Electronic Structure of Graphene and Topological Insulators

The study of the electronic band structure of solids is a central task in materials science. Indeed, knowing a material's band structure is key to an understanding of its macroscopic electronic properties. In recent years, a new class of materials has emerged whose unifying feature is an electronic structure that breaks with conventional band theory. Rather than obeying the usual Schrödinger Hamiltonian, the low-energy quasiparticle excitations in the band structure of these materials are better described as chiral, massless Dirac-like carriers, similar in nature to the relativistic quantum particles known from high-energy physics. Prominent members of this class are graphene and topological insulators. Despite being vastly different materials, they share a number of intriguing electronic properties that render them highly attractive for both fundamental and application-oriented studies. The thrust of this thesis work is to investigate the photoexcited Dirac carriers in graphene and in the series of topological insulators (Sb2)m-Sb2Te3 by means of angle-resolved photoemission spectroscopy (ARPES) and XUV laser-based time-resolved ARPES. The aim is to push the research frontier further towards a more complete understanding of the fate of a Dirac carrier when it is brought out of thermodynamic equilibrium by an optical excitation; and what role the substrate material, doping level, laser excitation and the introduction of a band gap play, as well as how one can possibly engineer such a Dirac-like electronic structure. To this end, we take advantage of ARPES' momentum and energy resolving capabilities that can be extended into the time domain by adding femtosecond time-resolution in a pump-probe scheme. By taking the Dirac carriers out of their equilibrium state by a laser pump pulse and watching directly with a second probe pulse how they interact and relax back to equilibrium, a movie of the in situ carrier dynamics is obtained. This dynamical view on the ultrafast scattering processes of photoexcited Dirac carriers in graphene allows us to show a quasi-instant sub 40 femtosecond thermalization to a hot carrier distribution. The carriers cool back to equilibrium on femto- and picosecond timescales via excitations of optical phonons and acoustic phonons assisted by disorder-scattering in supercollisions processes. A method is introduced to accurately extract the hot carriers¿ temperature that is used to quantify the carrier multiplication. Cooling times and carrier multiplication are found to display a remarkable dependence on the doping level of graphene to the extent that a substantial carrier multiplication is possible. The hot carrier dynamics is found to be severely perturbed by the presence of a metal, and also pump-induced electric fields are shown to affect a correct interpretation of TR-ARPES data by masking the intrinsic carrier dynamics. Furthermore, we demonstrate that, in the case of bilayer graphene, the existence of a single-particle band gap in the electronic structure leads to a markedly enhanced carrier lifetime over monolayer graphene, despite the existence of in-gap states. Finally, a complete picture of the evolution of the band structure and Dirac nature of the carriers across a series of compounds, from Sb2Te3 to elemental Sb, is drawn, suggesting a promising strategy for engineering the electronic states.

Experimental studies of the equilibrium and out-of-equilibrium electronic structure of non-symmorphic topological materials

Gianmarco Gatti

Symmetry and topology are fundamental properties of nature. Mathematics provides us with a general framework to understand these concepts. On one side, symmetry describes the invariance properties of an object for specific transformations. On the other side, topology classifies objects under continuous deformations. Two objects with different topologies cannot be deformed one into each other without creating or annihilating a singularity, sometimes referred to as 'node'. These concepts gradually found applications in physics, namely in the description of the electronic properties of solids, which is the focus of this thesis. Symmetry and topology protect special nodes in the band structure of a crystal, where several states are degenerate in energy. Close to a node, the electron wave function obeys the Dirac or Weyl Hamiltonians, which were formally introduced to describe fermions in high-energy particle physics. These exotic fermions exhibit unique optical and transport properties, fully manifesting their quantum nature. Symmetry guides us in the search for which classes of materials may host topological nodes. Recently the attention of the scientific community has been attracted by crystals with non-symmorphic symmetries (screw axes and glide planes), as promising candidates for topological phases. This thesis focuses on two families of non-symmorphic crystals, whose topological properties have been investigated by combining conventional angle-resolved photoelectron spectroscopy (ARPES) with state-of-the-art spin-resolved (spARPES) and time-resolved ARPES (trARPES). The experimental results are supported by calculations carried out in collaboration with theory groups. ZrSiTe and ZrSiSe belong to the same class of non-trivial semimetals. They host Dirac electrons with large mobility. The results of my spARPES experiments clarify that spin-orbit interaction (SOI) not only removes the topological nodes in ZrSiTe, but also induces a 'hidden' spin polarization of its bulk electronic states, otherwise forbidden by the inversion symmetry of the lattice. Moreover, trARPES data provide evidence that the electron-electron interaction is only partially screened in the metallic state of ZrSiSe. As a consequence, the band velocity is enhanced, at odds with general expectations. More importantly, I show that this band renormalization can be controlled at the ultrafast time scale (namely fs scale, with 1 fs=10^{-15} s) via intense optical excitation, paving the way for engineering the band structure of Dirac semimetals. Tellurium is a chiral semiconductor, with a small and direct band gap. The low-symmetry of its lattice and the simple chemical composition make it the ideal case to study the interplay between symmetry and topology. With ARPES I determine several Weyl nodes in its electronic structure. By means of spARPES, I demonstrate that in their surrounding the spin exhibits a hedgehog configuration. This observation is new and it highlights the connection between spin-dependent and topology-related properties in Te. Finally, I illustrate promising preliminary results based on trARPES that explore the appealing possibility of optically controlling the topology of the electronic structure of Te upon excitation of coherent phonons.

