Enhanced thermoelectric power in dual-gated bilayer graphene

Sub-Sharvin Conductance and Incoherent Shot-Noise in Graphene Disks at Magnetic Field

Highly doped graphene samples show reduced conductance and enhanced shot-noise power compared with standard ballistic systems in two-dimensional electron gas. These features can be understood within a model that assumes incoherent scattering of Dirac electrons between two interfaces separating the sample and the leads. Here we find, by adopting the above model for the edge-free (Corbino) geometry and by computer simulation of quantum transport, that another graphene-specific feature should be observable when the current flow through a doped disk is blocked by a strong magnetic field. When the conductance drops to zero, the Fano factor approaches the value of F≈0.56, with a very weak dependence on the ratio of the disk radii. The role of finite source-drain voltages and the system behavior when the electrostatic potential barrier is tuned from a rectangular to a parabolic shape are also discussed.

Demonstration and imaging of cryogenic magneto-thermoelectric cooling in a van der Waals semimetal

Attaining viable thermoelectric cooling at cryogenic temperatures is of considerable fundamental and technological interest for electronics and quantum materials applications. In-device temperature control can provide more efficient and precise thermal environment management compared with conventional global cooling. The application of a current and perpendicular magnetic field gives rise to cooling by generating electron-hole pairs on one side of the sample and to heating due to their recombination on the opposite side, which is known as the Ettingshausen effect. Here we develop nanoscale cryogenic imaging of the magneto-thermoelectric effect and demonstrate absolute cooling and an Ettingshausen effect in exfoliated WTe2 Weyl semimetal flakes at liquid He temperatures. In contrast to bulk materials, the cooling is non-monotonic with respect to the magnetic field and device size. Our model of magneto-thermoelectricity in mesoscopic semimetal devices shows that the cooling efficiency and the induced temperature profiles are governed by the interplay between sample geometry, electron-hole recombination length, magnetic field, and flake and substrate heat conductivities. The observations open the way for the direct integration of microscopic thermoelectric cooling and for temperature landscape engineering in van der Waals devices.

Thermoelectric Properties of the Corbino Disk in Graphene

Thermopower and the Lorentz number for an edge-free (Corbino) graphene disk in the quantum Hall regime is calculated within the Landauer-Büttiker formalism. By varying the electrochemical potential, we find that amplitude of the Seebeck coefficient follows a modified Goldsmid-Sharp relation, with the energy gap defined by the interval between the zero and the first Landau levels in bulk graphene. An analogous relation for the Lorentz number is also determined. Thus, these thermoelectric properties are solely defined by the magnetic field, the temperature, the Fermi velocity in graphene, and fundamental constants including the electron charge, the Planck and Boltzmann constants, being independent of the geometric dimensions of the system. This suggests that the Corbino disk in graphene may operate as a thermoelectric thermometer, allowing to measure small temperature differences between two reservoirs, if the mean temperature magnetic field are known.

Evidence of Lifshitz Transition in the Thermoelectric Power of Ultrahigh-Mobility Bilayer Graphene

Resolving low-energy features in the density of states (DOS) holds the key to understanding a wide variety of rich novel phenomena in graphene-based 2D heterostructures. The Lifshitz transition in bilayer graphene (BLG) arising from trigonal warping has been established theoretically and experimentally. Nevertheless, the experimental realization of its effects on transport properties has been challenging because of its relatively low energy scale (∼1 meV). In this work, we demonstrate that the thermoelectric power (TEP) can be used as an effective probe to investigate fine changes in the DOS of BLG. We observed additional entropy features in the vicinity of the charge neutrality point (CNP) in gapped BLG. This apparent violation of the Mott formula can be explained quantitatively by considering the effects of trigonal warping, thereby serving as possible evidence of a Lifshitz transition.

