arXiv subjects

Matthias Vojta

Publications and source records attributed to Matthias Vojta.

At least 73 records · Page 4Linked to original sources

arXiv2019

Magnon Landau levels and emergent supersymmetry in strained antiferromagnets

Inhomogeneous strain applied to lattice systems can induce artificial gauge fields for particles moving on this lattice. Here we demonstrate how to engineer a novel state of matter, namely an antiferromagnet with a Landau-level excitation spectrum of magnons. We consider a honeycomb-lattice Heisenberg model and show that triaxial strain leads to equally spaced pseudo-Landau levels at the upper end of the magnon spectrum, with degeneracies characteristic of emergent supersymmetry. We also present a particular strain protocol which induces perfectly quantized magnon Landau levels over the whole bandwidth. We discuss experimental realizations and generalizations.

cond-mat.str-el↗

arXiv2019

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators $α$-RuCl$_3$ and Na$_2$IrO$_3$, which are believed to realize this fascinating physics.

cond-mat.str-el↗

arXiv2019

Theory of partial quantum disorder in the stuffed honeycomb Heisenberg antiferromagnet

Recent numerical results [Gonzalez $\textit{et al.}$, Phys. Rev. Lett. $\textbf{122}$, 017201 (2019); Shimada $\textit{et al.}$, J. Phys. Conf. Ser. $\textbf{969}$, 012126 (2018)] point to the existence of a partial-disorder ground state for a spin-1/2 antiferromagnet on the stuffed honeycomb lattice, with 2/3 of the local moments ordering in an antiferromagnetic Néel pattern, while the remaining 1/3 of the sites display short-range correlations only, akin to a quantum spin liquid. We derive an effective model for this disordered subsystem, by integrating out fluctuations of the ordered local moments, which yield couplings in a formal $1/S$ expansion, with $S$ being the spin amplitude. The result is an effective triangular-lattice XXZ model, with planar ferromagnetic order for large $S$ and a stripe-ordered Ising ground state for small $S$, the latter being the result of frustrated Ising interactions. Within the semiclassical analysis, the transition point between the two orders is located at $S_c=0.646$, being very close to the relevant case $S=1/2$. Near $S=S_c$ quantum fluctuations tend to destabilize magnetic order. We conjecture that this applies to $S=1/2$, thus explaining the observed partial-disorder state.

cond-mat.str-el↗

arXiv2018

Carrier dynamics in doped bilayer iridates near magnetic quantum criticality

Motivated by experiments on the carrier-doped bilayer iridate $(\text{Sr}_{1-x}\text{La}_x)_3\text{Ir}_2\text{O}_7$, we study the dynamics of a single doped electron in a bilayer magnet in the presence of spin-orbit coupling, taking into account the spatially staggered rotation of IrO$_6$ octahedra. We employ an effective single-orbital bilayer $t$-$J$ model, concentrating on the quantum paramagnetic phase near the magnetic quantum critical point. We determine the carrier dispersion using a combination of self-consistent Born and bond-operator techniques. Extrapolating to finite small carrier density we find that, for experimentally relevant parameters, the combination of octahedral rotation and spin-orbit coupling induces a band folding which results in a Fermi surface of small double electron pockets, in striking agreement with experimental observations. We also determine the influence of spin-orbit coupling on the location of the quantum critical point in the undoped case, and discuss aspects of the global phase diagram of doped bilayer Mott insulators.

cond-mat.str-el↗

arXiv2018

Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching

We consider two-dimensional Fermi systems with quadratic band touching and $C_3$ symmetry, as realizable in Bernal-stacked honeycomb bilayers. Within a renormalization-group analysis, we demonstrate the existence of a quantum critical point at a finite value of the density-density interactions, separating a semimetallic disordered phase at weak coupling from a gapped ordered phase at strong coupling. The latter may be characterized by, for instance, antiferromagnetic, quantum anomalous Hall, or charge density wave order. In the semimetallic phase, each point of quadratic band touching splits into four Dirac cones as a consequence of the nontrivial interaction-induced self-energy correction, which we compute to the two-loop order. We show that the quantum critical point is in the $(2+1)$-dimensional Gross-Neveu universality class characterized by emergent Lorentz invariance and a dynamic critical exponent $z=1$. At finite temperatures, $T > 0$, we hence conjecture a crossover between $z=2$ at intermediate $T$ and $z=1$ at low $T$, and we construct the resulting nontrivial phase diagram as function of coupling strength and temperature.

