Gate-Controlled Anyon Generation and Detection in Kitaev Spin Liquids.

Reliable manipulation of non-Abelian Ising anyons supported by Kitaev spin liquids may enable intrinsically fault-tolerant quantum computation. Here, we introduce a standalone scheme for both generating and detecting individual Ising anyons using tunable gate voltages in a heterostructure containing a non-Abelian Kitaev spin liquid and a monolayer semiconductor. The key ingredients of our setup are a Kondo coupling to stabilize an Ising anyon in the spin liquid around each electron in the semiconductor, and a large charging energy to allow control over the electron numbers in distinct gate-defined regions of the semiconductor. In particular, a single Ising anyon can be generated at a disk-shaped region by gate tuning its electron number to one, while it can be interferometrically detected by measuring the electrical conductance of a ring-shaped region around it whose electron number is allowed to fluctuate between zero and one. We provide concrete experimental guidelines for implementing our proposal in promising candidate materials like α-RuCl_{3}.

Vacancy Spectroscopy of Non-Abelian Kitaev Spin Liquids.

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This "quasi-zero-voltage peak" is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material α-RuCl_{3}.

Emergent Magnetism with Continuous Control in the Ultrahigh-Conductivity Layered Oxide PdCoO2.

The current challenge to realizing continuously tunable magnetism lies in our inability to systematically change properties, such as valence, spin, and orbital degrees of freedom, as well as crystallographic geometry. Here, we demonstrate that ferromagnetism can be externally turned on with the application of low-energy helium implantation and can be subsequently erased and returned to the pristine state via annealing. This high level of continuous control is made possible by targeting magnetic metastability in the ultrahigh-conductivity, nonmagnetic layered oxide PdCoO2 where local lattice distortions generated by helium implantation induce the emergence of a net moment on the surrounding transition metal octahedral sites. These highly localized moments communicate through the itinerant metal states, which trigger the onset of percolated long-range ferromagnetism. The ability to continuously tune competing interactions enables tailoring precise magnetic and magnetotransport responses in an ultrahigh-conductivity film and will be critical to applications across spintronics.

Structure and magnetism of the triangular lattice material YbBO3.

YbBO3is a member of the orthoborate family of materials which contains a triangular arrangement of Yb3+ions. Here we study the physical properties of YbBO3with neutron diffraction, inelastic neutron scattering, specific heat, and ac susceptibility measurements. The neutron diffraction measurements confirm that our samples of YbBO3crystallize in the monoclinic space groupC2/c(#15) which contains two crystallographically distinct Yb3+sites decorating a slightly distorted triangular lattice. Heat capacity and ac susceptibility measurements indicate a potential transition to magnetic order at 0.4 K. In agreement with these observations, neutron diffraction measurements at 0.044 K observe magnetic Bragg peaks which can be indexed by a propagation vector of (0 0 1). Although determining a unique spin configuration corresponding to the observed magnetic Bragg peaks is not possible, model refinements indicate that the ordered moments are likely in the range of 0.4-0.9 µBand, notably, require moments on both Yb sites. In addition to the magnetic Bragg peaks, diffuse scattering at lowQis observed indicating that the transition does not correspond to complete long range magnetic order. The two-site picture for YbBO3is further evidenced by the number of crystal field excitations observed by inelastic neutron scattering measurements. Together these results show that YbBO3is a two-site triangular lattice material with signatures of long-range order as well as shorter ranged spin correlations.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Theory of the Kitaev model in a [111] magnetic field.

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev's 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3.

The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.

Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice.

In quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl3. A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl3 as a benchmark material for quantum magnetism on the honeycomb lattice.

Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice.

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

Quantization of the Thermal Hall Conductivity at Small Hall Angles.

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ_{xx} due to phonons is much larger than the expected quantized thermal Hall conductance κ_{xy}^{q}=(πT/12)(k_{B}^{2}/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L≫ℓ, where ℓ is a thermalization length. We obtain ℓ∼T^{-5} for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ_{xy}/κ_{xx}∼10^{-3}, in α-RuCl_{3}.

Probing Spinon Nodal Structures in Three-Dimensional Kitaev Spin Liquids.

We propose that resonant inelastic x-ray scattering (RIXS) is an effective probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin liquids. While the non-spin-conserving RIXS responses are dominated by the gauge-flux excitations and reproduce the inelastic-neutron-scattering response, the spin-conserving (SC) RIXS response picks up the Majorana-fermion excitations and detects whether they are gapless at Weyl points, nodal lines, or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS response is suppressed around the Γ point. On a technical level, we calculate the exact SC RIXS responses of the Kitaev models on the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices, arguing that our main results also apply to generic 3D Kitaev spin liquids beyond these exactly solvable models.

Fracton Topological Phases from Strongly Coupled Spin Chains.

