Monolayer NaCrX2 (X=Te,Se,S) were theoretically proposed to be two-dimensional intrinsic ferromagnetic semiconductors while their physical properties have not been thoroughly investigated in bulk single crystals. We report the single-crystal growth, structural, magnetic and electronic transport properties of NaCr(Te1-xSex)2 (0 6 x 6 1) and NaCrS2. For NaCr(Te1-xSex)2, the strong perpendicular magnetic anisotropy of NaCrTe2 can be gradually tuned to be a nearly isotropic one by Se-doping. Meanwhile, a systematic change in the conductivity with increasing x is observed, displaying a doping-induced metal-insulator-like transition. Under magnetic field larger than 30 koe, both NaCrTe2 and NaCrSe2 can be polarized to a ferromagnetic state. While for NaCrS2, robust antiferromagnetism is observed up to 70 kOe and two field-induced metamagnetic transitions are identified along H||ab. These intriguing properties together with the potential to be exfoliated down to few-layer thickness make NaCrX2 (X=Te,Se,S) promising for exploring spintronic applications.
We prepared polycrystalline samples of the A_xBO_2 type layered oxides Na_0.77MnO_2 and LiCoO_2, and measured thermal conductivity from 15 to 280 K. Na0.77MnO_2 shows a low thermal conductivity of 15 mW/cmK, while LiCoO_2 shows a much higher value of 40 mW/cmK at 280 K. By comparing them with the data of NaCo_2O_4, we have found that the low thermal conductivity of A_xBO_2 comes essentially from the A-ion deficiency, not from the layered structure itself.
We show that a moving Josephson vortex in spatially modulated layered superconductors generates out-of-plane THz radiation. Remarkably, the magnetic and in-plane electric fields radiated are of the same order, which is very unusual for any good-conducting medium. Therefore, the out-of-plane radiation can be emitted to the vacuum without the standard impedance mismatch problem. Thus, the proposed design can be more efficient for tunable THz emitters than previous proposals, for radiation only propagating along the ab-plane.
2D layered ferroelectric materials such as CuInP$_2$S6 (CIPS) are promising candidates for novel and high-performance photocatalysts, owning to their ultrathin layer thickness, strong interlayer coupling, and intrinsic spontaneous polarization, while how to control the photocatalytic activity in layered CIPS remains unexplored. In this work, we report for the first time the photocatalytic activity of ferroelectric CIPS for the chemical deposition of silver nanostructures (AgNSs). The results show that the shape and spatial distribution of AgNSs on CIPS are tunable by controlling layer thicknes…
The phonon dispersion, density of states, Grüneisen parameters, and the lattice thermal conductivity of single- and multi-layered boron nitride were calculated using first-principles methods. For the bulk {\it h}-BN we also report the two-phonon density of states. We also present simple analytical solutions to the acoustic vibrational mode-dependent lattice thermal conductivity. Moreover, computations based on the elaborate Callaway-Klemens and the real space super cell methods are presented to calculate the sample length and temperature dependent lattice thermal conductivity of single- and mu…
In-plane thermal conductivity of the thermoelectric layered cobalt oxides has been measured using the Harman method, in which thermal conductivity is obtained from temperature gradient induced by applied current. We have found that the charge reservoir block (the block other than the CoO$_2$ block) dominates the thermal conduction, where a nano-block integration concept is effective for material design. We have further found that the thermal conductivity shows a small but finite in-plane anisotropy between $a$ and $b$ axes, which can be ascribed to the misfit structure.
