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Using exact numerical techniques we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram…
In condensed-matter physics, electronic Mott insulators have triggered considerable research due to their intricate relation with high-temperature superconductors. However, unlike atomic systems for which Mott phases were recently shown for…
Engineered assemblies of interacting magnetic elements-magnetic metamaterials-provide a powerful route to tailor collective magnetic order and dynamics. By structuring matter at the mesoscale, they bridge atomic magnetism and macroscopic…
The exciton insulator (EI) is a unique many-body ground state of condensed, spontaneously formed excitons (electron-hole pairs) in equilibrium, distinct from conventional band or Mott insulators. Originally proposed over half a century ago,…
Two-dimensional magnetic semiconductors provide a unique materials platform in which long-range magnetic order coexists with strongly bound excitons. Because excitonic states and magnetic moments originate from the same electronic orbitals…
This thesis deals with the Hubbard model as prototypical model to describe the physics of electrons in the two-dimensional copper-oxide planes of high-$T_c$ cuprates. To get approximate solutions, we employ functional renormalization group…
The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we…
Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower…
The stability of the excitonic condensation at low temperature driven by a coupling of electrons to vibrational degrees of freedom in semimetal two-dimensional electronic system is discussed. In the framework of the unrestricted…
Controlling matter to simultaneously support multiple coupled properties is of fundamental and technological importance. For example, the simultaneous presence of magnetic and ferroelectric orders in multiferroic materials leads to enhanced…
Interlayer excitons in semiconducting bilayers separated by insulating hBN layers constitute a promising platform for investigation of strongly correlated bosonic phases. Here, we report an optical method for the generation and…
Identifying materials hosting an excitonic insulator ground state has been one of the major pursuits in condensed matter physics in recent years. Promising candidates in transition metal chalcogenide compounds (TMC), including…
We present a rigorous proof of an ordering transition for a two-component two-dimensional antiferromagnet with nearest and next-nearest neighbor interactions. The low-temperature phase contains two states distinguished by local order among…
We discuss the conditions under which the predicted (but not yet observed) zero-field interlayer excitonic condensation in double layer graphene has a critical temperature high enough to allow detection. Crucially, disorder arising from…
We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64 \times 64$ square lattice we demonstrate the…
We prove the existence of long-range order for the 3-state Potts antiferromagnet at low temperature on $\mathbb{Z}^d$ for sufficiently large $d$. In particular, we show the existence of six extremal and ergodic infinite-volume Gibbs…
Two-dimensional semiconductors have emerged as a new class of materials for nanophotonics for their strong exciton-photon interaction and flexibility for engineering and integration. Taking advantage of these properties, we engineer an…
A two dimensional electronic system with novel electronic properties forms at the interface between the insulators LaAlO$_3$ and SrTiO$_3$. Samples fabricated until now have been found to be either magnetic or superconducting, depending on…
Exciton polaritons are hybrid particles of excitons (bound electron-hole pairs) and cavity photons, which are renowned for displaying Bose Einstein condensation and other coherent phenomena at elevated temperatures. However, their formation…
Moir\'e superlattices open an unprecedented opportunity for tailoring interactions between quantum particles and their coupling to electromagnetic fields. Strong superlattice potential generates moir\'e minibands of excitons -- bound pairs…