The presence of topologically non-trivial electronic band structures in condensed matter systems leads to a number of unusual consequences. A rich variety of phenomena have been discovered in gapless topological materials, such as those exhibiting Dirac-fermion excitations near the points of linear crossings of bands close to the Fermi energy EF. The breaking of either spatial inversion symmetry or time reversal symmetry splits the degeneracy of the Dirac points, leading to a pair of topologically protected Weyl points. Weyl fermions have been found to cause distinct experimental signatures, such as the chiral anomaly in transport measurements, a topological Hall effect, and Fermi arcs. Weyl fermions have mainly been studied in weakly correlated electron systems, while strong electronic correlations are frequently found to lead to novel electronic properties beyond those of simple metals or insulators, and heavy fermion systems are the prototype examples showing phenomena characteristic for strongly correlated electron systems. Here, due to strong Kondo coupling between the f-electron and conduction-band states, below the Kondo temperature , the electronic bands in the vicinity of EF may become strongly renormalized, showing a strong f-character and a huge enhancement of the quasiparticle mass. When the chemical potential lies within the hybridization gap, insulating behavior is found at low temperatures and in the topological Kondo insulators, such as has been proposed for SmB6, square plant pots the resulting electronic structure is topologically non-trivial, again leading to conducting states on the surface.
It is therefore of particular interest to look for topological heavy fermion semimetals with gapless excitations, i.e. Weyl fermions in the presence of strongly renormalized bands. Such a Weyl–Kondo semimetal phase has been predicted from calculations based on the periodic Anderson model with broken inversion symmetry. While it was proposed that Ce3Bi4Pd3 displays the low-temperature thermodynamic signatures of a Weyl–Kondo semimetal, other signatures of Weyl fermions such as the chiral anomaly have not been reported. A Weyl heavy fermion state was also proposed for CeRu4Sn6 from ab initio calculations, but no experimental evidence for Weyl fermions has been demonstrated. Consequently, whether Weyl fermions exist in the presence of a strong Kondo effect needs to be determined experimentally. Furthermore, the influence of electronic correlations on Weyl fermions is to be explored, specifically how such a system evolves from high temperatures, where the f-electrons are well localized, to low temperatures where there is a strong Kondo interaction and a reconstruction of the electronic bands. It was recently found that the half-Heusler GdPtBi, which has a strongly localized 4f-electron shell, shows evidence for Weyl fermions in an applied magnetic field due to the presence of the chiral anomaly and topological Hall effect. Here, we examine the isostructural compound YbPtBi. Although at high temperatures the Yb 4f-electrons are localized similar to GdPtBi, upon cooling YbPtBi becomes a prototypical heavy-fermion semimetal, where the enormous Sommerfeld coefficient of γ ≈ 8 J mol−1 K−2 demonstrates the enhanced effective mass of the charge carriers. This compound is therefore highly suited to look for Weyl fermions, which are strongly affected by electronic correlations. In this work, we report evidence for Weyl fermions in YbPtBi, where the bands hosting the Weyl points are strongly modified as the Kondo coupling strengthens at low temperatures.
Electronic structure calculations and angle-resolved photoemission spectroscopy measurements indicate the presence of triply degenerate fermion points in the high-temperature regime, which will each split into a Weyl node and a trivial crossing in applied fields. At these temperatures, evidence for the chiral anomaly is revealed by field-angle-dependent magnetotransport measurements. As the temperature is lowered, the chiral anomaly is not detected in the magnetotransport, but experimental signatures of Weyl fermions are found in measurements of the specific heat. This is consistent with a greatly reduced Fermi velocity due to the influence of the Kondo effect on the electronic bands near the Weyl points. Furthermore, the observation of a topological Hall effect contribution, which can arise from the Berry curvature generated by the Weyl nodes, provides additional evidence for the existence of Weyl fermions at both low and elevated temperatures.At higher temperatures, the band structure of YbPtBi can be calculated treating f-electrons as core states, as displayed in Fig. 1. The Λ6 bands cross the two hole bands near EF, forming two triply degenerate fermion points. Under amagnetic field, each triply degenerate point will further split into a Weyl point and a trivial crossing, with energies close to the bottom of the electron bands. The calculated bulk band structure with triply degenerate points is in good agreement with the ARPES results in Fig. 1b, which shows the energy–momentum dispersion relations along the surface ΓMdirection. Note that the sample can only be cleaved well with the orientation.
