Remark on charge conjugation in the non relativistic limit

We study the non relativistic limit of the charge conjugation operation $\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\cal C$, $\cal P$ (parity) and $\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Also, and most important, the limit exists in the context of galilean relativity. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\mu$, then the explicit form of the matrix for $\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\vec{x} \to \vec{x}^*$. This result is natural in a fiber bundle description.Comment: 8 page

Band Structure Dynamics in Indium Wires

One-dimensional Indium wires grown on Si(111) substrates, which are metallic at high temperatures, become insulating below $\sim100$ K due to the formation of a Charge Density Wave (CDW). The physics of this transition is not conventional and involves a multiband Peierls instability with strong interband coupling. This CDW ground state is readily destroyed with femtosecond laser pulses resulting in a light-induced insulator-to-metal phase transition. The current understanding of this transition remains incomplete, requiring measurements of the transient electronic structure to complement previous investigations of the lattice dynamics. Time- and angle-resolved photo\-emission spectroscopy with extreme ultra-violet radiation is applied to this end. We find that the transition from the insulating to the metallic band structure occurs within $\sim660$ fs that is a fraction of the amplitude mode period. The long life time of the transient state ($>100$ ps) is attributed to trapping in a metastable state in accordance with previous work.Comment: 14 pages, 7 figure

Direct evidence for efficient ultrafast charge separation in epitaxial WS2_2/graphene heterostructure

We use time- and angle-resolved photoemission spectroscopy (tr-ARPES) to investigate ultrafast charge transfer in an epitaxial heterostructure made of monolayer WS$_2$ and graphene. This heterostructure combines the benefits of a direct gap semiconductor with strong spin-orbit coupling and strong light-matter interaction with those of a semimetal hosting massless carriers with extremely high mobility and long spin lifetimes. We find that, after photoexcitation at resonance to the A-exciton in WS$_2$, the photoexcited holes rapidly transfer into the graphene layer while the photoexcited electrons remain in the WS$_2$ layer. The resulting charge transfer state is found to have a lifetime of $\sim1$\,ps. We attribute our findings to differences in scattering phase space caused by the relative alignment of WS$_2$ and graphene bands as revealed by high resolution ARPES. In combination with spin-selective excitation using circularly polarized light the investigated WS$_2$/graphene heterostructure might provide a new platform for efficient optical spin injection into graphene.Comment: 28 pages, 14 figure

Direct evidence for efficient ultrafast charge separation in epitaxial WS₂/graphene heterostructures

We use time- and angle-resolved photoemission spectroscopy (tr-ARPES) to investigate ultrafast charge transfer in an epitaxial heterostructure made of monolayer WS2 and graphene. This heterostructure combines the benefits of a direct-gap semiconductor with strong spin-orbit coupling and strong light-matter interaction with those of a semimetal hosting massless carriers with extremely high mobility and long spin lifetimes. We find that, after photoexcitation at resonance to the A-exciton in WS2, the photoexcited holes rapidly transfer into the graphene layer while the photoexcited electrons remain in the WS2 layer. The resulting charge-separated transient state is found to have a lifetime of ∼1 ps. We attribute our findings to differences in scattering phase space caused by the relative alignment of WS2 and graphene bands as revealed by high-resolution ARPES. In combination with spin-selective optical excitation, the investigated WS2/graphene heterostructure might provide a platform for efficient optical spin injection into graphene

Ultrafast Momentum Imaging of Pseudospin-Flip Excitations in Graphene

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photo-excited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization, and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy and in-plane momentum. We first show that the rapidly-established quasi-thermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photo-excited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photo-control experiments and optoelectronic device applications.Comment: 23 pages, 12 figure

Tracking primary thermalization events in graphene with photoemission at extreme timescales

Direct and inverse Auger scattering are amongst the primary processes that mediate the thermalization of hot carriers in semiconductors. These two processes involve the annihilation or generation of an electron-hole pair by exchanging energy with a third carrier, which is either accelerated or decelerated. Inverse Auger scattering is generally suppressed, as the decelerated carriers must have excess energies higher than the band gap itself. In graphene, which is gapless, inverse Auger scattering is instead predicted to be dominant at the earliest time delays. Here, $<8$ femtosecond extreme-ultraviolet pulses are used to detect this imbalance, tracking both the number of excited electrons and their kinetic energy with time- and angle-resolved photoemission spectroscopy. Over a time window of approximately 25 fs after absorption of the pump pulse, we observe an increase in conduction band carrier density and a simultaneous decrease of the average carrier kinetic energy, revealing that relaxation is in fact dominated by inverse Auger scattering. Measurements of carrier scattering at extreme timescales by photoemission will serve as a guide to ultrafast control of electronic properties in solids for PetaHertz electronics.Comment: 16 pages, 8 figure