arXiv subjects

Matthias Vojta

Publications and source records attributed to Matthias Vojta.

At least 55 records · Page 3Linked to original sources

arXiv2021

Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

It was argued many years ago that translational symmetry breaking due to the appearance of spin-Peierls ordering (or bond-charge stripe order) is a fundamental property of the quantum paramagnetic states of a large class of square lattice antiferromagnets. Recently, such states were shown to be a convenient point of departure for studying translational symmetry breaking in doped antiferromagnets: these results are briefly reviewed here with an emphasis on experimental implications. In the presence of stronger frustration, it was also argued that the insulating antiferromagnet can undergo a transition to a deconfined state with no lattice symmetry breaking. This transition is described by a fully-frustrated Ising model in a transverse field: details of this earlier derivation of the Ising model are provided here--this is motivated by the reappearance of the same Ising model in a recent study of the competition between antiferromagnetism and d-wave superconductivity by Senthil and Fisher (cond-mat/9910224).

cond-mat.str-el↗

arXiv2021

Limits to magnetic quantum criticality from nuclear spins

The phenomenology of quantum phase transitions concerns physics at low temperatures and energies, and corresponding solid-state experiments often reach millikelvin temperatures. However, this is a scale where in many solids the influence of nuclear spins and their hyperfine interaction is no longer negligible. This may limit the observability of electronic quantum critical phenomena. Here we discuss how continuous magnetic quantum phase transitions get influenced, modified, or destroyed by the coupling to nuclear spins. We use simple yet paradigmatic spin models for magnetic quantum criticality and determine modifications to the phase diagram, the excitation spectrum, and thermodynamics due to the presence of nuclear spins. We estimate crossover scales below which purely electronic quantum criticality is no longer observable, and discuss the novel physics emerging at low temperatures. Our results are relevant for a variety of compounds displaying magnetic quantum phase transitions and, more generally, highlight the sensitivity of quantum critical systems to small perturbations.

cond-mat.str-el↗

arXiv2021

Field-induced intermediate ordered phase and anisotropic interlayer interactions in $α$-RuCl$_3$

In $α$-RuCl$_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-field ordered state at fields below the transition to the disordered phase. Neutron diffraction results show that the magnetic structure in this phase is characterized by a six-layer periodicity in the direction perpendicular to the honeycomb planes. Theoretically, the intermediate ordered phase can be accounted for by including spin-anisotropic couplings between the layers in a three-dimensional spin model. Together, this demonstrates the importance of interlayer exchange interactions in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2021

Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids

Spin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and $Γ$-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of $\mathrm{SO}(2)$- and $\mathrm{SO}(3)$-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to $\mathrm{SO}(ν)$-symmetric models with arbitrary integer $ν> 1$. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modellings of candidate materials.

cond-mat.str-el↗

arXiv2020

Fractionalized fermionic quantum criticality in spin-orbital Mott insulators

We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-$V$ model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ $ε$-expansion and large-$N$ methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with $d^1$ electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.

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arXiv2020

Microscopic models for Kitaev's sixteenfold way of anyon theories

In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $ν$ is classified by $ν\; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by $Γ$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(ν)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $ν$. We show that all these models are exactly solvable by using a Majorana representation and characterize the topological order by calculating the topological spin of an anyonic quasiparticle and the ground-state degeneracy. The possible relevance of the $ν=2$ and $ν=3$ models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.

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arXiv2020

Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion

The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which $\mathrm{Na}_{2}\mathrm{IrO}_{3}$ and $α-\mathrm{RuCl}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-$1$ and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in $1/S$ and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

cond-mat.str-el↗

arXiv2020

High-field thermal transport properties of the Kitaev quantum magnet alpha-RuCl3: evidence for low-energy excitations beyond the critical field

