Frustration, Orbital Fluctuations, and Topology in Kondo Lattices and their relatives

Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising of the Kitaev cluster is coupled to a bath of non-interacting fermions. We characterize the ground state properties of the system and determine the temperature dependence of the crossover scale for the emergence of fractionalized degrees of freedom in the model.

In recent years, heavy-transition metal oxides and halidates such as A2IrO3 (A=Na, Li) or \alpha-RuCl3 have been intensively scrutinized as Kitaev physics candidates due to the presence of sizable nearest neighbor bond-dependent Ising interactions between effective spin-1/2 local moments. However, all these systems display long-range magnetic order instead of the Kitaev quantum spin liquid ground state at ambient pressure, which could be related to the presence of additional Heisenberg and off-diagonal magnetic exchange interactions between first, second and third neighbors. In this contribution, we discuss that the physics is even richer and there are more instabilities which interfere with the Kitaev interaction, in particular under the application of hydrostatic pressure. [1] V. Hermann, M. Altmeyer, J. Ebad-Allah, F. Freund, A. Jesche, A.A. Tsirlin, M. Hanfland, P. Gegenwart, I.I. Mazin, D.I. Khomskii, R. Valentí, C.A. Kuntscher, Phys. Rev. B 97, 020104(R) (2018). [2] M. Majumder, R.S. Manna, G. Simutis, J.C. Orain, T. Dey, F. Freund, A. Jesche, R. Khasanov, P.K. Biswas, E. Bykova, N. Dubrovinskaia, L.S. Dubrovinsky, R. Yadav, L. Hozoi, S. Nishimoto, A.A. Tsirlin, P. Gegenwart, arXiv:1802.06819.

The Kitaev model exhibits a quantum spin liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large scale matrix product based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator based time evolution method.

Kitaev's honeycomb model is a remarkable exactly solvable spin-1/2 model, consisting of bond dependent Ising interactions, and with a gapless quantum spin liquid ground state. Even more remarkably such interactions are actually realized in a number of spin-orbit entangled Mott insulators, alongside other more conventional interactions. Here, motivated by the recent surge in interest in the behaviour of these materials in a magnetic field, we map out the complete phase diagram of the pure Kitaev model in tilted magnetic fields. Besides the expected gapped quantum spin liquid at low fields and the trivial polarized state at high fields we report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless gauge field resulting in a dense continuum of low-energy states. We discuss its stability in the presence of perturbations, Heisenberg and off-diagonal symmetric exchange interactions, that naturally arise in spin-orbit entangled Mott insulators alongside Kitaev interactions.

We derive the general scaling equation to the second order for a model, describing any point scatterer, with degenerate energy levels, embedded into a gas of itinerant electrons. We show how the obtained previously scaling equations for the spin-anisotropic Kondo model and power law density of states (DOS) for itinerant electrons follow from it. We introduce the anisotropic Coqblin– Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.

We consider a single magnetic impurity described by the spin-anisotropic s-d(f ) exchange (Kondo) model and formulate a scaling equation for the spin-anisotropic model when the density of states (DOS) of electrons is a power-law function of energy (measured relative to the Fermi energy).We solve this equation containing terms up to the second order in coupling constants in terms of elliptic functions. From the obtained solution we find the phases corresponding to the infinite isotropic antiferromagnetic Heisenberg exchange, to the impurity spin decoupled from the electron environment (only for the pseudogap DOS), and to the infinite Ising exchange (only for the diverging DOS). We analyze the critical surfaces, corresponding to the finite isotropic antiferromagnetic Heisenberg exchange for the pseudogap DOS.

Motivated by the search for materials with large spin-Hall conductivities, we study a ferromagnetic Kondo lattice model in the presence of Rashba spin-orbit coupling on a square lattice. A variational phase diagram for the model at quarter filling is presented. We additionally characterize different phases in terms of their spin-Hall conductivities. Results for the ground states are also verified using a hybrid Monte Carlo method that combines classical Monte Carlo for spins with exact diagonalization for fermions. We find that non-collinear and non-coplanar magnetic structures are realized as ground states -- a consequence of competing tendencies of the Kondo and Rashba terms. Interestingly, the spin-Hall conductivities in some of these phases are enhanced. The model can be realized, for example, at the interfaces of manganites or other ferromagnetic Kondo systems. Therefore, tuning of background magnetic order seems to be viable route for enhancing spin-Hall conductivities in electronic systems.

