermoelectric properties of 2D magnets can be optimized by exploiting the sizable impact of spin-entropy and confirm thermoelectric measurements as a sensitive tool to investigate subtle magnetic phase transitions in low-dimensional magnets.

Thermoelectric Limitations of Graphene Nanodevices at Ultrahigh Current Densities.

Graphene is atomically thin, possesses excellent thermal conductivity, and is able to withstand high current densities, making it attractive for many nanoscale applications such as field-effect transistors, interconnects, and thermal management layers. Enabling integration of graphene into such devices requires nanostructuring, which can have a drastic impact on the self-heating properties, in particular at high current densities. Here, we use a combination of scanning thermal microscopy, finite element thermal analysis, and operando scanning transmission electron microscopy techniques to observe prototype graphene devices in operation and gain a deeper understanding of the role of geometry and interfaces during high current density operation. We find that Peltier effects significantly influence the operational limit due to local electrical and thermal interfacial effects, causing asymmetric temperature distribution in the device. Thus, our results indicate that a proper understanding and design of graphene devices must include consideration of the surrounding materials, interfaces, and geometry. Leveraging these aspects provides opportunities for engineered extreme operation devices.

Quantifying the local mechanical properties of twisted double bilayer graphene.

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7% and 17% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

Exceptionally clean single-electron transistors from solutions of molecular graphene nanoribbons.

Only single-electron transistors with a certain level of cleanliness, where all states can be properly accessed, can be used for quantum experiments. To reveal their exceptional properties, carbon nanomaterials need to be stripped down to a single element: graphene has been exfoliated into a single sheet, and carbon nanotubes can reveal their vibrational, spin and quantum coherence properties only after being suspended across trenches1-3. Molecular graphene nanoribbons4-6 now provide carbon nanostructures with single-atom precision but suffer from poor solubility, similar to carbon nanotubes. Here we demonstrate the massive enhancement of the solubility of graphene nanoribbons by edge functionalization, to yield ultra-clean transport devices with sharp single-electron features. Strong electron-vibron coupling leads to a prominent Franck-Condon blockade, and the atomic definition of the edges allows identifying the associated transverse bending mode. These results demonstrate how molecular graphene can yield exceptionally clean electronic devices directly from solution. The sharpness of the electronic features opens a path to the exploitation of spin and vibrational properties in atomically precise graphene nanostructures.

Magnetic-Field Universality of the Kondo Effect Revealed by Thermocurrent Spectroscopy.

Probing the universal low-temperature magnetic-field scaling of Kondo-correlated quantum dots via electrical conductance has proved to be experimentally challenging. Here, we show how to probe this in nonlinear thermocurrent spectroscopy applied to a molecular quantum dot in the Kondo regime. Our results demonstrate that the bias-dependent thermocurrent is a sensitive probe of universal Kondo physics, directly measures the splitting of the Kondo resonance in a magnetic field, and opens up possibilities for investigating nanosystems far from thermal and electrical equilibrium.

Controlling the Entropy of a Single-Molecule Junction.

Single molecules are nanoscale thermodynamic systems with few degrees of freedom. Thus, the knowledge of their entropy can reveal the presence of microscopic electron transfer dynamics that are difficult to observe otherwise. Here, we apply thermocurrent spectroscopy to directly measure the entropy of a single free radical molecule in a magnetic field. Our results allow us to uncover the presence of a singlet to triplet transition in one of the redox states of the molecule, not detected by conventional charge transport measurements. This highlights the power of thermoelectric measurements which can be used to determine the difference in configurational entropy between the redox states of a nanoscale system involved in conductance without any prior assumptions about its structure or microscopic dynamics.

Complete mapping of the thermoelectric properties of a single molecule.

Theoretical studies suggest that mastering the thermocurrent through single molecules can lead to thermoelectric energy harvesters with unprecedentedly high efficiencies.1-6 This can be achieved by engineering molecule length,7 optimizing the tunnel coupling strength of molecules via chemical anchor groups8 or by creating localized states in the backbone with resulting quantum interference features.4 Empirical verification of these predictions, however, faces considerable experimental challenges and is still awaited. Here we use a novel measurement protocol that simultaneously probes the conductance and thermocurrent flow as a function of bias voltage and gate voltage. We find that the resulting thermocurrent is strongly asymmetric with respect to the gate voltage, with evidence of molecular excited states in the thermocurrent Coulomb diamond maps. These features can be reproduced by a rate-equation model only if it accounts for both the vibrational coupling and the electronic degeneracies, thus giving direct insight into the interplay of electronic and vibrational degrees of freedom, and the role of spin entropy in single molecules. Overall these results show that thermocurrent measurements can be used as a spectroscopic tool to access molecule-specific quantum transport phenomena.

A Mechanically Tunable Quantum Dot in a Graphene Break Junction.