EPFL2020

Photoemission Spectroscopy of Low-Dimensional Charge-Density-Wave and Superconducting Materials

Peng Xu

The discovery in 1986 of the high-Tc superconducting cuprates has ushered in a new era of research in condensed matter physics. There is still a great interest for these materials, which stems not only from the lack of a clear theoretical picture, but also from the perspective of practical applications which could have an enormous impact on everyday's life. The complexity of the cuprates has stimulated a critical reassessment of many theoretical concepts and the development of new ideas, and fueled an unprecedented experimental activity to characterize their electronic structure. Besides the obvious occurrence of superconductivity, the two-dimensional character and the proximity to other ordered states, appear as prominent characteristics of these materials. The interplay of these properties is the subject of intense theoretical activity, since it is believed that it could play an important role in the emergence of the unconventional superconducting state. At the same time, it has been realized that similar situations may also arise in other classes of materials, where they lead to complex phase diagrams and to the emergence of new, unusual properties. These materials therefore offer interesting opportunities for related research. This thesis presents an investigation of the electronic structure of selected quasi-2D materials, and of their electronic instabilities – charge-density-wave (CDW), Mott metal-insulator transition, superconductivity – by means of angle resolved photoemission spectroscopy (ARPES). ARPES is a very powerful probe of solids which, thanks to its unique energy and momentum selectivity, provides a clear and direct view of the electronic states and of their interactions. Most of this work is concentrated on the low-energy excitations near the Fermi surface, the quasiparticles. These states play a crucial role in the thermodynamic, magnetic and transport of solids. Together with the shape of the Fermi surface, they determine the possible occurrence of electronic instabilities like charge- or spin-density waves, or again superconductivity (SC). A leitmotiv of this work is the study of how the nature of the quasiparticles, reflected in the ARPES spectral function, and the Fermi surface are influenced by an underlying instability, or by the competition between several instabilities. I have performed high-resolution ARPES experiments at the LSE-ICMP, and at two synchrotron radiation laboratories: the Swiss Light Source (PSI-Villigen) and SOLEIL (Paris). A large part of this work is concerned with the electronic properties of compounds which belong to the class of transition metal dichalcogenides (TMDs). TMDs are layered materials with rather strongly two-dimensional (2D) electronic properties. They often exhibit charge-density-wave (CDW) instabilities, and in selected cases superconductivity, but also peculiar metal-insulator (Mott) transitions. Among the TMDs, the 1T and 2H polytypes of TaS2 are representative of CDW materials which do not naturally exhibit SC, where SC can nonetheless be induced e.g. by applying external pressure. For 1T-TaS2 I show that a small amount of disorder entirely removes a Mott transition to a low-temperature insulating phase, opening the way to a non-homogeneous SC phase below ∼ 2K. ARPES here shows that SC emerges from a 'bad-metal' normal state. I have performed a detailed study of Sn-doped 2H-TaS2, where doping suppresses the CDW, but seems to enhance SC. I namely examine the partial gapping of the Fermi surface, as well as the spectral signatures of the interaction with the lattice. The spectral consequences of disorder induced by doping are also captured by ARPES in the degenerate semiconductor 1T-NbxTi1-xS 2. The second part of the thesis is the devoted to two members of the high-Tc cuprate BSCCO family. The two-layer Bi2212 member of this family has been the object of countless spectroscopic studies. I present here results for two considerably less-studied members of this family: the three-layer Bi2223, which has the highest Tc, and the single-layer Bi2201. In Bi2223 I found circumstantial evidence for the elusive threefold splitting of the Fermi surface expected from interlayer coupling. The momentum- and temperature dependence of the d-wave SC gap are illustrated by the ARPES data. The data also contain interesting information on the normal state low-energy kink (∼ 70 meV) – the fingerprint of the coupling of the electrons to a bosonic mode – and the high-energy anomaly in this compound. The originality of the results for Bi2201 lies in the nature of the samples, thin films prepared in situ by pulsed-laser-deposition (PLD), in the framework of a collaboration with the CREAM-ICMP laboratory. The ARPES results clearly demonstrated the feasibility of such studies, but also evidenced some difficulties related to the twinned nature of the films, which will have to be addressed in future studies. The ARPES data on the cuprates are complemented by the results of high-resolution resonant inelastic x-ray scattering (RIXS) experiments performed at the new SAXES end-station of the SLS. At variance with ARPES, which probes electron-removal states, RIXS probes neutral excitations, and therefore provides a complementary view of the electronic structure, similar to optics, but not limited to zero-momentum transitions. The resolution of RIXS is at present insufficient to address the low-energy gap scale, but it opens an entirely new window on the magnetic excitations, namely in the insulating parent compounds.