Two-dimensional (2D) layered materials with diverse properties have attracted significant interest in the past decade. The layered materials discovered so far have covered a wide, yet discontinuous electromagnetic spectral range from semimetallic graphene, insulating boron nitride, to semiconductors with bandgaps from middle infrared to visible light. Here, we introduce new layered semiconductors, black arsenic-phosphorus (b-AsP), with highly tunable chemical compositions and electronic and optical properties. Transport and infrared absorption studies demonstrate the semiconducting nature of b…
We calculated the optical properties of an $N$-layer graphene by formulating the dynamical conductivity of each layer. This is the conductivity when an electromagnetic field is localized at a particular layer and differs from the standard conductivity calculated assuming a uniform field throughout all layers. By combining these conductivities with a transfer matrix method, we took into account the spatial variation of the electromagnetic field caused by internal reflections. The results obtained from the two conductivities show that similar peak structures originating from the interlayer elect…
The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band structure method is improved from the computational point of view by applying the Gauss-Konrod quadrature for the integrals along the different parts of the contour and by designing a cumulative special points scheme for two-dimensional Brillouin zone integrals corresponding to cubic systems.
Conductive and paintable inks of 2D layered MoS2 with aspect ratio-dependent conductivity are demonstrated. Using ultrasonically assisted solvent-exfoliation of MoS2, high concentration 2D and few-layer suspensions become inks that provide coherent films when painted. Conductivity of paintable 2D MoS2 inks can be modulated by length and width, where the conductivity is linked to the painting direction. Reducing the painted film width, increases conductivity for similar length, and the films conductivity is aspect ratio-dependent. Inks of solvent-exfoliated 2D MoS2 can be painted without polyme…
The semiconducting p-n junction is a simple device structure with great relevance for electronic and optoelectronic applications. The successful integration of low-dimensional materials in electronic circuits has opened the way forward for producing gate-tunable p-n junctions. In that context, here we present an organic (Cu-phthalocyanine)-2D layered material (MoS2) hybrid p-n junction with both gate-tunable diode characteristics and photovoltaic effect. Our proof-of-principle devices show multifunctional properties with diode rectifying factors of up to 10^4, while under light exposure they e…
In non-centrosymmetric metals, spin-orbit coupling (SOC) induces momentum-dependent spin polarization at the Fermi surfaces. This is exemplified by the valley-contrasting spin polarization in monolayer transition metal dichalcogenides (TMDCs) with in-plane inversion asymmetry. However, the valley configuration of massive Dirac fermions in TMDCs is fixed by the graphene-like structure, which limits the variety of spin-valley coupling. Here, we show that the layered polar metal BaMn$X_2$ ($X =$Bi, Sb) hosts tunable spin-valley-coupled Dirac fermions, which originate from the distorted $X$ square…
Unlike other switchable mirrors, Mg2NiHx films show large changes in reflection that yield very low reflectance (high absorptance) at different hydrogen contents, far before reaching the semiconducting state. The resulting reflectance patterns are of interference origin, due to a self-organized layered hydrogenation mechanism that starts at the substrate interface, and can therefore be tuned by varying the film thickness. This tunability, together with the high absorptance contrast observed between the solar and the thermal energies, strongly suggests the use of these films in smart coatings f…
Optical conductivity of layered topological semimetal TaNiTe$_5$
University of Zagreb（萨格勒布大学）；TU Wien（维也纳工业大学）；University of Fribourg（弗里堡大学）；University of West Bohemia in Pilsen（比尔森西波希米亚大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）
The frequency dependence of conductivity in In$_4$Se$_3$, pure and with copper admixture crystals, in the region of nitrogen temperatures is investigated. It was found out that variable length hops on the localized levels in the vicinity of Fermi level is pre-dominant mechanism of charge transfer in the crystals. For pure In$ _4$Se$ _3$ crystals the density of localized states is $10^{17}-10^{18}$ eV$^{-1}\cdot$cm$^{-3}$, the mean hop length is 220--350 Å. The reasons for the occurrence of localized states are considered within the model of a layered crystal as a quasi-disordered system.
