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Single Electron Transport and Possible Quantum Computing in 2D Materials
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Because of the large valley separation in momentum space, the valley index is expected to be robust against scattering by smooth deformations and long-wavelength phonons. To manipulate such a valley degree of freedom for valleytronic applications, measurable physical quantities that distinguish the ±K valleys are required. The Berry curvature (Ω) and the orbital magnetic moment (m) are two physical quantities for ±K valleys to have opposite values. The Berry curvature is defined as a gauge field tensor derived from the Berry vector potential An (R) through the relation Ωn(R)=∇R × An(R), where n is the energy band index (in the case of 2H-TMDs and at the ±K points, n is either the conduction or valence band), and R is the parameter to be varied in a physical system (in the case below, R is the wavevector k) [45]. The Berry curvature can be written as a summation over the eigenstates as follows [46]: Ωn(k)=iℏ2m2∑i≠nPn,i(k)×Pi,n(k)[En0(k)−Ei0(k)]2
Energy-harvesting materials based on the anomalous Nernst effect
Published in Science and Technology of Advanced Materials, 2019
Masaki Mizuguchi, Satoru Nakatsuji
The large anomalous Nernst and Hall effects in Mn3Sn are unexpected according to their conventional scaling law with M, and thus should arise from the mechanism distinct from the conventional one for ferromagnets [7]. The anomalous Hall conductivity is the measure of the sum of the Berry curvature for all the occupied bands. On the other hand, ANE, or more precisely, the transverse thermoelectric conductivity αxy is determined by the Berry curvature around the Fermi level [45,46]. Therefore, the large αxy means that the Berry curvature is significantly enhanced at EF. In fact, a recent first-principles calculation has confirmed the Weyl points nearby EF [47]. While it is theoretically expected that when the Weyl points locate exactly at EF, the ANE is small as the Hall effect becomes maximized with (∂σH/∂E)EF = 0, a slight tuning of the Fermi energy away from the Weyl point may enhance the ANE significantly (Figure 11(c)). The calculated anomalous transverse thermoelectric conductivity is found as large as seen in experiment, and has a peak with different signs around the Weyl point at E = 60 meV away from EF (Figure 11(c)). Our observation of the dramatic change in the large anomalous Nernst as a function of the Fermi energy, which is fully consistent with theory, supports the idea that the Weyl points play a major role in their mechanism. Our results thus indicate that the ANE in Mn3Sn is particularly enhanced because of the characteristic structure of the Berry curvature with several Weyl points nearby the Fermi level [47,54]. Further developing the concept of application of Weyl magnet for enhancing ANE, we have recently found that a magnetic Weyl semimetal in the vicinity of the Lifshitz transition between Type-I and Type-II Weyl fermion states would lead to a giant ANE. In fact, the Weyl ferromagnet Co2MnGa is found to exhibit a record high ANE of 6 μV/K at room temperature, one order magnitude larger than the ordinary ferromagnet [26].