Graphene quantum dots (QDs) are intensively studied as platforms for the next generation of quantum electronic devices. Fine tuning of the transport properties in monolayer graphene QDs, in particular with respect to the independent modulation of the tunnel barrier transparencies, remains challenging and is typically addressed using electrostatic gating. We investigate charge transport in back-gated graphene mechanical break junctions and reveal Coulomb blockade physics characteristic of a single, high-quality QD when a nanogap is opened in a graphene constriction. By mechanically controlling the distance across the newly formed graphene nanogap, we achieve reversible tunability of the tunnel coupling to the drain electrode by 5 orders of magnitude, while keeping the source-QD tunnel coupling constant. The break junction device can therefore become a powerful platform to study the physical parameters that are crucial to the development of future graphene-based devices, including energy converters and quantum calorimeters.

Geometrically Enhanced Thermoelectric Effects in Graphene Nanoconstrictions.

The influence of nanostructuring and quantum confinement on the thermoelectric properties of materials has been extensively studied. While this has made possible multiple breakthroughs in the achievable figure of merit, classical confinement, and its effect on the local Seebeck coefficient has mostly been neglected, as has the Peltier effect in general due to the complexity of measuring small temperature gradients locally. Here we report that reducing the width of a graphene channel to 100 nm changes the Seebeck coefficient by orders of magnitude. Using a scanning thermal microscope allows us to probe the local temperature of electrically contacted graphene two-terminal devices or to locally heat the sample. We show that constrictions in mono- and bilayer graphene facilitate a spatially correlated gradient in the Seebeck and Peltier coefficient, as evidenced by the pronounced thermovoltage Vth and heating/cooling response Δ TPeltier, respectively. This geometry dependent effect, which has not been reported previously in 2D materials, has important implications for measurements of patterned nanostructures in graphene and points to novel solutions for effective thermal management in electronic graphene devices or concepts for single material thermocouples.

Mechanically controlled quantum interference in graphene break junctions.

The ability to detect and distinguish quantum interference signatures is important for both fundamental research and for the realization of devices such as electron resonators1, interferometers2 and interference-based spin filters3. Consistent with the principles of subwavelength optics, the wave nature of electrons can give rise to various types of interference effects4, such as Fabry-Pérot resonances5, Fano resonances6 and the Aharonov-Bohm effect7. Quantum interference conductance oscillations8 have, indeed, been predicted for multiwall carbon nanotube shuttles and telescopes, and arise from atomic-scale displacements between the inner and outer tubes9,10. Previous theoretical work on graphene bilayers indicates that these systems may display similar interference features as a function of the relative position of the two sheets11,12. Experimental verification is, however, still lacking. Graphene nanoconstrictions represent an ideal model system to study quantum transport phenomena13-15 due to the electronic coherence16 and the transverse confinement of the carriers17. Here, we demonstrate the fabrication of bowtie-shaped nanoconstrictions with mechanically controlled break junctions made from a single layer of graphene. Their electrical conductance displays pronounced oscillations at room temperature, with amplitudes that modulate over an order of magnitude as a function of subnanometre displacements. Surprisingly, the oscillations exhibit a period larger than the graphene lattice constant. Charge-transport calculations show that the periodicity originates from a combination of the quantum interference and lattice commensuration effects of two graphene layers that slide across each other. Our results provide direct experimental observation of a Fabry-Pérot-like interference of electron waves that are partially reflected and/or transmitted at the edges of the graphene bilayer overlap region.

Massively parallel fabrication of crack-defined gold break junctions featuring sub-3 nm gaps for molecular devices.

Break junctions provide tip-shaped contact electrodes that are fundamental components of nano and molecular electronics. However, the fabrication of break junctions remains notoriously time-consuming and difficult to parallelize. Here we demonstrate true parallel fabrication of gold break junctions featuring sub-3 nm gaps on the wafer-scale, by relying on a novel self-breaking mechanism based on controlled crack formation in notched bridge structures. We achieve fabrication densities as high as 7 million junctions per cm2, with fabrication yields of around 7% for obtaining crack-defined break junctions with sub-3 nm gaps of fixed gap width that exhibit electron tunneling. We also form molecular junctions using dithiol-terminated oligo(phenylene ethynylene) (OPE3) to demonstrate the feasibility of our approach for electrical probing of molecules down to liquid helium temperatures. Our technology opens a whole new range of experimental opportunities for nano and molecular electronics applications, by enabling very large-scale fabrication of solid-state break junctions.

Field-Effect Control of Graphene-Fullerene Thermoelectric Nanodevices.

Although it was demonstrated that discrete molecular levels determine the sign and magnitude of the thermoelectric effect in single-molecule junctions, full electrostatic control of these levels has not been achieved to date. Here, we show that graphene nanogaps combined with gold microheaters serve as a testbed for studying single-molecule thermoelectricity. Reduced screening of the gate electric field compared to conventional metal electrodes allows control of the position of the dominant transport orbital by hundreds of meV. We find that the power factor of graphene-fullerene junctions can be tuned over several orders of magnitude to a value close to the theoretical limit of an isolated Breit-Wigner resonance. Furthermore, our data suggest that the power factor of an isolated level is only given by the tunnel coupling to the leads and temperature. These results open up new avenues for exploring thermoelectricity and charge transport in individual molecules and highlight the importance of level alignment and coupling to the electrodes for optimum energy conversion in organic thermoelectric materials.

Scaling Limits of Graphene Nanoelectrodes.