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines or planes. We demonstrate that a wide range of these fracton phases can be constructed by strongly coupling mutually intersecting spin chains and explain via a concrete example how such a coupled-spin-chain construction illuminates the generic properties of a fracton phase. In particular, we describe a systematic translation from each coupled-spin-chain construction into a parton construction where the partons correspond to the excitations that are mobile along lines. Remarkably, our construction of fracton phases is inherently based on spin models involving only two-spin interactions and thus brings us closer to their experimental realization.

Resonant Inelastic X-Ray Scattering Response of the Kitaev Honeycomb Model.

We calculate the resonant inelastic x-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. We find that the fundamental RIXS channels, the spin-conserving (SC) and the non-spin-conserving (NSC) ones, do not interfere and give completely different responses. SC RIXS picks up exclusively the Majorana sector with a pronounced momentum dispersion, whereas NSC RIXS also creates immobile fluxes, thereby rendering the response only weakly momentum dependent, as in the spin structure factor measured by inelastic neutron scattering. RIXS can, therefore, pick up the fractionalized excitations of the Kitaev spin liquid separately, making it a sensitive probe to detect spin-liquid character in potential material incarnations of the Kitaev honeycomb model.

All Majorana Models with Translation Symmetry are Supersymmetric.

We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but involving only translation symmetry and for Majorana modes. In particular, we show that all states are at least doubly degenerate in any one- and two-dimensional array of Majorana modes with translation symmetry, periodic boundary conditions, and an odd number of modes per unit cell. Moreover, we show that all such systems have an underlying N=2 supersymmetry and explicitly construct the generator of the supersymmetry. Furthermore, we establish that there cannot be a unique gapped ground state in such one-dimensional systems with antiperiodic boundary conditions. These general results are fundamentally a consequence of the fact that translations for Majorana modes are represented projectively, which in turn stems from the anomalous nature of a single Majorana mode. An experimental signature of the degeneracy arising from supersymmetry is a zero-bias peak in tunneling conductance.

Large Superconducting Spin Valve Effect and Ultrasmall Exchange Splitting in Epitaxial Rare-Earth-Niobium Trilayers.

Epitaxial Ho/Nb/Ho and Dy/Nb/Dy superconducting spin valves show a reversible change in the zero-field critical temperature (ΔT(c0)) of ∼400 mK and an infinite magnetoresistance on changing the relative magnetization of the Ho or Dy layers. Unlike transition-metal superconducting spin valves, which show much smaller ΔT(c0) values, our results can be quantitatively modeled. However, the fits require an extraordinarily low induced exchange splitting which is dramatically lower than known values for rare-earth Fermi-level electrons, implying that new models for the magnetic proximity effect may be required.

Topological Rényi entropy after a quantum quench.

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Supercurrent enhancement in Bloch domain walls.

Conventional spin-singlet Cooper pairs convert into spin-triplet pairs in ferromagnetic Josephson junctions in which the superconductor/ferromagnet interfaces (S/F) are magnetically inhomogeneous. Although much of the theoretical work describing this triplet proximity effect has considered ideal junctions with magnetic domain walls (DW) at the interfaces, in practice it is not easily possible to isolate a DW and propagate a supercurrent through it. The rare-earth magnet Gd can form a field-tuneable in-plane Bloch DW if grown between non-co-linearly aligned ferromagnets. Here we report supercurrents through magnetic Ni-Gd-Ni nanopillars: by field annealing at room temperature, we are able to modify the low temperature DW-state in Gd and this result has a striking effect on the junction supercurrent at 4.2 K. We argue that this result can only be explained in terms of the interconversion of triplet and singlet pairs, the efficiency of which depends on the magnetic helicity of the structure.

Enhanced supercurrents in Josephson junctions containing nonparallel ferromagnetic domains.

π coupling may arise when a ferromagnet forms a link between two superconductors of an artificial Josephson junction. Using a trilayer Fe/Cr/Fe barrier in which the Cr thickness determines the alignment of the Fe layers, we show that the critical currents are substantially enhanced in the antiparallel configuration. The result agrees with existing superconductor-ferromagnet proximity theory according to which the phase-controlling effects of ferromagnets on Cooper pairs can be minimized by arranging their moments in a nonparallel way [Bergeret, Phys. Rev. Lett. 86, 3140 (2001); Blanter, Phys. Rev. B 69, 024525 (2004)].

Crossover induced by spin-density-wave interference in the coherence of singlet electron pairs in Cr.

To study the interaction of s-wave superconductivity with spin-density waves (SDWs), we have measured a series of Nb/Cr/Nb Josephson junctions and determined the coherence length xi describing the decay of the critical current with Cr thickness, L. We observe a crossover in xi from approximately 14 nm to 4 nm as L increases to 10 nm, which is consistent with a transition from commensurate to incommensurate SDWs expected for this thickness range.