Along this orientation, the symmetry-equivalent bulk ΓL direction projects on the surface ΓM direction at a slanted angle, allowing for the dispersion in the vicinity of the triply degenerate points to be revealed via a careful comparison with the projected bulk band structure calculations . Two hole bands crossing EF can be clearly identified in the ARPES experiments, as well as an additional electron band with a band bottom right below EF. These experimentally observed bands are confirmed to be three dimensional bulk bands based on their photon energy dependence, and they correspond well to the theoretical calculations. The direct observation of both electron and hole pockets and their close proximity with different group velocities confirms the existence of the triply degenerate fermion points near EF, which is not affected by the slight discrepancy between the experimental results and calculations. This discrepancy is mainly related to the details of the separation and slope of the two hole bands, which could be caused by the limitations of frozen f-shell calculations and correlation effects not taken into account by the local density approximation. The good correspondence between ARPES measurements and density functional theory calculations therefore provides evidence for Weyl fermions at elevated temperatures.Based on the above experimental findings, we propose the diagram shown in Fig. 5 to describe the Weyl fermions in YbPtBi. At high temperatures there are Weyl nodes formed from the conduction bands, while the f electrons are well localized. This is consistently shown from electronic structure calculations, ARPES, and magnetotransport measurements. At lower temperatures, the strong band renormalization due to Kondo coupling enhances the effective quasiparticle mass, which modifies the dispersion ofthe bands in the vicinity of the topologically protected Weyl points, as shown schematically in the diagram. The renormalization also leads to a greatly reduced effective Fermi velocity v* compared to the bare band value, which eventually causes the disappearance of the chiral anomaly in transport measurements, but allows for the observation of a sizeable specific heat contribution C ~ 3. Importantly, there is evidence for the Berry curvature associated with the Weyl nodes from the anomalous Hall effect, which can be detected in both the intermediate and low-temperature regimes. Our results highlight the existence of Weyl fermions in YbPtBi, where we find evidence for their modification as the Kondo coupling is strengthened upon lowering the temperature. How precisely the Weyl points are modified as the electronic correlations become stronger needs to be determined by future studies. While the topological Hall effect and specific heat provide evidence for the survival of Weyl fermions at low temperatures, looking for spectroscopic evidence from ARPES or scanning tunneling spectroscopy is very important. One possible approach to reveal Weyl fermions in the heavy fermion state from f-bands is resonant photo emission. However, plastic potting pots our measurements across the Yb N edge do not show obvious resonance contrast . Although ARPES measurements with hν > 100 eV indeed reveal the bulk f bands near EF , resolving the hybridized bands deep inside the heavy fermion state is still challenging, and therefore further ARPES measurements with greater energy and momentum resolution are highly desirable. The presence of Weyl fermions in YbPtBi is different from the cases of both CeSb and GdPtBi, where the bands hosting Weyl fermions do not have a significant f-electron contribution.
Meanwhile, evidence for Weyl fermions has also been found in some magnetic d-electron systems such as Mn3Sn and YbMnBi2, where in the case of Mn3Sn a significant topological Hall effect is also observed. On the other hand, it is of great interest to look for the kind of dichotomy observed here for YbPtBi in other potential Weyl heavy-fermion semimetals, such as Ce3Bi4Pd3 where a similarly small v* was inferred from the specific heat, yet evidence for the chiral anomaly at elevated temperatures has not yet been reported. Furthermore, the strength of the Kondo interaction in heavy fermion systems can be readily tuned by non-thermal control parameters, such as pressure and magnetic field, and in particular, a quantum critical point can be reached in YbPtBi at a critical field of 0.4 T. Therefore, our findings may open up the opportunity to explore the exciting relationship between Weyl fermions, electron–electron correlations and quantum criticality.Increasing temperatures and temperature variability associated with a changing climate have become a major concern for many wine grape growing regions due to their effect on grape and wine composition. As is true for other crops, adequate sun exposure is vital because grapevines need sunlight for photosynthesis, growth, and development, and absorbed radiation by the berries is crucial for the biochemical and physiological processes that determine grape berry quality. Regrettably, excess sunlight and elevated temperatures are negatively affecting grape productivity in many growing regions. In California, minimum and maximum annual temperatures have increased from 1985 to 2011 by 2.34◦C and 1.77◦C, respectively, and in the summers by 3.88◦C and 3.31◦C, respectively . In Oakville, CA, Mart´ınez-Luscher et al. ¨ reported that elevated temperatures for grape clusters resulted in unbalanced wines with higher pH and lower levels of anthocyanins. Other research in Murrumbidgee, Australia reported that temperatures exceeding 40◦C result in delaying ripening and causing berry sunburn. Thus, strategies to minimize harmful berry temperatures are needed to sustain production in warm climates. It is challenging to manage the grapevine canopy to reduce the effect of excess temperature because of the complex interactions between plant architecture and the environment. Traditionally, it has been recommended to time canopy management to maintain sun-exposure for young fruits, but also to allow some shading of mature grape clusters to prevent excess sun exposure. Although increasing the shade in vineyards palliates the effect of elevated temperature, trade-offs need to be evaluated as well. For instance, shaded clusters can cause delay in fruit ripening, reduce wine quality, and increase disease prevalence due to pathogens such as bunch rot and powdery mildew. The negative effects of elevated temperature on grape berries could likely be mitigated in many cases if the complex interactions between canopy architecture and microclimate were better understood and predicted at the berry level. Developing and evaluating proposed mitigation strategies experimentally based on field trials is costly and time-consuming, which can limit their breadth and generalizability. Crop models can have the potential to extrapolate the results of a limited set of experiments through systematic variation of relevant variables, however, there are currently no models available that can represent varying grapevine architectures and their effect on spatial and temporal fluctuations in grape berry temperature. Through three different studies, this dissertation aims to 1) investigate the impact of the heterogeneous and anisotropic vegetation structure characteristic of grapevines on light interception, 2) develop a 3D model to simulate grape berry temperature in response to varying vineyard architecture and topography, and 3) identify strategies that have the potential to mitigate unfavorable temperatures in grape berries. Chapter 2 evaluates widely used assumptions when modeling solar radiation interception in plant canopies. The solar radiation intercepted by plant canopies is a fundamental driver of biophysical processes on Earth, and thus, quantifying such interception is a critical part of understanding and predicting a wide range of processes occurring at the land-atmosphere interface. The study showed that using a 1D model to simulate light interception for discontinuous canopies resulted in overestimation of light interception by up to 115% for the cases considered.