We investigate the phononic in-plane longitudinal low-temperature thermal conductivity kappa_ab of the Kitaev quantum magnet alpha-RuCl3 for large in-plane magnetic fields up to 33 T. Our data reveal for fields larger than the critical field Bc ~ 8 T, at which the magnetic order is suppressed, a dramatic increase of kappa_ab at all temperatures investigated. The analysis of our data shows that the phonons are not only strongly scattered by a magnetic mode at relatively large energy which scales roughly linearly with the magnetic field, but also by a small-energy mode which emerges near Bc with a square-root-like field dependence. While the former is in striking agreement with recent spin wave theory (SWT) results of the magnetic excitation spectrum at the Gamma point, the energy of the latter is too small to be compatible with the SWT-expected magnon gap at the M point, despite the matching field dependence. Therefore, an alternative scenario based on phonon scattering off the thermal excitation of random-singlet states is proposed.

cond-mat.str-el↗

arXiv2020

Susceptibility anisotropy and its disorder evolution in models for Kitaev materials

Mott insulators with strong spin-orbit coupling display a strongly anisotropic response to applied magnetic fields. This applies in particular to Kitaev materials, with $α$-RuCl$_3$ and Na$_2$IrO$_3$ representing two important examples. Both show a magnetically ordered zigzag state at low temperatures, and considerable effort has been devoted to properly modeling these systems in order to identify routes towards realizing a quantum spin liquid. Here, we investigate the relevant Heisenberg-Kitaev-$Γ$ model primarily at elevated temperatures, focusing on the characteristic anisotropy between the in-plane and out-of-plane uniform susceptibility. For $α$-RuCl$_3$, we find that the experimentally observed anisotropy, including its temperature dependence, can be reproduced by combining a large off-diagonal $Γ_1$ coupling with a moderate $g$-factor anisotropy. Moreover, we study in detail the effect of magnetic dilution and provide predictions for the doping evolution of the temperature-dependent susceptibilities.

cond-mat.str-el↗

arXiv2020

Random-bond disorder in two-dimensional non-collinear XY antiferromagnets: From quasi-long-range order to spin glass

We study effects of quenched bond disorder in frustrated easy-plane antiferromagnets in two space dimensions, using a combination of analytical and numerical techniques. We consider local-moment systems which display non-collinear long-range order at zero temperature, with the antiferromagnetic triangular-lattice XY model as a prime example. We show that (i) weak bond disorder transforms the clean ground state into a state with quasi-long-range order, and (ii) strong bond disorder results in a short-range-ordered glassy ground state. Using extensive Monte Carlo simulations, we also track the fate of the quasi-long-range-ordered phase at finite temperature and the associated Kosterlitz-Thouless-like transition. Making contact with previous studies of disordered XY models, we discuss similarities and differences concerning the interplay of disorder and frustration. Our results are also of relevance to non-collinear Heisenberg magnets in an external magnetic field.

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arXiv2020

Observation of a random singlet state in a diluted Kitaev honeycomb material

We report a $^{35}$Cl nuclear magnetic resonance (NMR) study of the diluted Kitaev material $α$-Ru$_{1-x}$Ir$_x$Cl$_3$ ($x=0.1$ and $0.2$) where non-magnetic Ir$^{3+}$ dopants substitute Ru$^{3+}$ ions. Upon dilution, the $^{35}$Cl spectra exhibit unusual large magnetic inhomogeneity, which sets in at temperatures below the Kitaev exchange energy scale. At the same time, the $^{35}$Cl spin-lattice relaxation rate $T_1^{-1}$ as a function of dilution and magnetic field unravels a critical doping of $x_c\approx 0.22$, towards which both the field-induced spin gap and the zero-field magnetic ordering are simultaneously suppressed, while novel gapless low-energy spin excitations dominate the relaxation process. These NMR findings point to the stabilization of a random singlet phase in $α$-Ru$_{1-x}$Ir$_x$Cl$_3$, arising from the interplay of dilution and exchange frustration in the quantum limit.