Preparation and physical characteristics of graphene ceramics

Graphene, a two-dimensional structure of carbon, due to its structure has unique physico-chemical properties that can be used in numerous research and industry areas. Although this structure is already well known, there are still technological (and cost) barriers which do not allow to produce this material in large quantities and hence prevent its use in various applications. For this reason, many technologies are currently being developed to obtain graphene in forms that would enable its widespread use. The graphene-like ceramics were fabricated by the high isostatic pressure method at different temperatures. This technique allows to obtain dense ceramics with various shapes. The structure and morphology of sintered graphene were investigated by XRD, SEM and the Raman spectroscopy. The hardness, thermal conductivity and electric transport measurements recorded in a wide range of temperatures were used to analyze the physical properties of the obtained ceramics.

Recent Progress of Two-Dimensional Thermoelectric Materials

Thermoelectric generators have attracted a wide research interest owing to their ability to directly convert heat into electrical power. Moreover, the thermoelectric properties of traditional inorganic and organic materials have been significantly improved over the past few decades. Among these compounds, layered two-dimensional (2D) materials, such as graphene, black phosphorus, transition metal dichalcogenides, IVA-VIA compounds, and MXenes, have generated a large research attention as a group of potentially high-performance thermoelectric materials. Due to their unique electronic, mechanical, thermal, and optoelectronic properties, thermoelectric devices based on such materials can be applied in a variety of applications. Herein, a comprehensive review on the development of 2D materials for thermoelectric applications, as well as theoretical simulations and experimental preparation, is presented. In addition, nanodevice and new applications of 2D thermoelectric materials are also introduced. At last, current challenges are discussed and several prospects in this field are proposed.

Role of the Lifshitz topological transitions in the thermodynamic properties of graphene

The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. The peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, the zone corners K in the vicinity of the Dirac points, and at the saddle point M. A general formulation of the thermodynamics at the LTT in graphene is given. The thermodynamic characteristics of graphene are investigated at the Lifshitz topological transitions. Anomalies are found in the electron specific heat C_e, the electron thermal coefficient of pressure, and the coefficients of electron compressibility and thermal expansion in graphene at the LTT. All the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points. This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.

The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established.

Thermoelectric properties of gapped bilayer graphene

Unlike in conventional semiconductors, both the chemical potential and the band gap in bilayer graphene (BLG) can be tuned via application of external electric field. Among numerous device implications, this property also designates BLG as a candidate for high-performance thermoelectric material. In this theoretical study we have calculated the Seebeck coefficients for abrupt interface separating weakly- and heavily-doped areas in BLG, and for a more realistic rectangular sample of mesoscopic size, contacted by two electrodes. For a given band gap ([Formula: see text]) and temperature (T) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value [Formula: see text], the deviations can be approximated by the asymptotic expression [Formula: see text], with the electron charge  -e, the Boltzmann constant [Formula: see text], and [Formula: see text]. Surprisingly, the effects of trigonal warping term in the BLG low-energy Hamiltonian are clearly visible at few-Kelvin temperatures, for all accessible values of [Formula: see text] meV. We also show that thermoelectric figure of merit is noticeably enhanced (ZT  >  3) when a rigid substrate suppresses out-of-plane vibrations, reducing the contribution from ZA phonons to the thermal conductivity.

Strong Valence Electrons Dependent and Logical Relations of Elemental Impurities in 2D Binary Semiconductor: a Case of GeP3 Monolayer from Ab Initio Studies

Using first-principle calculations within density functional theory, we investigate the electronic property and stability of substitutionally doped 2D GeP₃ monolayer with dopants from group III to VI. The conducting properties are found to be dramatically modified by both the doping sites and the number of valence electrons of dopants. Specifically, substitution on Ge site exhibits metal-semiconductor oscillations as a function of the number of valence electrons of dopants, while such oscillations are totally reversed when substitution on P site. Moreover, we also study the case of co-doping in GeP₃, showing that co-doping can produce a logical "AND" phenomenon, that is, the conducting properties of co-doped GeP₃ can be deduced via a simple logical relation according to the results of single doping. Finally, we investigate the formation energy of dopants and find that the electron-hole and hole-hole co-doped systems are much more energetically favorable due to the Coulomb attraction. Our findings not only present a comprehensive understanding of 2D doping phenomenon, but also propose an intriguing route to tune the electronic properties of 2D binary semiconductors.

