Herein we cover the key concepts in the field of thermoelectric materials research, present the current understanding, and show the latest developments. Current research is aimed at increasing the thermoelectric figure of merit (ZT) by maximizing the power factor and/or minimizing the thermal conductivity. Attempts at maximizing the power factor include the development of new materials, optimization of existing materials by doping, and the exploration of nanoscale materials. The minimization of the thermal conductivity can come through solid-solution alloying, use of materials with intrinsically low thermal conductivity, and nanostructuring. Herein we describe the most promising bulk materials with emphasis on results from the last decade. Single-phase bulk materials are discussed in terms of chemistry, crystal structure, physical properties, and optimization of thermoelectric performance. The new opportunities for enhanced performance bulk nanostructured composite materials are examined and a look into the not so distant future is attempted.

New and Old Concepts in Thermoelectric Materials

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians Analytical approaches are complemented by advanced numerical simulations

Anderson Transitions

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

This review describes recent groundbreaking results in Si, Si/SiGe, and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade, and single-shot readout of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress toward the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics.

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Silicon quantum electronics

Electrical-resistivity, magnetic-susceptibility, and specific-heat data reveal that UBe13 is superconducting below 0.85 K. Highly anomalous low-temperature electronic properties in both the normal and superconducting states result in an enormous electronic specific-heat coefficient γ=1.1J/mole K2 and a corresponding magnetic susceptibility X =1.5×10-2 emu/mole. The superconducting state appears to be extremely stable with an initial slope of the temperature derivative of the critical field(∂H c2/∂T) Tc =-257kOe/K.

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Ube13 - an unconventional actinide superconductor

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T K CKS (T K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (∼k B T K) high-amplitude Abrikosov-Suhl resonance E R in the vicinity of the Fermi level E F. This resonance is situated exactly at E F in low T K CKS with T K ΔCF (ΔCF is the crystal field splitting). In low T K ‘j=1/2’ CKS the condition E R=E F leads to an increase of the density of states at E F, which is large enough to induce heavy fermion superconductivity in CeCu2Si2, UBe13. We demonstrate that the transition from low T K (E R=E F) to high T K CKS (E R≠E F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition...

Concentrated Kondo systems

The new class of intermetallic compounds RNiSn(R=Ti,Zr,Hf) may be characterised by the presence of an ordered sublattice of Ni atom vacancies in comparison with normal metals RNi2Sn with no Ni vacancies. We report unusual transport and optical properties of the RNiSn system. The electrical resistivity of RNiSn is very high (3<p<100) mOhm*cm; the temperature coefficient of resistivity (TCR) is negative and strongly dependent on the annealing conditions. For some samples ZrNiSn and for a single crystal of TiNiSn the resistivity can be described by the Mott's law at temperatures 0.1<T<20 K. A phase transition nearT=100 K without change of crystal structure was deduced from Hall effect data and the temperature dependence of the lattice constant. Preliminary data on transport phenomena in RPtSn and RPdSn(R=Ti,Zr,Hf) compounds are also reported. The unusual properties of RNiSn system might be related to a gap of the electron spectrum near the Fermi energy.

Gap at the Fermi level in the intermetallic vacancy system RBiSn(R=Ti,Zr,Hf)

The presence of a narrow band below conduction band of nonmagnetic compounds MNiSn (M=Ti, Zr, Hf) is assumed to explain their low temperature properties such as the heat capacity, IR optics, electronics transport. A computation of the Seebeck coefficient supplies support for this assumption.

Narrow band in the intermetallic compounds MNiSn (M=Ti, Zr, Hf)

We report on the details of the insulator-metal transition (IMT) induced in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$(${\mathrm{Ca}}_{\mathit{z}}$,${\mathit{R}}_{1\mathrm{\ensuremath{-}}\mathit{z}}$)${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8+\mathit{y}}$ (R=Y, Gd, Nd) by ${\mathrm{Ca}}^{2+}$ doping. The resistivity in the insulating regime is analyzed using a generalized hopping approach based on the connectivity criterion. This enables us to estimate the dependence of the localization radius ${\mathit{a}}_{\mathit{H}}$ on the Ca concentration independent of dimensionality. Insulating samples with a Y content not too far from the critical concentration ${\mathit{z}}_{\mathit{C}}$=(0.43\ifmmode\pm\else\textpm\fi{}0.02) show metallic conduction at high temperature and hopping conduction at low temperature. This shows the coexistence of delocalized and localized states separated by a disorder-induced mobility edge. Ultraviolet-photoemission-spectroscopy (UPS) spectra give evidence for both a shift in the Fermi level to lower energies and the development of new states at the Fermi level. The existence of a mobility edge together with the shift in ${\mathit{E}}_{\mathit{F}}$ upon ${\mathrm{Ca}}^{2+}$ doping shows that the transition is probably of the Anderson type. We present a schematic picture for the density of states in the vicinity of ${\mathit{E}}_{\mathit{F}}$ based on the results of spectroscopic and transport data. For this density of states we calculate the electrical resistivity using the Kubo-Greenwood formula. The results are in good qualitative agreement with the experiments. At the IMT the localization radius diverges and the metallic conductivity vanishes following a scaling law \ensuremath{\sigma}=${\mathrm{\ensuremath{\sigma}}}_{0}${1-z/${\mathit{z}}_{\mathit{C}}$${\mathrm{}}}^{\mathrm{\ensuremath{\eta}}}$, with a critical exponent \ensuremath{\eta}=1A.