cond-mat.str-el↗

arXiv2018

Bilayer Kitaev models: Phase diagrams and novel phases

Kitaev's honeycomb-lattice spin-$1/2$ model has become a paradigmatic example for $\mathbb{Z}_2$ quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilayer versions of the Kitaev model. Increasing the ratio between the inter-layer Heisenberg coupling $J_\perp$ and the intra-layer Kitaev couplings $K^{x,y,z}$ destroys the topological spin liquid in favor of a paramagnetic dimer phase. We study phase diagrams as a function of $J_\perp/K$ and Kitaev coupling anisotropies using Majorana-fermion mean-field theory, and we employ different expansion techniques in the limits of small and large $J_\perp/K$. For strongly anisotropic Kitaev couplings, we derive effective models for the different layer stackings which we use to discuss the quantum phase transition out of the Kitaev phase. We find that the phase diagrams depend sensitively on the nature of the stacking and anisotropy strength. While in some stackings and at strong anisotropies we find a single transition between the Kitaev and dimer phases, other stackings are more involved: Most importantly, we prove the existence of two novel macro-spin phases which can be understood in terms of Ising chains which can be either coupled ferromagnetically or remain degenerate, thus realizing a classical spin liquid. In addition, our results suggest the existence of a flux phase with spontaneous inter-layer coherence.

cond-mat.str-el↗

arXiv2018

Frustration and quantum criticality

This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to frustrated systems can lead to multi-criticality.

cond-mat.str-el↗

arXiv2018

Cluster-glass phase in pyrochlore XY antiferromagnets with quenched disorder

We study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order-by-disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on details of the disorder configuration. Using a combination of analytical considerations and classical Monte-Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magnetic domains due to random exchange anisotropies, becoming, therefore, a glass of spin clusters, in accordance with the available experimental data. These random anisotropies originate from off-diagonal exchange couplings in the microscopic Hamiltonian, establishing their relevance to other magnets with strong spin-orbit coupling.

cond-mat.str-el↗

arXiv2018

Fractionalized Fermi liquids and exotic superconductivity in the Kitaev-Kondo lattice

Fractionalized Fermi liquids (FL$^\ast$) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL$^\ast$ phases based on Kitaev's $\mathbb{Z}_2$ spin liquid. We characterize the FL$^\ast$ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find triplet superconducting phases which mask the quantum phase transition between fractionalized and conventional Fermi liquid phases. Their pairing structure is inherited from the Kitaev spin liquid, i.e., superconductivity is driven by Majorana glue.

cond-mat.str-el↗

arXiv2017

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $α$-RuCl$_3$ and Na$_2$IrO$_3$

We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a combination of Monte-Carlo simulations, classical energy minimization, and spin-wave theory. We consider a number of different parameter sets, previously proposed to describe the magnetic behavior of $α$-RuCl$_3$ and Na$_2$IrO$_3$ with their antiferromagnetic zigzag ground states. By classifying these parameter sets, we reveal the existence of three distinct mechanisms to stabilize zigzag states, which differ in the sign of the nearest-neighbor Kitaev interaction, the role of longer-range interactions, and the magnitude of the off-diagonal $Γ_1$ interaction. While experimentally hardly distinguishable at zero field, we find that the three different scenarios lead to significantly different magnetization processes in applied magnetic fields. In particular, we show that a sizable off-diagonal interaction $Γ_1 > 0$ naturally explains the strongly anisotropic field responses observed in $α$-RuCl$_3$ without the need for a strong anisotropy in the effective $g$ tensor. Moreover, for a generic field direction, it leads to a high-field state with a finite transversal magnetization, which should be observable in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2017