Carbon nanosheets are mechanically stable free-standing two-dimensional materials with a thickness of ~1 nm and well defined physical and chemical properties. They are made by radiation induced cross-linking of aromatic self-assembled monolayers. Here we present a route to the scalable fabrication of multilayer nanosheets with tunable electrical, optical and chemical properties on insulating substrates. Stacks up to five nanosheets with sizes of ~1 cm^2 on oxidized silicon were studied. Their optical characteristics were investigated by visual inspection, optical microscopy, UV/Vis reflection …
The group IV-VI compound SnSe, with an orthorhombic lattice structure, has recently attracted particular interest due to its unexpectedly low thermal conductivity and high power factor, showing great promise for thermoelectric applications. SnSe displays intriguing anisotropic properties due to the puckered low-symmetry in-plane lattice structure. Low-dimensional materials have potential advantages in improving the efficiency of thermoelectric conversion, due to the increased power factor and decreased thermal conductivity. A complete study of the optical and electrical anisotropies of SnSe na…
Nanoscale engineered materials combined with wearable wireless technologies can deliver a new level of health monitoring. A reduced graphene oxide-nylon composite material is developed and tested, demonstrating its usefulness as a material for sensors in wearable, long-term electrocardiogram (ECG) monitoring via a comparison to one of the widely used ECG sensors. The structural analysis by scanning electron (SEM) and atomic force microscopy (AFM) shows a limited number of defects on a macroscopic scale. Fourier Transform Infrared (FTIR) and Raman spectroscopy confirm the presence of rGOx, and …
High performance thermoelectric devices requires materials with low lattice thermal conductivities. Many strategies, such as phonon engineering, have been made to reduce lattice thermal conductivity without simultaneously decrease of the charge transport performance. It is a simple and effective approach to use materials with heavy element to reduce the lattice thermal conductivity. Here, based on the first-principles calculations and phonon Boltzmann transport equations, we find the replacement of Zr with heavy element Hf in ZrNCl doesn't reduce the lattice thermal conductivity, instead, it s…
For a class of 2D hybrid organic-inorganic perovskite semiconductors based on $π$-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alig…
Molecular dynamics simulations combined with periodic electronic structure calculations are performed to decipher structural, thermodynamical and dynamical properties of the interfaced vs. confined water adsorbed in hexagonal 1D channels of the 2D layered electrically conductive Cu3(HHTP)2 and Cu3(HTTP)2 metal-organic frameworks (HHTP=2,3,6,7,10,11-hexahydroxytriphenylene and HTTP = 2,3,6,7,10,11-hexathiotriphenylene). Comparing water adsorption in bulk vs. slab models of the studied 2D MOFs shows that water is preferentially adsorbed on the framework walls via forming hydrogen bonds to the or…
Identifying intrinsic low-dimensional ferromagnets with high transition temperature and electrically tunable magnetism is crucial for the development of miniaturized spintronics and magnetoelectrics. Recently long-range 2D ferromagnetism was observed in van der Waals crystals CrI$_3$ and Cr$_2$Ge$_2$Te$_6$, however their Curie temperature is significantly lowered when reducing down to monolayer/few layers. Herein, using renormalized spin-wave theory and first-principles electronic structure theory, we present a theoretical study of electrically tunable 2D ferromagnetism in van der Waals layere…
Structural defects in the molybdenum disulfide (MoS2) monolayer are widely known for strongly altering its properties. Therefore, a deep understanding of these structural defects and how they affect MoS2 electronic properties is of fundamental importance. Here, we report on the incorporation of atomic hydrogen in mono-layered MoS2 to tune its structural defects. We demonstrate that the electronic properties of single layer MoS2 can be tuned from the intrinsic electron (n) to hole (p) doping via controlled exposure to atomic hydrogen at room temperature. Moreover, this hydrogenation process rep…
Building on discoveries in graphene and two-dimensional (2D) transition metal dichalcogenides, van der Waals (VdW) layered heterostructures - stacks of such 2D materials - are being extensively explored with resulting new discoveries of novel electronic and magnetic properties in the ultrathin limit. Here we review a class of naturally occurring heterostructures - so called misfits - that combine disparate VdW layers with complex stacking. Exhibiting remarkable structural complexity and diversity of phenomena, misfits provide a platform on which to systematically explore the energetics and loc…
