A complete theory of the orbital magnetic susceptibility of an isolated multiband electron system was developed in 2015. Here, the authors study whether one can control this orbital susceptibility by opening the electron system to a fermionic bath. They show that, as the system-bath coupling is increased, a properly engineered bath can enhance the diamagnetic susceptibility of the system and even change its orbital paramagnetic response into a diamagnetic one. The work also discusses how a Van Hove singularity in the bath density of states can be exploited to generate a giant enhancement of the orbital magnetic response. These results are counterintuitive, relative to the common belief, that bath-induced decoherence merely leads to the quenching of the orbital magnetic susceptibility.
A complete theory of the orbital magnetic susceptibility of an isolated multiband electron system was developed in 2015. Here, the authors study whether one can control this orbital susceptibility by opening the electron system to a fermionic bath. They show that, as the system-bath coupling is increased, a properly engineered bath can enhance the diamagnetic susceptibility of the system and even change its orbital paramagnetic response into a diamagnetic one. The work also discusses how a Van Hove singularity in the bath density of states can be exploited to generate a giant enhancement of the orbital magnetic response. These results are counterintuitive, relative to the common belief, that bath-induced decoherence merely leads to the quenching of the orbital magnetic susceptibility.
Controlling the ordered phases of correlated electron systems remains a central challenge in quantum materials design. Divergences in the electronic density of states, known as Van Hove singularities (VHSs), are one obvious route to such control. It is clear from recent work that the exact functional form of these divergences can profoundly affect which phases are realized; a full picture, however, remains elusive. In this work, we use both the hot-spot parquet renormalization group and the truncated-unity functional renormalization group to theoretically study the emergent correlated states of a two-dimensional square-lattice Hubbard model with VHSs at or near the Fermi level. By varying a single hopping parameter, t3, we are able to change the strength of the VHS divergence in the density of states from logarithmic (for t3<t3c) to power-law (for t3=t3c). Further increase of t3 (t3>t3c) causes each original Van Hove point to split into two, both of the conventional logarithmic type. We show that which of these regimes we are in strongly influences the predicted ordered states. We also study the dependence on doping, and find that the ferromagnetic state that occurs at Van Hove filling in these models is unstable to very small shifts in the Fermi level, often giving way to distinct ordered states depending on whether the model is electron- or hole-doped. These results highlight the importance of tuning VHS properties to control ordered states in correlated materials, and offer design rules to engineer these phases in novel systems.
Orbital magnetism is a purely quantum phenomenon that reflects intrinsic electronic properties of solids, yet its microscopic description in interacting multiband systems remains incomplete. We develop a general quantum many-body framework for orbital magnetic responses based on the Luttinger-Ward functional. Starting from the Dyson equation, we reformulate the thermodynamic potential in a weak magnetic field and construct a controlled expansion in powers of B applicable to correlated electron systems. A key technical advance is a modified ``Fourier'' representation using noncommutative coordinates, which allows the thermodynamic potential to be expressed in an effective momentum space where the magnetic field acts perturbatively. This formulation makes analytic progress possible within the Moyal algebra. As an application, we derive the spontaneous orbital magnetization and express it entirely in terms of the zero-field Hamiltonian renormalized by the self-energy. For frequency-dependent but Hermitian self-energies, we generalize the orbital magnetic moment and Berry curvature to momentum-frequency space and identify two gauge-invariant contributions built from these quantities. For frequency-independent self-energies the result reduces to the familiar geometric formula for noninteracting systems. This framework provides a unified foundation for computing orbital magnetic responses in correlated multiband materials.
Under the self-consistent mean-field approach for the BCS-BEC crossover problem, we derive a closed-form analytical expression for the general spin response of noncentrosymmetric Fermi superfluids with arbitrary spin-orbit coupling and Zeeman fields. In addition to the paramagnetic, i.e., the Pauli intrahelicity and Van Vleck type interhelicity, contributions to the spin-susceptibility tensor that have normal-state counterparts, we identify a diamagnetic interhelicity contribution that is unique to the superfluid state. Our extensive numerical calculations for the Weyl, Rashba, and equal Rashba-Dresselhaus spin-orbit couplings illustrate that it is this diamagnetic contribution that grows gradually with pairing and cancels precisely the Van Vleck contribution away from the BCS regime in general.