Bound states of fractionalized excitations in a modulated Kitaev spin liquid

Fractionalization is a hallmark of spin-liquid behavior; it typically leads to response functions consisting of continua instead of sharp modes. However, microscopic processes can enable the formation of short-distance bound states of fractionalized excitations, despite asymptotic deconfinement. Here we study such bound-state formation for the $Z_2$ spin liquid realized in Kitaev's honeycomb compass model, supplemented by a kekule distortion of the lattice. Bound states between flux pairs and Majorana fermions form in the Majorana band gaps. We calculate the dynamic spin susceptibility and show that bound states lead to sharp modes in the magnetic response of the spin liquid, with the momentum dependence of the corresponding spectral weight encoding internal symmetry of the bound state. As a byproduct, we also show that isolated fluxes may produce Majorana bound states at exactly zero energy. Generalizations and implications of the results are discussed.

cond-mat.str-el↗

arXiv2017

Quantized charge transport in chiral Majorana edge modes

Majorana fermions can be realized as quasiparticles in topological superconductors, with potential applications in topological quantum computing. Recently, lattices of magnetic adatoms deposited on the surface of s-wave superconductors - Shiba lattices - have been proposed as a new platform for topological superconductivity. These systems possess the great advantage that they are accessible via scanning-probe techniques, and thus enable the local manipulation and detection of Majorana modes. Realizing quantum bits on this basis will rely on the creation of nanoscopic Shiba lattices, so-called Shiba islands. Here, we demonstrate that the topological Majorana edge modes of such islands display universal electronic and transport properties. Most remarkably, these Majorana modes possess a quantized charge conductance that is proportional to the topological Chern number, C, and carry a supercurrent whose chirality reflects the sign of C. These results establish nanoscopic Shiba islands as promising components in future topology-based devices.

cond-mat.supr-con↗

arXiv2017

Open Wilson chains for quantum impurity models: Keeping track of all bath modes

When constructing a Wilson chain to represent a quantum impurity model, the effects of truncated bath modes are neglected. We show that their influence can be kept track of systematically by constructing an "open Wilson chain" in which each site is coupled to a separate effective bath of its own. As a first application, we use the method to cure the so-called mass-flow problem that can arise when using standard Wilson chains to treat impurity models with asymmetric bath spectral functions at finite temperature. We demonstrate this for the strongly sub-Ohmic spin-boson model at quantum criticality where we directly observe the flow towards a Gaussian critical fixed point.

cond-mat.str-el↗

arXiv2017

Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum

Certain non-uniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudo-magnetic field for electrons near the Dirac points. However, this Landau level structure is in general approximate and restricted to low energies. Here we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3 our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

cond-mat.mes-hall↗

arXiv2016

Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A$_2$IrO$_3$ (A = Na, Li) and $α$-RuCl$_3$. Here we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte-Carlo simulations and spin-wave theory we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.

cond-mat.str-el↗

arXiv2016

Kondo impurities in the Kitaev spin liquid: Numerical renormalization group solution and gauge-flux-driven screening

Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, and otherwise becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.

cond-mat.str-el↗

arXiv2016

Landau levels of Majorana fermions in a spin liquid

Majorana fermions were originally proposed as elementary particles acting as their own antiparticles. In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here we propose a physical system which realizes Landau levels - highly degenerate single-particle states usually resulting from an orbital magnetic field acting on charged particles - for Majorana fermions. This is achieved in a variant of a quantum spin system due to Kitaev which is distorted by triaxial strain. This strained Kitaev model displays a spin-liquid phase with charge-neutral Majorana-fermion excitations whose spectrum corresponds to that of Landau levels, here arising from a tailored pseudo-magnetic field. We show that measuring the dynamic spin susceptibility reveals the Landau-level structure by a remarkable mechanism of probe-induced bound-state formation.

cond-mat.str-el↗

arXiv2016

Cotunneling into a Kondo lattice with odd hybridization

Cotunneling into Kondo systems, where an electron enters a $f$-electron material via a cotunneling process through the local-moment orbital, has been proposed to explain the characteristic lineshapes observed in scanning-tunneling-spectroscopy (STS) experiments. Here we extend the theory of electron cotunneling to Kondo-lattice systems where the bulk hybridization between conduction and $f$ electrons is odd under inversion, being particularly relevant to Kondo insulators. Compared to the case of even hybridization, we show that the interference between normal tunneling and cotunneling processes is fundamentally altered: it is entirely absent for layered, i.e., quasi-two-dimensional materials, while its energy dependence is strongly modified for three-dimensional materials. We discuss implications for STS experiments.

cond-mat.str-el↗