We investigate multiple Fano, comblike scattering resonances in single-layered, concentric core-shell nanoparticles composed of magnetic materials. Using the Lorenz-Mie theory, we derive, in the long-wavelength limit, an analytical condition for the occurrence of comblike resonances in the single scattering by coated spheres. This condition establishes that comblike scattering response uniquely depends on material parameters and thickness of the shell, provided that it is magnetic and thin compared to the scatterer radius. We also demonstrate that comblike scattering response shows up beyond t…
We present a new route for the fabrication of ultrathin (~1 nm) carbon films and membranes, whose electrical behavior can be tuned from insulating to conducting. Self-assembled monolayers of biphenyls are cross-linked by electrons, detached from the surfaces and subsequently pyrolized. Above 1000K, the cross-linked aromatic monolayer forms a mechanically stable graphitic phase. The transition is accompanied by a drop of the sheet resistivity from ~10^8 to ~10^2 kOhm/sq and a mechanical stiffening of the nanomembranes from ~10 to ~50 GPa. The technical applicability of the nanosheets is demonst…
A tunable conductivity has been achieved by controllable substitution of a novel UV light activated electronic conductor. The transparent conducting oxide system H-doped Ca12-xMgxAl14O33 (x = 0; 0.1; 0.3; 0.5; 0.8; 1.0) presents a conductivity that is strongly dependent on the substitution level and temperature. Four-point dc-conductivity decreases with x from 0.26 S/cm (x = 0) to 0.106 S/cm (x = 1) at room temperature. At each composition the conductivity increases (reversibly with temperature) until a decomposition temperature is reached; above this value, the conductivity drops dramatically…
Understanding the electronic transport properties of layered, van der Waals transition metal halides (TMHs) and chalcogenides is a highly active research topic today. Of particular interest is the evolution of those properties with changing thickness as the 2D limit is approached. Here, we present the electrical conductivity of exfoliated single crystals of the TMH, cluster magnet, Nb3Cl8, over a wide range of thicknesses both with and without hexagonal boron nitride (hBN) encapsulation. The conductivity is found to increase by more than three orders of magnitude when the thickness is decrease…
We measure the thermal conductivity ($κ$) of individual InAs nanowires (NWs), and find that it is 3 orders of magnitude smaller than the bulk value in the temperature range of 10 to 50 K. We argue that the low $κ$ arises from the strong localization of phonons in the random superlattice of twin-defects oriented perpendicular to the axis of the NW. We observe significant electronic contribution arising from the surface accumulation layer which gives rise to tunability of $κ$ with the application of electrostatic gate and magnetic field. Our devices and measurements of $κ$ at different carrier c…
In 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the contrary, in the bilayer, the inversion symmetry is restored, but the reflection symmetry is broken. As a consequence of these contrasting symmetries, here we show that bilayer WS$_2$ exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrary to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial inter-conversion betwee…
To elucidate the relationship between a crystal's structure, its thermal conductivity, and its phonon dispersion characteristics, an analysis is conducted on layered diatomic Lennard-Jones crystals with various mass ratios. Lattice dynamics theory and molecular dynamics simulations are used to predict the phonon dispersion curves and the thermal conductivity. The layered structure generates directionally dependent thermal conductivities lower than those predicted by density trends alone. The dispersion characteristics are quantified using a set of novel band diagram metrics, which are used to …
Transition metal dichalcogenide (TMD) alloys have attracted great interests in recent years due to their tunable electronic properties, especially the semiconductor-metal phase transition, along with their potential applications in solid-state memories and thermoelectrics. However, the thermal conductivity of layered two-dimensional (2D) TMD alloys remains largely unexplored despite that it plays a critical role in the reliability and functionality of TMD-enabled devices. In this work, we study the temperature-dependent anisotropic thermal conductivity of the phase-transition 2D TMD alloys WSe…
