RESUMEN
The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.
RESUMEN
Photocathodes-materials that convert photons into electrons through a phenomenon known as the photoelectric effect-are important for many modern technologies that rely on light detection or electron-beam generation1-3. However, current photocathodes are based on conventional metals and semiconductors that were mostly discovered six decades ago with sound theoretical underpinnings4,5. Progress in this field has been limited to refinements in photocathode performance based on sophisticated materials engineering1,6. Here we report unusual photoemission properties of the reconstructed surface of single crystals of the perovskite oxide SrTiO3(100), which were prepared by simple vacuum annealing. These properties are different from the existing theoretical descriptions4,7-10. In contrast to other photocathodes with a positive electron affinity, our SrTiO3 surface produces, at room temperature, discrete secondary photoemission spectra, which are characteristic of efficient photocathode materials with a negative electron affinity11,12. At low temperatures, the photoemission peak intensity is enhanced substantially and the electron beam obtained from non-threshold excitations shows longitudinal and transverse coherence that differs from previous results by at least an order of magnitude6,13,14. The observed emergence of coherence in secondary photoemission points to the development of a previously undescribed underlying process in addition to those of the current theoretical photoemission framework. SrTiO3 is an example of a fundamentally new class of photocathode quantum materials that could be used for applications that require intense coherent electron beams, without the need for monochromatic excitations.
