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.

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.

Here we highlight 35 researchers approximately under the age of 35. Age, of course, is just a number—our target was emerging early-career academics. Contributors were recruited in a self-propagating “pay-it-forward” manner, with each invitee being suggested by a peer who had already contributed. The final collection is an inspiring look at the challenges the current generation of materials researchers are tackling.

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.

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.

In transition metal dichalcogenides, defects have been found to play an important role, affecting doping, spin-valley relaxation dynamics, and assisting in proximity effects of spin-orbit coupling. Here we study localized states in WS2 and how they affect tunneling through van der Waals heterostructures of h-BN/graphene/ WS2/metal. The obtained conductance maps as a function of bias and gate voltage reveal single-electron transistor behavior (Coulomb blockade) with a rich set of transport features including excited states and negative differential resistance regimes. Applying a perpendicular magnetic field, we observe a shift in the energies of the quantum levels and information about the orbital magnetic moment of the localized states is extracted.

The power factor of a thermoelectric device is a measure of the heat-to-energy conversion efficiency in nanoscopic devices. Yet, even as interest in low-dimensional thermoelectric materials has increased, experimental research on what influences the power factor in these systems is scarce. Here, we present a detailed thermoelectric study of graphene quantum dot devices. We show that spin degeneracy of the quantum dot states has a significant impact on the zero-bias conductance of the device and leads to an increase of the power factor. Conversely, we demonstrate that nonideal heat exchange within the leads can suppress the power factor near the charge degeneracy point and nontrivially influences its temperature dependence.

Studying local variations in the Seebeck coefficient of materials is important for understanding and optimizing their thermoelectric properties, yet most thermoelectric measurements are global over a whole device or material, thus overlooking spatial divergences in the signal and the role of local variation and internal structure. Such variations can be caused by local defects, metallic contacts or interfaces that often substantially influence thermoelectric properties, especially in two dimensional materials. Here, we demonstrate scanning thermal gate microscopy, a non-destructive method to obtain high resolution 2-dimensional maps of the thermovoltage, to study graphene samples. We demonstrate the efficiency of this newly developed method by measuring local Seebeck coefficient in a graphene ribbon and in a junction between single-layer and bilayer graphene.

On-chip temperature sensing on a micro- to nanometer scale is becoming more desirable as the complexity of nanodevices keeps increasing and their downscaling continues. The continuation of this trend makes thermal probing and management more and more challenging. This highlights the need for scalable and reliable temperature sensors, which have the potential to be incorporated into current and future device structures. Here, it is shown that U-shaped graphene stripes consisting of one wide and one narrow leg form a single material thermocouple that can function as a self-powering temperature sensor. It is found that the graphene thermocouples increase in sensitivity with a decrease in leg width, due to a change in the Seebeck coefficient, which is in agreement with previous findings and report a maximum sensitivity of ΔS ≈ 39 μV K⁻¹.

The energy dependent thermoelectric response of a single molecule contains valuable information about its transmission function and its excited states. However, measuring it requires devices that can efficiently heat up one side of the molecule while being able to tune its electrochemical potential over a wide energy range. Furthermore, to increase junction stability, devices need to operate at cryogenic temperatures. In this work, we report on a device architecture to study the thermoelectric properties and the conductance of single molecules simultaneously over a wide energy range. We employ a sample heater in direct contact with the metallic electrodes contacting the single molecule which allows us to apply temperature biases up to ΔT = 60 K with minimal heating of the molecular junction. This makes these devices compatible with base temperatures T_bath < 2 K and enables studies in the linear (Δ T ≪ T molecule) and nonlinear (Δ T ≫ T molecule) thermoelectric transport regimes.

It is known that the quantum mechanical ground state of a nanoscale junction has a significant impact on its electrical transport properties. This becomes particularly important in transistors consisting of a single molecule. Because of strong electron-electron interactions and the possibility of accessing ground states with high spins, these systems are eligible hosts of a current-blockade phenomenon called a ground-state spin blockade. This effect arises from the inability of a charge carrier to account for the spin difference required to enter the junction, as that process would violate the spin selection rules. Here, we present a direct experimental demonstration of a ground-state spin blockade in a high-spin single-molecule transistor. The measured transport characteristics of this device exhibit a complete suppression of resonant transport due to a ground-state spin difference of 3/2 between subsequent charge states. Strikingly, the blockade can be reversibly lifted by driving the system through a magnetic ground-state transition in one charge state, using the tunability offered by both magnetic and electric fields.

Single-molecule junctions — devices in which a single molecule is electrically connected by two electrodes — enable the study of a broad range of quantum-transport phenomena even at room temperature. These quantum features are related to molecular orbital and spin degrees of freedom and are characterized by various energy scales that can be chemically and physically tuned: level spacings, charging energies, tunnel couplings, exchange energies, vibrational energies and Kondo correlation energies. The competition between these different energy scales leads to a rich variety of processes, which researchers are now starting to be able to control and tune experimentally. In this Technical Review, we present the status of the molecular electronics field from this quantum-transport perspective with a focus on recent experimental results obtained using break-junction devices, including scanning probe and mechanically controlled break junctions, as well as electromigrated gold and 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 tubes^9,10. 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 sheets^11,12. Experimental verification is, however, still lacking. Graphene nanoconstrictions represent an ideal model system to study quantum transport phenomena^13–15 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.

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.

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 V_th and heating/cooling response T_Peltier, 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.

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.

We have characterized the dynamics of the polar nanoregions in Pb (Mg _1/3 Nb_2/3)O₃ through high-resolution neutron-backscattering and spin-echo measurements of the diffuse-scattering cross section. We find that the diffuse-scattering intensity consists of both static and dynamic components. The static component first appears at the Curie temperature Θ∼400 K while the dynamic component freezes completely at the temperature T_f ∼200 K; together, these components account for all of the observed spectral weight contributing to the diffuse-scattering cross section. The integrated intensity of the dynamic component peaks near the temperature at which the frequency-dependent dielectric constant reaches a maximum (T_max) when measured at 1 GHz, i.e., on a time scale of ∼1 ns. Our neutron-scattering results can thus be directly related to dielectric and infrared measurements of the polar nanoregions. Finally, the global temperature dependence of the diffuse scattering can be understood in terms of just two temperature scales, which is consistent with random-field models.