Topological Kondo insulators (TKIs) are a new class of topological insulators, emerging through the interplay of strong correlations and spin-orbit coupling. In TKIs, the bulk is a narrow band insulator due to the appearance of a localised Kondo resonance near the Fermi level and its hybridisation with the conduction band. Additionally, the strong spin-orbit coupling of the localised moments generates a nonlocal hybridisation between the local moments and the conduction band, which results in a ground-state with nontrivial topology and gapless surface states [1]. In this work we study TKIs in a slab geometry and address the problems of space charges and screening near the surfaces. The strong Kondo correlations in the 4f-orbitals are treated by a layer-dependent slave boson mean field (SBMF) theory, while the Coulomb repulsion in the conduction band is described by Hartree-Fock (HF) approximation. We solve the coupled SBMF+HF theory self-consistently and thereby analyse the existence of topological surface states. [1] M. Dzero et al., Topological Kondo insulators, Physical Review Letters $\textbf{104}$, 106408 (2010)

By performing finite-temperature quantum Monte Carlo simulations of the Kondo model we elucidate necessary conditions for the emergence of the coherent Kondo lattice behavior in a nanosystem composed of a few magnetic atoms only. To this end, we start with a single magnetic impurity deposited in the middle part of the metallic surface and in consecutive steps we place symmetrically a certain amount of magnetic moments onto specific superlattice sites around the initial impurity such that they form closed shells. We observe a fast (at $\sim$ 2th-3rd shell) opening of the hybridization gap signaling the onset of a coherent Kondo insulator in the case of a regular Kondo superlattice. By contrast, in the same temperature range, the formation of a 1/2 depleted (one impurity per two conduction electrons) superlattice opens up a partial hybridization gap which marks the onset of a coherent heavy-fermion metal.

Although most of magnetic materials, proposed to be used in the eld of spintronics, are based on magnetic metals and insulators, there exists a hope that semiconductors dilutely doped by magnetic impurities can be used in this eld as well. In these materials, the magnetic impurities mostly interact indirectly via the itinerant electrons of the host system (known as RKKY interaction) and so one can control the magnetic properties by tuning the electronic properties of the system which is the most desirable in the eld of spintronics [1, 5]. Among novel structures, topological insulators (TI) have special features that their surface states resemble a pure Rashba spin-orbit Hamiltonian. In such materials with strong Rashba spin-orbit coupling, this interaction comprises various contributions including isotropic Heisenberg-like and anisotropic symmetric Ising-like couplings as well as antisymmetric Dzyaloshinskii-Moriya (DM)-like couplings whitin linear response theory [6, 7]. The DM-like interaction which is a cause of spin-orbit coupling in materials becomes a rapidly growing topic in the eld of spintronics. While the usual isotropic Heisenberg interaction together with the Ising term in magnetic materials prefer a collinear alignment of spins, this anisotropic term prefers perpendicular orientation of spins and results in exotic phases such as skyrmions, helices and chiral domain walls [2]. Moreover, although, at the Dirac point and consequently small values at low Fermi energy, because of low density of electron states [8], the DM term takes zero magnitude [3], the impurities enhance DM contribution as a result of the modication of electronic structure by inducing new local states in the material. In our recent study, we address the electronic structure of the surface states of three- dimensional TI with embedded local non-magnetic and magnetic impurities by using the T-matrix [8, 9, 10, 11, 12, 13]. We revise the theory of the indirect exchange interaction between magnetic impurities beyond the linear response theory to establish the eect of impurity resonances in the surface states of a three-dimensional TI. we found that all three contributions are nite at the Dirac point, which is in stark contrast to the linear response theory which predicts a vanishing Dzyaloshinskii-Moriya-type contribution. We show that the spin-independent component of the impurity scattering can generate large values of the Dzyaloshinskii-Moriya-type coupling in comparison with the Heisenberg and Ising types of coupling, while these latter contributions drastically reduce in magnitude and undergo sign changes in some range of parameters. As a result, both collinear and non-collinear congurations are allowed magnetic congurations of the impurities. [1] F. Matsukura, Y. Tokura, and H. Ohno, Nat Nano 10, 209 (2015). [2] A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, Nature 539, 509 (2016). [3] R. Wakatsuki, M. Ezawa, and N. Nagaosa, Scientic Reports 5, 13638 (2015). [4] C.-Z. Chang, et, al., Science 340, 167 (2013). [5] M. G. Vergniory, et, al., Phys. Rev. B 89, 165202 (2014). [6] Sessi, P., et, al., Nature communications, 5, 5349 (2014). [7] P. Sessi, et, al., Nat. Commun. 7, 12027 (2016). [8] R. R. Biswas and A. V. Balatsky, Phys. Rev. B 81, 233405, (2010). [9] Q. Liu, C.-X. Liu, C. Xu, X.-L. Qi and S.-C. Zhang, Phys. Rev. L 102, 156603 (2009). [10] J. Fransson, A. M. Black-Schaer, and A. V. Balatsky, Phys. Rev. B 90, 241409(R), (2014). [11] N. M. R. Peres, F. Guinea and A. H. Castro Neto, Phys. Rev. B 73, 125411 (2006). [12] A. V. Balatsky, I. Vekhter and J. X. Zhu, Rev. Mod. Phys., Volume 78 (2006). [13] Y.L. Zou, J. Song, Ch. Bai and Kai Chang Phys. Rev. B 94, 035431 (2016).