Incorporating magnetism into two dimensional (2D) van der Waals (VdW) heterostrutures is crucial for the development of functional electronic and magnetic devices. Here we show that Nb3X8 (X = Cl, Br) is a family of 2D layered trimerized kagomé magnets that are paramagnetic at high temperatures and undergo a first order phase transition on cooling to a singlet magnetic state. X-ray diffraction shows that a rearrangement of the VdW stacking accompanies the magnetic transition, with high and low temperature phases consistent with STEM images of the end members α-Nb3Cl8 and \b{eta}-Nb3Br8. The te…
Invisible cloak has long captivated the popular conjecture and attracted intensive research in various communities of wave dynamics, e.g., optics, electromagnetics, acoustics, etc. However, their inhomogeneous and extreme parameters imposed by transformation-optic method will usually require challenging realization with metamaterials, resulting in narrow bandwidth, loss, polarization-dependence, etc. On the contrary, we demonstrate that tunable thermodynamic cloak can be achieved with homogeneous and finite conductivity only employing naturally available materials. The controlled localization …
Resonance Raman scattering, a very effective and sensitive technique for atomically thin semiconducting transition metal dichalcogenide, can be used to observe the phonons from the entire Brillouin zone. In addition to the significance of resonance effect on the Raman spectrum it may also be used to probe the electron-phonon coupling. Our study is devoted to understand the phonons in layered MoS2, especially for very low frequency range (i.e. below 100 cm-1), as a function of temperature under the resonance effect. Understanding the phonon-phonon and electron-phonon coupling and the effects of…
First-principles calculations are employed to investigate the phonon transport of BiCuOSe. Our calculations reproduce the lattice thermal conductivity of BiCuOSe. The calculated gruneisen parameter is 2.4~2.6 at room temperature, a fairly large value indicating a strong anharmonicity in BiCuOSe, which leads to its ultralow lattice thermal conductivity. The contribution to total thermal conductivity from high-frequency optical phonons, which are mostly contributed by the vibrations of O atoms, is larger than 1/3, remarkably different from the usual picture with very little contribution from hig…
Ultralow and Tunable Thermal Conductivity of Parylene C for Thermal Insulation in Advanced Packaging
School of Software & Microelectronics, Peking University（北京大学软件与微电子学院）；School of Integrated Circuits and Beijing Advanced Innovation Center for Integrated Circuits, Peking University（北京大学集成电路学院及北京集成电路先进创新中心）
We use a combination of polarized Raman spectroscopy experiment and model magnetism-phonon coupling calculations to study the rich magneto-Raman effect in the two-dimensional (2D) magnet $\mathrm{CrI_3}$. We reveal a novel layered-magnetism-assisted phonon scattering mechanism below the magnetic onset temperature, whose Raman excitation breaks time-reversal symmetry, has an antisymmetric Raman tensor, and follows the magnetic phase transitions across critical magnetic fields, on top of the presence of the conventional phonon scattering with symmetric Raman tensors in $N$-layer $\mathrm{CrI_3}$…
Atomic-scale tunable phonon transport at tailored grain boundaries and Their Impact on Thermal Conductivity
University of California, Irvine（加州大学尔湾分校）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Irvine Materials Research Institute, University of California-Irvine（加州大学尔湾分校欧文材料研究所）；University of California, San Diego（加州大学圣迭戈分校）
The possibility of tuning the vibrational properties and the thermal conductivity of layered van der Waals materials either chemically or mechanically paves the way to significant advances in nanoscale heat management. Using first-principles calculations we investigate the modulation of heat transport in MoS2 by lithium intercalation and cross-plane strain. We find that both the in-plane and cross-plane thermal conductivity (kr, kz) of MoS2 are extremely sensitive to both strain and electrochemical intercalation. Combining lithium intercalation and strain, the in-plane and cross-plane thermal …
Understanding the interplay between various design strategies (for instance, bonding heterogeneity and lone pair induced anharmonicity) to achieve ultralow lattice thermal conductivity ($κ_l$) is indispensable for discovering novel functional materials for thermal energy applications. In the present study, we investigate layered PbXF (X = Cl, Br, I), which offers bonding heterogeneity through the layered crystal structure, anharmonicity through the Pb$^{2+}$ $6s^2$ lone pair, and phonon softening through the mass difference between F and Pb/X. The weak inter-layer van der Waals bonding and the…