Some peculiarities of thermopower at the Lifshitz topological transitions due to stacking change in bilayer and multilayer graphene

Singularities of thermopower (the Seebeck coefficient) are considered at the Lifshitz topological transitions (LTT) in bilayer graphene (BLG) and multilayer graphene (MLG) due to stacking change from AB to AA . The dependence of singularities on μ , γ 1 and Δ is investigated ( μ is the chemical potential, γ 1 is the interlayer hopping parameter and Δ is the gap value) for the gapped graphene, as well as for the gapless one. The present paper results indicate that effects of the thermopower singularities are appreciable and can be used to observe the LTT, and to explore the degree of stacking change from AB to AA in graphene. Therefore, the thermopower singularities at LTT due to stacking change from AB to AA can be used as a powerful tool to control electronic properties of BLG- and MLG-based structures.

Modification of thermal and electronic properties of bilayer graphene by using slow Na+ ions

Bilayer graphene (BLG) has an extensive list of industrial applications in graphene-based nanodevices such as energy storage devices, flexible displays, and thermoelectric devices. By doping slow Na⁺ ions on Li-intercalated BLG, we find significantly improved thermal and electronic properties of BLG by using angle-resolved photoemission and high-resolution core level spectroscopy (HRCLS) with synchrotron photons. Our HRCLS data reveal that the adsorbed Na⁺ ions on a BLG produced by Li-intercalation through single layer graphene (SLG) spontaneously intercalate below the BLG, and substitute Li atoms to form Na-Si bonds at the SiC interface while preserving the same phase of BLG. This is in sharp contrast with no intercalation of Na⁺ ions on SLG though neutral Na atoms intercalate. The Na⁺-induced BLG is found to be stable upon heating up to T = 400 °C, but returns to SLG when heated at T _d = 500 °C. The evolution of the π-bands upon doping the Na⁺ ions followed by thermal annealing shows that the carrier concentration of the π-band may be artificially controlled without damaging the Dirac nature of the π-electrons. The doubled desorption temperature from that (T _d = 250 °C) of the Na-intercalated SLG together with the electronic stability of the Na⁺-intercalated BLG may find more practical and effective applications in advancing graphene-based thermoelectric devices and anode materials for rechargeable batteries.

High thermoelectricpower factor in graphene/hBN devices

Fast and controllable cooling at nanoscales requires a combination of highly efficient passive cooling and active cooling. Although passive cooling in graphene-based devices is quite effective due to graphene's extraordinary heat conduction, active cooling has not been considered feasible due to graphene's low thermoelectric power factor. Here, we show that the thermoelectric performance of graphene can be significantly improved by using hexagonal boron nitride (hBN) substrates instead of SiO₂ We find the room temperature efficiency of active cooling in the device, as gauged by the power factor times temperature, reaches values as high as 10.35 W⋅m^-1⋅K^-1, corresponding to more than doubling the highest reported room temperature bulk power factors, 5 W⋅m^-1⋅K^-1, in YbAl₃, and quadrupling the best 2D power factor, 2.5 W⋅m^-1⋅K^-1, in MoS₂ We further show that the Seebeck coefficient provides a direct measure of substrate-induced random potential fluctuations and that their significant reduction for hBN substrates enables fast gate-controlled switching of the Seebeck coefficient polarity for applications in integrated active cooling devices.