The honeycomb lattice iridates A2IrO3 (A = Na, Li) were proposed as candidates for the realization of the Kitaev-Heisenberg model with hopes of stabilizing Kitaev’s quantum Spin-Liquid (QSL). However, both materials were experimentally found to have magnetically ordered ground states. We report discovery of a new layered honeycomb lattice iridate K2IrO3 with a structure built up of edge-sharing IrO6 octahedral. Using magnetic susceptibility χ versus temperature T data we find Seff = 1/2 moments interacting strongly with a Weiss temperature $\theta ≈ -200$~K and no sign of magnetic order or spin freezing down to T = 1.8 K. Heat capacity data confirm absence of any phase transition down to T = 1.8 K and show $C \sim T^2$ at low temperatures which is insensitive to magnetic fields. These observations strongly suggest that K2IrO3 could be the first experimental realization of Kitaev’s QSL.

The notion of quasiparticles constitutes the foundation of condensed matter physics. Recently it became evident that various solid state compounds, such as the well studied Dirac or Weyl materials, can support nodal quasiparticles around few isolated points in the Brillouin zone. In particular, I will focus on a collection of spin-3/2 excitations, which in three dimensions display a bi-quadratic touching of the valence and conduction bands near the $\Gamma$ point. Such peculiar band touching can be realized in the normal state of 227 pyrochlore iridates, half-Heuslers, HgTe, or gray tin, to name a few. Once the electron-electron interactions are accounted for, such system can display an intriguing confluence of a plethora of exotic broken symmetry phases, among which nematic, magnetic, and superconducting orders are the most prominent ones. Using a controlled renormalization group analysis at finite temperature and chemical doping, I will demonstrate the competition among these phases, as well as the associated quantum critical phenomena. In addition, I will present various cuts of the global phase diagram of interacting spin-3/2 fermions, and discuss the importance of emergent topology inside various ordered phases. Experimental ramifications of our findings will also be highlighted.

Heavy-fermion compounds exhibit an interplay of a variety of phenomena,including Kondo effect, lattice coherence and crystal-field (CF) excitations. These lead to multiple energy scales in thermodynamic properties. Understanding these features is crucial for identifying the relevant energy scales in a heavy-fermion system and for separating them from other energy scales that may arise near quantum phase transitions. However, even in the Fermi-liquid phase of a heavy-fermion system, the signatures of crystal-field excitations or of lattice coherence in thermodynamic quantities, especially their temperature dependence, are not fully understood. The reason is that the crystal-field split angular-momentum multiplets of the rare-earth ions induce spectral resonances near the Fermi energy (CF satellites), which are of Kondo-like many-body origin. Thus, not only their occupation number is thermally activated, but their spectral weight depends on temperature as well, leading to complex thermodynamic behavior. The theoretical description of the thermodynamics has been hampered by the difficulty of accurately calculating the free energy and entropy of heavy-fermion systems. We develop the Dynamical Mean-Field Theory (DMFT) for the multiorbital Anderson lattice model, using the self-consistent slave particle technique as an impurity solver. The multiple orbitals represent the CF-split ground state multiplet of the rare-earth ions. We employ a novel gauge fixing technique for fixing the U(1) gauge of the slave particle fields which enables a highly accurate calculation of the temperature dependent free energy. Thermodynamic and spectroscopic results both for the multilevel single-impurity case and the dense multi-orbital Anderson lattice are presented.