The ionic conduction properties of the technologically important two-dimensional (2D) layered battery material Na2Mn3O7, with exceptional small-voltage hysteresis between charge and discharge curves, have been investigated as a function of temperature and frequency by an impedance spectroscopy. The detailed analyses of the impedance data in the form of dc-conductivity, ac-conductivity, electrical modulus, dielectric constant and complex polarizability reveal a long-range Na-ionic conductivity with negligible contribution from a local dipole relaxation. A significant enhancement (~10^4 times) o…
Layered materials have uncommonly anisotropic thermal properties due to their strong in-plane covalent bonds and weak out-of-plane van der Waals interactions. Here we examine heat flow in graphene (graphite), h-BN, MoS2, and WS2 monolayers and bulk films, from diffusive to ballistic limits. We determine the ballistic thermal conductance limit (Gball) both in-plane and out-of-plane, based on full phonon dispersions from first-principles calculations. An overall phonon mean free path (λ) is expressed in terms of Gball and the diffusive thermal conductivity, consistent with kinetic theory if prop…
In the design of materials with low lattice thermal conductivity, compounds with high density, low speed of sound, and complexity at either the atomic, nano- or microstructural level are preferred. The layered compound Mg$_3$Sb$_2$ defies these prevailing paradigms, exhibiting lattice thermal conductivity comparable to PbTe and Bi$_2$Te$_3$, despite its low density and simple structure. The excellent thermoelectric performance ($zT$ $\sim$ 1.5) in $n$-type Mg$_3$Sb$_2$ has thus far been attributed to its multi-valley conduction band, while its anomalous thermal properties have been largely ove…
We analyze the anisotropic electrical and thermal transport measurements in single crystals of In2Te5 belonging to monoclinic space group C12 c1 with the temperature gradient applied parallel and perpendicular to the crystallographic c-axis of the crystals. The thermal conductivity along the c-axis thermal conductivity parallel was found to smaller by a factor of 2 compared to the thermal conductivity along the direction perpendicular to the c-axis over the entire temperature range. In contrast, the Seebeck coefficient along the c-axis parallel was found to be higher than its value along the d…
Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL), including exchange and Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topologi…
With the miniaturization and integration of nanoelectronic devices, efficient heat removal becomes a key factor affecting the reliable operation of the nanoelectronic device. With the high intrinsic thermal conductivity, good mechanical flexibility, and precisely controlled growth, two-dimensional (2D) materials are widely accepted as ideal candidates for thermal management materials. In this work, by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations, we comprehensively investigated the thermal conductivity of novel 2D layered MSi$_2$N$_4$ (M = Mo, W)…
We report on the successful terahertz emission (0.6$\sim$1 THz) that is continuous and tunable in its frequency and power, by driving Josephson vortices in resonance with the collective standing Josephson plasma modes excited in stacked Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ intrinsic Josephson junctions. Shapiro-step detection was employed to confirm the terahertz-wave emission. Our results provide a strong feasibility of developing long-sought solid-state terahertz-wave emission devices.
Inspired by the recent first-principles calculations showing the high thermoelectric performance of layered pnictogen chalcogenides, we experimentally characterise the crystal structure and high-temperature transport properties of the layered antimony selenides REOSbSe2 (RE = La, Ce). The crystal structure of REOSbSe2 was the tetragonal P4/nmm space group, consisting of alternate stacks of SbSe2 and REO layers. These two compounds were n-type semiconductors. The optical band gaps of LaOSbSe2 and CeOSbSe2 were evaluated to be 1.0 and 0.6 eV, respectively. The room-temperature thermal conductivi…
We predict high thermoelectric efficiency in the layered perovskite La$_2$Ti$_2$O$_7$, based on calculations (mostly ab-initio) of the electronic structure, transport coefficients, and thermal conductivity in a wide temperature range. The figure of merit $ZT$ computed with a temperature-dependent relaxation time increases monotonically from just above 1 at room temperature to over 2.5 at 1200 K, at an optimal carrier density of around 10$^{20}$ cm$^{-3}$. The Seebeck thermopower coefficient is between 200 and 300 $μ$V/K at optimal doping, but can reach nearly 1 mV/K at low doping. Much of the …