Nanoscale solid-state cooling: a review

The recent developments in nanoscale solid-state cooling are reviewed. This includes both theoretical and experimental studies of different physical concepts, as well as nanostructured material design and device configurations. We primarily focus on thermoelectric, thermionic and thermo-magnetic coolers. Particular emphasis is given to the concepts based on metal-semiconductor superlattices, graded materials, non-equilibrium thermoelectric devices, Thomson coolers, and photon assisted Peltier coolers as promising methods for efficient solid-state cooling. Thermomagnetic effects such as magneto-Peltier and Nernst-Ettingshausen cooling are briefly described and recent advances and future trends in these areas are reviewed. The ongoing progress in solid-state cooling concepts such as spin-calorimetrics, electrocalorics, non-equilibrium/nonlinear Peltier devices, superconducting junctions and two-dimensional materials are also elucidated and practical achievements are reviewed. We explain the thermoreflectance thermal imaging microscopy and the transient Harman method as two unique techniques developed for characterization of thermoelectric microrefrigerators. The future prospects for solid-state cooling are briefly summarized.

Thermoelectric Power in Bilayer Graphene Device with Ionic Liquid Gating

The quest for materials showing large thermoelectric power has long been one of the important subjects in material science and technology. Such materials have great potential for thermoelectric cooling and also high figure of merit ZT thermoelectric applications. We have fabricated bilayer graphene devices with ionic-liquid gating in order to tune its band gap via application of a perpendicular electric field on a bilayer graphene. By keeping the Fermi level at charge neutral point during the cool-down, we found that the charge puddles effect can be greatly reduced and thus largely improve the transport properties at low T in graphene-based devices using ionic liquid gating. At (V_ig, V_bg) = (−1 V, +23 V), a band gap of about 36.6 ± 3 meV forms, and a nearly 40% enhancement of thermoelectric power at T = 120 K is clearly observed. Our works demonstrate the feasibility of band gap tuning in a bilayer graphene using ionic liquid gating. We also remark on the significant influence of the charge puddles effect in ionic-liquid-based devices.

Liquid Exfoliated Graphene as Dopant for Improving the Thermoelectric Power Factor of Conductive PEDOT:PSS Nanofilm with Hydrazine Treatment

Here, we fabricated a highly conductive poly(3,4-ethylenedioxythiophene):poly(4-styrenesulfonate) (

PEDOT

PSS) nanofilm via vacuum filtration with enhanced thermoelectric power factor by doping of liquid exfoliated graphene (GE) and hydrazine treatment. The effect of GE exfoliated in dimethylformamide (DMF) and N-methyl-2-pyrrolidone (NMP) on the electrical conductivity and thermopower of

PEDOT

PSS was investigated. Although electrical conductivity decreased with increasing GE, thermoelectric power factors of

PEDOT

PSS nanofilms were improved with 3 wt % GE in DMF (38.6 μW m(-1) K(-2)) and in NMP (28.0 μW m(-1) K(-2)) compared to pure

PEDOT

PSS (11.5 μW m(-1) K(-2)). The mechanism of improvement was proposed to be the removal of PSS and the good interaction between PEDOT and GE. With hydrazine treatment, 3 wt % GE-doped

PEDOT

PSS nanofilm (PG3) showed a further enhanced power factor of 53.3 μW m(-1) K(-2) (∼5 times higher than that of pristine

PEDOT

PSS nanofilm). The effects of hydrazine containing concentration, treatment time, and temperature on the electrical conductivity and Seebeck coefficient of PG3 were investigated systematically. An estimated thermoelectric figure of merit (ZT) is 0.05 with the optimized power factor at room temperature.