Scaling behavior at the insulator-metal transition in Bi2Sr2(CazR1-z)Cu2O8+y where R is a rare-earth element.

Electric, magnetic, and thermoelectric properties of Ce
 x
 La1−x
Cu2Si2 (0⩽x⩽1) compounds have been studied over a wide temperature interval 0.04 ⩽T⩽300 K in magnetic fieldsH⩽40 kOe. The paramagnetic-magnetic ordering transition temperatureT

 M
 is found to rise from ∼0.32 K for cerium concentrationx=0.2 to 1.6 K forx=0.6. A further increase inx from ∼0.8 to 1.0 leads to a decrease inT

 M
 . Simultaneously, the susceptibility kink is smeared out and atx≈1.0 it is transformed into temperature-independent enhanced Pauli paramagnetism. The magnetic phase diagram has been found to be similar to that proposed by Doniach for the one-dimensional Kondo-necklace model. The Kondo-lattice compound CeCu2Si2 exhibits a superconducting transition atT

 c
 ⋍0.5 K. The variation of the magnetic properties of Ce
 x
 La1−x
Cu2Si2 from magnetic ordering at 0.2≲x≲0.8 to the nonmagnetic superconducting state atx → 1.0 is caused by the crossover from the magnetic regimeT
RKKY≫T
K (in which the RKKY temperatureT
RKKY exceeds the Kondo temperatureT
K) to the nonmagnetic singlet ground state corresponding to the situation whenT
K≫T
RKKY. This crossover is accompanied by a sharp increase in the low-temperature Hall coefficientR
H(T) in Ce
 x
 La1−x
Cu2Si2 compounds atx → 1. At the same time, a minimum of the negative Seebeck coefficient with a high amplitude appears at 10<T<100 K. The anomalous low-temperature properties of Kondo lattices have been shown to be due to the rise of the narrow Abrikosov-Suhl resonance in the vicinity of the Fermi level eF as the temperature is lowered fromT≫T
K toT≪T
K. This resonance has a giant amplitude in concentrated Kondo systems and is responsible for the existence in CeCu2Si2 of heavy fermions with extremely low degeneracy temperatureT*F estimated to be 10 K from theR
H versusT curve. Further increase of the Kondo coupling constantJ in CeCu2Si2 under pressure induces an increase in (1) the Hall coefficientR
H(T=4.2 K), (2) the superconducting transition temperatureT

 c
 , (3) the derivative of the upper critical fielddH

c2/dT

 c
 , and (4) the low-temperature Seebeck coefficientS(T), which have maximum values at the same pressurep
K1≈3 kbar, corresponding to the Kondo-lattice state with the maximum amplitude of the Abrikosov-Suhl resonance in CeCu2Si2 atp=p
KL. At higher pressuresp>p
KL, a continuous transition from the Kondo lattice to the intermediate valence state is observed, which is accompanied by a complete smearing out of the resonance near the Fermi level. Therefore the Kondo lattices represent a new class of solids, which can be characterized as the link between stable magnetism of metals with a deep 4f level and unstable magnetism associated with fluctuating valence. This novel state can be described by a set of anomalous low-temperature properties related to the giant Abrikosov-Suhl resonance near the Fermi level.

Victor Moshchalkov

Papers

Concentrated Kondo systems

Gap at the Fermi level in the intermetallic vacancy system RBiSn(R=Ti,Zr,Hf)

Narrow band in the intermetallic compounds MNiSn (M=Ti, Zr, Hf)

Scaling behavior at the insulator-metal transition in Bi2Sr2(CazR1-z)Cu2O8+y where R is a rare-earth element.

Electric and magnetic-properties of the kondo lattice compound cecu2si2