EPFL2010

Resonant Inelastic X-ray Scattering Studies of Low-Dimensional and Frustrated 3d Transition-Metal Oxides

Yi Tseng

3d transition-metal oxide materials with strong electron correlations and low dimensionality give rise to emerging exotic phases. Resonant inelastic X-ray scattering (RIXS) has developed as a powerful spectroscopic tool for probing the collective excitations in such correlated materials. The RIXS technique provides an ideal approach for assessing electronic instabilities in condensed matter. This thesis comprises the experimental RIXS response of the spin chain-ladder cuprates Sr14-xCax(Cu,Co)24O41 and frustrated honeycomb nickelate Na2Ni2TeO6. The spin and charge excitations of Sr14-xCaxCu24O41 (x=0 & 12.2) are studied by Cu L3-edge RIXS. With increasing Ca content, a crossover from collective two-triplon excitations (x=0) to a damped incoherent magnetic spectrum ~280 meV (x=12.2) in the ladders is uncovered from the RIXS spectra, dominated by spin-flip ÎS=1 scattering. With model calculations, the localized broad magnetic mode at x=12.2 is shown to be a consequence of enhanced elecrtronic localization. This is supported by polarization-dependent measurements, where the evaluated non-spin-flip ÎS=0 scattering is showing weight depletion below 1 eV. The RIXS spectral evolution suggests that a suppressed carrier mobility dominates the low-energy physics in Ca-rich phases. The low-energy excitations of Sr14Cu24O41 are also studied by O K-edge RIXS at the upper Hubbard band. The RIXS spectra show a sharp dispersing peak of similar energies to the ÎS=1 two-triplon excitations, and a broad non-dispersive mode at higher-energy. By comparing the experimental results to the existing theories of doped ladders, the observed spectral modes are attributed to interacting holon-spinon quasiparticles, with additional spectral contributions from the ÎS=0 multi-triplon bound states and continuum. These observations highlight the RIXS capability for resolving composite spin-charge quasiparticles and long-lived ÎS=0 magnetic excitations, which are difficult to detect by other experiments. Charge order and phonons for the two-leg ladders of Sr14(Cu,Co)24O41 are studied. At the ladder hole peak in O K-edge XAS signal, a concomitant elastic enhancement and phonon-softening is observed across all Co doping levels. The in-plane diffraction and phonon-softening response are found to enhance with increasing Co doping. Morevoer, the observed diffraction signal is further characterized by energy- and temperature-dependent measurements. Lastly, given the strong electron-phonon coupling (EPC) observed in O K-edge RIXS spectra, the EPC strength can be analyzed from the RIXS intensity decay of the phonon overtones . The observed in-plane resonant diffraction and inelastic phonon response strongly suggest an enhanced stripe order via magnetic impurities, reminiscent of the reports in CuO4 plaquettes. Electronic structure and EPC of the honeycomb nickelate Na2Ni2TeO6 are studied. Compared with current literature, the localized excitations (1-4 eV) in the Ni L3-edge RIXS spectra are dominated by the crystal-field splitting of a Ni2+ ion in octahedral coordination. At the O K-edge, the large EPC ~285 meV with 5 recognizable overtones (frequency of ~80 meV) are revealed in the RIXS spectra. The observed modes provide a systematic characterization of charge, orbital and lattice dynamics for a newly proposed frustrated antiferromagnet. This thesis has been carried out in a collaboration between the Paul Scherrer Institut and the Laboratory for Quantum Magnetism at EPFL.

EPFL2021