Thermoelectric effects in graphene nanostructures

The thermoelectric properties of graphene and graphene nanostructures have recently attracted significant attention from the physics and engineering communities. In fundamental physics, the analysis of Seebeck and Nernst effects is very useful in elucidating some details of the electronic band structure of graphene that cannot be probed by conductance measurements alone, due in particular to the ambipolar nature of this gapless material. For applications in thermoelectric energy conversion, graphene has two major disadvantages. It is gapless, which leads to a small Seebeck coefficient due to the opposite contributions of electrons and holes, and it is an excellent thermal conductor. The thermoelectric figure of merit ZT of a two-dimensional (2D) graphene sheet is thus very limited. However, many works have demonstrated recently that appropriate nanostructuring and bandgap engineering of graphene can concomitantly strongly reduce the lattice thermal conductance and enhance the Seebeck coefficient without dramatically degrading the electronic conductance. Hence, in various graphene nanostructures, ZT has been predicted to be high enough to make them attractive for energy conversion. In this article, we review the main results obtained experimentally and theoretically on the thermoelectric properties of graphene and its nanostructures, emphasizing the physical effects that govern these properties. Beyond pure graphene structures, we discuss also the thermoelectric properties of some hybrid graphene structures, as graphane, layered carbon allotropes such as graphynes and graphdiynes, and graphene/hexagonal boron nitride heterostructures which offer new opportunities. Finally, we briefly review the recent activities on other atomically thin 2D semiconductors with finite bandgap, i.e. dichalcogenides and phosphorene, which have attracted great attention for various kinds of applications, including thermoelectrics.

Thermal and thermoelectric properties of graphene

The subject of thermal transport at the mesoscopic scale and in low-dimensional systems is interesting for both fundamental research and practical applications. As the first example of truly two-dimensional materials, graphene has exceptionally high thermal conductivity, and thus provides an ideal platform for the research. Here we review recent studies on thermal and thermoelectric properties of graphene, with an emphasis on experimental progresses. A general physical picture based on the Landauer transport formalism is introduced to understand underlying mechanisms. We show that the superior thermal conductivity of graphene is contributed not only by large ballistic thermal conductance but also by very long phonon mean free path (MFP). The long phonon MFP, explained by the low-dimensional nature and high sample purity of graphene, results in important isotope effects and size effects on thermal conduction. In terms of various scattering mechanisms in graphene, several approaches are suggested to control thermal conductivity. Among them, introducing rough boundaries and weakly-coupled interfaces are promising ways to suppress thermal conduction effectively. We also discuss the Seebeck effect of graphene. Graphene itself might not be a good thermoelectric material. However, the concepts developed by graphene research might be applied to improve thermoelectric performance of other materials.

Large thermoelectricity via variable range hopping in chemical vapor deposition grown single-layer MoS2

Ultrathin layers of semiconducting molybdenum disulfide (MoS2) offer significant prospects in future electronic and optoelectronic applications. Although an increasing number of experiments bring light into the electronic transport properties of these crystals, their thermoelectric properties are much less known. In particular, thermoelectricity in chemical vapor deposition grown MoS2, which is more practical for wafer-scale applications, still remains unexplored. Here, for the first time, we investigate these properties in grown single layer MoS2. Microfabricated heaters and thermometers are used to measure both electrical conductivity and thermopower. Large values of up to ∼30 mV/K at room temperature are observed, which are much larger than those observed in other two-dimensional crystals and bulk MoS2. The thermopower is strongly dependent on temperature and applied gate voltage with a large enhancement at the vicinity of the conduction band edge. We also show that the Seebeck coefficient follows S ∼ T(1/3), suggesting a two-dimensional variable range hopping mechanism in the system, which is consistent with electrical transport measurements. Our results help to understand the physics behind the electrical and thermal transports in MoS2 and the high thermopower value is of interest to future thermoelectronic research and application.

Thermoelectric detection of chiral heat transport in graphene in the quantum Hall regime

We report measurements of heat transport along the edge conducting channels in monolayer graphene in the integer quantum Hall regime. Hot charge carriers are injected to the edge channels, and the thermoelectric voltage is measured at a distance along the edge from the heat injection point. We confirm that heat transport in graphene in the quantum Hall regime is chiral and the thermoelectric signal is correlated with the charge conductance of ballistic transport, following the Mott relation. The thermoelectric signal decays with distance from the heater, indicating that carriers are partially thermalized during edge transmission.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.