This thesis reports original research on strongly interacting fermions described by Hubbard-like models which can be realized with ultracold atom experiments. In particular, two main directions have been pursued: (i) the control of magnetic and topological properties in a honeycomb lattice through a suitable tuning of the trapping potential, and (ii) the possibility to observe orbital-selective Mott physics in a multicomponent Fermi system where the SU(N) symmetry is broken in a controlled way. The first line of research is based on the idea that increasing the strength of a trapping potential, one can trap a strongly interacting fermions in a limited portion of space, thereby changing their average density and the related magnetic properties. In particular it was demonstrated that this confinement protocol can be used to designeffective “nanoflakes” which are reminiscent of a solid-state proposal [1]. The second step was to extend the same philosophy to the so-called Kane-Mele model, a spinful version of the paradigmatic model proposed by Haldane which presents quantum Hall states. This model can be realized with cold-atom systems using artificial gauge fields. In this thesis we consider a Kane-Mele-Hubbard model where the electronic structure of the Kane-Mele model is supplemented by the onsite Hubbard interaction, allowing us to study the interplay between the correlations and magnetism induced by the repulsion, with the non-trivial topological properties. Also for this model, we follow the strategy discussed above, namely the possibility to engineer an effective “nanoflake” by tuning the lattice potential. The final outcome in this case is even reacher, because it leads, among other results, to a situation where the effective flake hosts an inhomogeneous state which presents at the same time topologically non-trivial properties and magnetism, realizing a spin-Chern insulator [2]. Besides the remarkable application for topological matter, artificial gauge fields, which rely on the coupling of spin states, offer also great insides into mutli-orbital physics. In the second main research line reported in the thesis we study in collaboration with the experimental group of Leonardo Fallani, the controlled symmetry breaking on a 173Yb many-body system, where coupling between spin states is exploited to simulate the mechanism relevant for the physics of multi-orbital materials, such as iron-based superconductors. In order to reveal this mechanism in cold atoms we focus on interacting SU(3) lattice fermions where the SU(3) spin symmetry is explicitly broken by a Raman coupling between the spin states. Combining experiments and theory, we demonstrate that this setup reveals orbital-selective physics and it shows that the SU(3)-symmetry-breaking Raman coupling favours Mott localization and selective properties [3]. Our results show a clear evidence of orbital-selective correlations, which reflect in contrasting transport properties in different orbitals, the extreme case being an orbital-selective Mott state where only some of the orbitals are Mott localized while others remain metallic. Moreover, the coupling between spin states favors Mott localization with respect to the symmetric case, hence it reduces the critical interaction needed for a full Mott localization.
We demonstrate the existence of a nonequilibrium "Floquet Fermi liquid" state arising in partially filled Floquet Bloch bands weakly coupled to ideal fermionic baths, which possess a collection of "Floquet Fermi surfaces" enclosed inside each other, resembling matryoshka dolls. We elucidate several properties of these states, including their quantum oscillations under magnetic fields which feature slow beating patterns of their amplitude reflecting the different areas of the Floquet Fermi surfaces, consistent with those observed in microwave induced resistance oscillation experiments. We also investigate their specific heat and thermodynamic density of states and demonstrate how by controlling properties of the drive, such as its frequency, one can tune some of the Floquet Fermi surfaces toward nonequilibrium Van Hove singularities without changing the electron density.
We describe the enhanced magnetic transition temperatures Tc of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold-atom experiments. We determine the phase diagram at half filling using the dynamical mean-field theory. The dominant mechanism of enhanced Tc gradually changes from the ($\ensuremath{\delta}$-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.