Defects in strongly correlated and spin-orbit entangled quantum matter

The inherent complexity of interacting quantum many-body systems poses an outstanding challenge to both theory and experiment. Especially in the presence of strong electronic correlations, highly interesting and perplexing physical phenomena can occur. In this thesis, we focus on three different examples of strongly correlated electron systems in which different types of defects occur. First, we investigate the Heisenberg-Kitaev model formulated on a triangular lattice. Using a mixture of numerical and analytical techniques we map out the entire phase diagram for the classical and quantum models. We provide an analytical foundation to the intriguing Z2-vortex ground state, in which strong spin-orbit coupling leads to the formation of a lattice of topological point defects. This state was observed previously in classical Monte Carlo simulations. We furthermore propose the iridate Ba3IrTi2O9 to be a prime candidate for the realization of such a state. The second part deals with the physics of a defect in the form of a localized magnetic moment which is embedded into a metallic environment: the Kondo effect. Although this effect has been a cornerstone of condensed matter physics for more than 50 years, its properties in real-space are still not fully understood. What is the Kondo screening cloud---the extended many-body state of entangled conduction electrons? We present numerical results in 1D and 2D for the charge density oscillations created by the impurity. We find that the entire RG flow of the problem is recovered in these oscillations, elucidating the internal structure of the screening cloud. Finally, we investigate the competition between the Kondo effect and Majorana physics. Majorana bound states are highly interesting objects which exhibit unusual statistics and could be used as a building block of a topological quantum computer. Recently, signatures of their existence were observed in experiment, and we here examine how Kondo physics (which might play a role in real systems) interact with such Majorana bound states

Spin-Orbital Order Modified by Orbital Dilution in Transition Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals

We study the $3d$ substitution in $4d$ transition metal oxides in the cases of $3d^3$ doping at either $3d^2$ or $4d^4$ sites which realize orbital dilution. We derive the effective $3d-4d$ (or $3d-3d$) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites and demonstrate that it is qualitatively different from that encountered in the host itself. This derivation shows that the interaction between the host and the impurity depends in a crucial way on the type of doubly occupied $t_{2g}$ orbital. One finds that in some cases, due to the quench of the orbital degree of freedom at the $3d$ impurity, the spin and orbital order within the host is drastically modified by doping. The impurity acts either as a spin defect accompanied by an orbital vacancy in the spin-orbital structure when the host-impurity coupling is weak, or it favors doubly occupied active orbitals (orbital polarons) along the $3d-4d$ bond leading to antiferromagnetic or ferromagnetic spin coupling. This competition between different magnetic couplings leads to quite different ground states. We find that magnetic frustration and spin degeneracy can be lifted by the quantum orbital flips of the host but they are robust in special regions of the incommensurate phase diagram. The spin-orbit coupling can lead to anisotropic spin and orbital patterns along the symmetry directions and cause a radical modification of the order imposed by the spin-orbital superexchange. Our findings are expected to be of importance for future theoretical understanding of experimental results for doped $4d$ transition metal oxides doped with $3d^3$ ions. We suggest how the local or global changes of the spin-orbital order induced by such impurities could be detected experimentally.Comment: 27 pages, 16 figures, submitte

Quantum Spin Liquids

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.Comment: 60 pages, 8 figures, 1 tabl

Charge and orbital order in transition metal oxides

A short introduction to the complex phenomena encountered in transition metal oxides with either charge or orbital or joint charge-and-orbital order, usually accompanied by magnetic order, is presented. It is argued that all the types of above ordered phases in these systems follow from strong Coulomb interactions as a result of certain compromise between competing instabilities towards various types of magnetic order and optimize the gain of kinetic energy in doped systems. This competition provides a natural explanation of the stripe order observed in doped cuprates, nickelates and manganites. In the undoped correlated insulators with orbital degrees of freedom the orbital order stabilizes particular types of anisotropic magnetic phases, and we contrast the case of decoupled spin and orbital degrees of freedom in the manganites with entangled spin-orbital states which decide about certain rather exotic phenomena observed in the perovskite vanadates at finite temperature. Examples of successful concepts in the theoretical approaches to these complex systems are given and some open problems of current interest are indicated.Comment: 20 pages, no figure

Orbital Symmetry and Orbital Excitations in High-TcT_c Superconductors

We discuss a few possibilities of high-$T_c$ superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of $x^2-y^2$ symmetry doped by holes. Next, several routes towards involving both $e_g$ orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO$_2$ monolayer on Bi2212 superconductors, Sr$_2$CuO$_{4-\delta}$, Ba$_2$CuO$_{4-\delta}$, while (ii) others as nickelate heterostructures or Eu$_{2-x}$Sr$_x$NiO$_4$, could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of $t_{2g}$ symmetry contribute in Sr$_2$RuO$_4$. Finally, electrons with both $t_{2g}$ and $e_g$ orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.Comment: 12 pages, 3 figures; in: Special Issue "From Cuprates to Room Temperature Superconductors", dedicated to the anniversary of Professor K. Alex M\"ulle