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arXiv2020

Soluble Fermionic Quantum Critical Point in Two Dimensions

We study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical behavior can be computed exactly, and we explicitly derive the scaling laws of various observables. While the order-parameter correlation function at criticality satisfies the usual power law with anomalous exponent $η_ϕ= 2$, the correlation length and the expectation value of the order parameter exhibit essential singularities upon approaching the quantum critical point from the insulating side, akin to the Berezinskii-Kosterlitz-Thouless transition. The susceptibility, on the other hand, has a power-law divergence with non-mean-field exponent $γ= 2$. On the semimetallic side, the correlation length remains infinite, leading to an emergent scale invariance throughout this phase.

cond-mat.str-el↗

arXiv2020

Impurity bound states as detectors of topological band structures revisited

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126 (2015)] has argued, based on theoretical results for a particular class of models, that insulators with topologically trivial and non-trivial band structures in two space dimensions display a qualitatively different response to point-like impurities. Here we present a comprehensive investigation of the impurity response of a large set of models of non-interacting electrons on the honeycomb lattice, driven insulating by either broken inversion, broken time reversal, broken $C_3$, or broken translation symmetry. These cases include Hofstadter bands, strain-induced pseudo-Landau levels and higher-order topological insulators. Our results confirm that for hopping models respecting the lattice symmetries, the response to a single impurity can indeed distinguish between trivial and non-trivial band topology. However, for modulated or inhomogeneous host systems we find that trivial states of matter can display an impurity response akin to that of topologically non-trivial states, and thus the diagnostic fails.

cond-mat.mes-hall↗

arXiv2020

Magnon dispersion and dynamic spin response in three-dimensional spin models for $α$-RuCl$_3$

In the search for experimental realizations of bond-anisotropic Kitaev interactions and resulting spin-liquid phases, the layered magnet $α$-RuCl$_3$ is a prime candidate. Its modelling typically involves Heisenberg, Kitaev, and symmetric off-diagonal $Γ$ interactions on the two-dimensional honeycomb lattice. However, recent neutron-scattering experiments point towards a sizeable magnetic interlayer coupling. Here we study three-dimensional exchange models for $α$-RuCl$_3$, for both possible $R\bar{3}$ and $C2/m$ crystal structures. We discuss the symmetry constraints on the interlayer couplings, construct minimal models, and use them to compute the magnetic mode dispersion and the dynamical spin structure factor, in both the zero-field zigzag phase and the paramagnetic high-field phase. Our predictions for the interlayer mode dispersion shall guide future experiments; they also call for a reevaluation of the quantitative model parameters relevant for $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2020

Kondo breakdown in a spin-1/2 chain of adatoms on a Dirac semimetal

We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the \textit{decoupled} fixed-point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

cond-mat.str-el↗

arXiv2020

Destruction of long-range order in non-collinear two-dimensional antiferromagnets by random-bond disorder

We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by non-collinear long-range order with non-zero vector chirality, and study the effects of quenched bond disorder, i.e., random exchange couplings. A single bond defect is known to induce a dipolar texture in the spin background independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension $d\leq 2$, in favor of a glassy state whose correlation length in $d=2$ is exponentially large for small randomness. Our results are relevant for a wide range of layered frustrated magnets.

cond-mat.str-el↗

arXiv2019

Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams

We discuss magnetically ordered states, arising in Heisenberg-Kitaev and related spin models, on three-dimensional (3D) harmonic honeycomb lattices. For large classes of ordered states, we show that they can be mapped onto two-dimensional (2D) counterparts on the honeycomb lattice, with the classical energetics being identical in the 2D and 3D cases. As an example, we determine the phase diagram of the classical nearest-neighbor Heisenberg-Kitaev model on the hyperhoneycomb lattice in a magnetic field: This displays rich and complex behavior akin to its 2D counterpart, with most phases and phase boundaries coinciding exactly. To make contact with the physics of the hyperhoneycomb iridate $β$-Li$_2$IrO$_3$, we also include a symmetric off-diagonal $Γ$ interaction, discuss its 3D-2D mapping, and determine the relevant phase diagrams. In particular, we demonstrate explicitly the adiabatic equivalence of the spiral magnetic orders in $α$- and $β$-Li$_2$IrO$_3$. Our results pave the way to a systematic common understanding of 2D and 3D Kitaev materials.

cond-mat.str-el↗

arXiv2019

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a \emph{different} power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.

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