Graphene nanogap electrodes have been of recent interest in a variety of fields, ranging from molecular electronics to phase change memories. Several recent reports have highlighted that scaling graphene nanogaps to even smaller sizes is a promising route to more efficient and robust molecular and memory devices. Despite the significant interest, the operating and scaling limits of these electrodes are completely unknown. In this paper, we report on our observations of consistent voltage driven resistance switching in sub-5 nm graphene nanogaps. We find that such electrical switching from an insulating state to a conductive state occurs at very low currents and voltages (0.06 µA and 140 mV), independent of the conditions (room ambient, low temperatures, as well as in vacuum), thus portending potential limits to scaling of functional devices with carbon electrodes. We then associate this phenomenon to the formation and rupture of carbon chains. Using a phase change material in the nanogap as a demonstrator device, fabricated using a self-alignment technique, we show that for gap sizes approaching 1 nm the switching is dominated by such carbon chain formation, creating a fundamental scaling limit for potential devices. These findings have important implications, not only for fundamental science, but also in terms of potential applications.

Distinguishing Lead and Molecule States in Graphene-Based Single-Electron Transistors.

Graphene provides a two-dimensional platform for contacting individual molecules, which enables transport spectroscopy of molecular orbital, spin, and vibrational states. Here we report single-electron tunneling through a molecule that has been anchored to two graphene leads. Quantum interference within the graphene leads gives rise to an energy-dependent transmission and fluctuations in the sequential tunnel-rates. The lead states are electrostatically tuned by a global back-gate, resulting in a distinct pattern of varying intensity in the measured conductance maps. This pattern could potentially obscure transport features that are intrinsic to the molecule under investigation. Using ensemble averaged magneto-conductance measurements, lead and molecule states are disentangled, enabling spectroscopic investigation of the single molecule.

Surface oxidation effect on the electrical behaviour of Bi2Te2Se nanoplatelets.

Charge transport in topological insulators is notably influenced by moisture and air in the surrounding environment. At present, however, little is known about the detailed composition of the oxidized surface and its impact on the electrical characteristics of these materials. Here, we investigate the surface oxide formation on the topological insulator Bi2Te2Se (BTS) and how this affects its electrical behavior. While ambient exposure of BTS nanoplatelets predominantly creates surface hydroxyl groups, oxygen plasma treatment yields a compact, few-nanometer thick surface oxide layer. The plasma causes p-type doping, accompanied by a decrease of the effective platelet thickness, the interplay of which is manifested in a resistance maximum as a function of plasma treatment time. It is furthermore demonstrated that the structural integrity of the plasma-derived surface oxide is sufficient to enable its use as a gate insulator layer in combination with a top gate.

Quantum Interference in Graphene Nanoconstrictions.

We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry-Pérot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry-Pérot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

Harnessing Topological Band Effects in Bismuth Telluride Selenide for Large Enhancements in Thermoelectric Properties through Isovalent Doping.

Dilute isovalent sulfur doping simultaneously increases electrical conductivity and Seebeck coefficient in Bi2 Te2 Se nanoplates, and bulk pellets made from them. This unusual trend at high electron concentrations is underpinned by multifold increases in electron effective mass attributable to sulfur-induced band topology effects, providing a new way for accessing a high thermoelectric figure-of-merit in topological-insulator-based nanomaterials through doping.

Dimensional crossover in the quantum transport behaviour of the natural topological insulator Aleksite.

Three-dimensional topological insulators comprise topologically protected surface states displaying massless, Dirac-like linear dispersion with spin-momentum locking. Electrical conduction through such surface states has been documented to manifest itself in a two-dimensional character of the angle-dependent magnetotransport behavior. Here, we explore the size-dependent electronic properties of nanostructures made of the lead-containing mineral Aleksite, a naturally occurring topological insulator. Compared to its sister compound Kawazulite, a member of the well-studied Tetradymite crystal class, the crystal structure of Aleksite is distinguished by its lack of any counterpart within the group of synthetic topological insulators. Low temperature Hall measurements on thin Aleksite nanosheets reveal a significant carrier mobility on the order of 1000 cm(2)/(Vs), and a high carrier density of n = 3.9 × 10(25) m(-3). Importantly, for Aleksite nanoribbons with a width below 150 nm, a 1D weak antilocalization effect along with 1D universal conductance fluctuations emerges, which transforms into 2D behavior for larger ribbon widths.

Growth of high-mobility Bi2Te2Se nanoplatelets on hBN sheets by van der Waals epitaxy.

The electrical detection of the surface states of topological insulators is strongly impeded by the interference of bulk conduction, which commonly arises due to pronounced doping associated with the formation of lattice defects. As exemplified by the topological insulator Bi(2)Te(2)Se, we show that via van der Waals epitaxial growth on thin hBN substrates the structural quality of such nanoplatelets can be substantially improved. The surface state carrier mobility of nanoplatelets on hBN is increased by a factor of about 3 compared to platelets on conventional Si/SiO(x) substrates, which enables the observation of well-developed Shubnikov-de Haas oscillations. We furthermore demonstrate the possibility to effectively tune the Fermi level position in the films with the aid of a back gate.