Banerjee, Arnab

One of the most direct ways to pin down the existence of the Majorana Fermions in a 2D quantum Kitaev material is its signature in the inelastic neutron spectrum. $\alpha$-RuCl$_3$ is one of the most promising candidates for the realization of the Kitaev quantum spin liquid. We use a combination of elastic and inelastic neutron scattering, XRD, and magnetization measurements to probe the material both in its powder and single crystal forms. Our single crystal neutron diffraction allows us to refine the zigzag spin ground state of the system as well as the ordered moment size - which we found to be 1/3rd of the net single-ion moment - indicative of a highly fluctuating ground state. The powder neutron diffraction shows the collective excitations arising from the ordered ground state. The analysis of the spectrum using spin-wave theory yields Kitaev interactions to be dominant. Crucially, a breakdown of the spin-wave picture is observed for a mode at E = 6 meV, which is broad and persists to temperatures several times the Neel temperature. The energy, Q and temperature dependence of the mode has been best explained by the higher energy mode of a pure Kitaev QSL calculation, which arises from itinerant Majorana Fermions. We further show the inelastic neutron scattering measurements in single crystals to elucidate the spatial structure of this mode, alongside theoretical predictions from exact QSL calculations. I will finally discuss our recent and future endeavors to tune to the pure Kitaev ground state using various techniques.

Bieri, Samuel

Recent progress in material science has led to novel quantum magnets described by frustrated spin S=1/2 Heisenberg models on the Kagome lattice with farther-neighbor exchange interactions. Motivated by these advances and by experimental indications for quantum spin liquid phases, we perform a projective symmetry group classification of chiral spin liquids with fermionic spinons on this lattice. We discuss general properties of these exotic spin states, such as emergent SU(2) gauge structure, fluxes, and order parameter. We present a variational phase diagram of the physically relevant Heisenberg model.

Breunig, Oliver

In the family of the ternary II-V-VI$_2$ compounds several materials have been identified as topological insulators. In the n-type TlBiTe$_2$ a topological surface state has been found, yet it is hardly accessible for transport studies due to the overlap with the bulk bands. Theoretical studies suggest that upon substituting Bi by Sb a narrow bulk band gap opens while preserving a single Dirac cone at the $\Gamma$ point, leading to a possible realization of a bulk-insulating system with an exposed Dirac point. Single crystals of TlBi$_x$Sb$_{1-x}$Te$_2$ were grown by a modified Bridgman technique using high-purity starting materials. They were characterized by ICP/EDX as well as transport measurements. For intermediate values $x$ we find insulating transport properties and a surprisingly strong negative magnetoresistance. We present our crystal growth results of TlBi$_x$Sb$_{1-x}$Te$_2$ and discuss the origin of the observed large negative magnetoresistance.

Buessen, Finn Lasse

We apply a recently developed functional renormalization group (FRG) approach to study the collective phenomena of spin-orbit entangled j=1/2 moments in Mott insulators. The microscopic exchange of these moments can be captured by a Heisenberg-Kitaev model for various lattice geometries. We discuss technical aspects of the application of the pseudo-fermion FRG approach developed by Reuther and Wölfle and its efficient numerical implementation. Model systems to be discussed include the Heisenberg-Kitaev model on honeycomb and triangular lattice geometries, for which we discuss the formation of unconventional magnetism in the form of spin liquids or non-trivial spin textures.

Buhl, Patrick

The quantum anomalous Hall (QAH) insulator with dissipationless chiral edge states has been observed experimentally in thin films of magnetically doped topological insulators (TIs), but at low temperatures around 30 mK [1]. Based on new families of two-dimensional (2D) TIs and 2D topological crystalline insulators (TCIs) -- functionalized Bi and (Sn/Pb)Te -- we theoretically predict the realization of the QAH effect with different Chern numbers, with a band gap that can be as large as 0.35 eV [2,3]. We further predict that the QAH state in semihydrogenated Bi is quite different from the normal one. It exhibits the properties of both the QAH state and quantum valley Hall (QVH) state, realizing a different quantum state, called a valley-polarized QAH insulator. In addition, we explore the phase diagram of 2D TCIs with respect to an applied exchange field due to magnetic adatoms or substrates and show the emergence of a robust QAH-phase, which survives irrespective of the mirror symmetry breaking. Financial support of the DFG (SPP 1666) and the Virtual Institute for Topological Insulators (VITI) are gratefully acknowledged. [1] C.Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, and L.L. Wang, Science {\bf 340}, 167 (2013). [2] C. Niu, G. Bihlmayer, H. Zhang, D. Wortmann, S. Blügel, and Y. Mokrousov, Phys. Rev. B {\bf 91}, 041303(R) (2015). [3] C. Niu, P. M. Buhl, G. Bihlmayer, D. Wortmann, S. Blügel, and Y. Mokrousov, Phys. Rev. B {\bf 91}, 201401(R) (2015).

Fujita, Hiroyuki

In relativistic fermions with chirality imbalance, electric current is predicted to be driven by a magnetic field. This is called chiral magnetic effect (CME). CME has been discussed in the context of high energy physics but recently it gathers growing attentions from condensed matter physicists since the concept of {¥it Weyl semimetals} was proposed. Here we consider how CME affects transport properties of Weyl semimetals by treating them in a way consistent with the law of electromagnetism including CME, or Maxwell-Chern-Simons equations. Using a perturbation theory, we have constructed a lowest order analytical solution of the electromagnetic equations for a cylindrical sample. We found that the consistency with the electromagnetism leads to a quite nontrivial solution. Based on the solution we predict two novel transport phenomena: universal imaginary conductance and resonant current.

Gupta, Satyendra

Inelastic light scattering studies on single crystals of (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ ($x = 0, 0.05$ and $0.15$) show a polarization independent broad band at $\sim $~2750 cm$^{-1}$ with a large band-width $\sim 1800$~cm$^{-1}$. For Na$_2$IrO$_3$ the broad band is seen for temperatures $ \leq 200$~K and persists inside the magnetically ordered state. The intensity of this mode increases with Li content, increasing by a factor of $\sim 1.6$ for $x = 0.15$, shifts to lower wave-numbers, and persists to much higher temperatures. Such a mode has recently been predicted theoretically for Na$_2$IrO$_3$ by Knolle et.al. as a signature of the gapless quantum spin liquid (SL) in the Kitaev limit of the Kitaev-Heisenberg model. We assign the observation of the broad band to be a signature of strong Kitaev-exchange correlations. The fact that the broad band persists even inside the magnetically ordered state suggests that dynamically fluctuating moments survive even below $T_{N}$. A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter to be $J_K\approx 57$~meV.

He, Yin-Chen

I will talk about our recent study on the spin liquid phases in kagome antiferromagnets, including the numerical discovery and theoretical investigation in the framework of the lattice gauge theory. I will first present our numerical (DMRG) study on kagome XXZ spin model that identifies two distinct spin liquid phases, namely the chiral spin liquid and the kagome spin liquid (the groundstate of the nearest neighbor kagome Heisenberg model). Both phases extend from the extreme easy-axis limit, through SU(2) symmetric point, to the pure easy-plane limit. And they are separated by a continuous phase transition. Motivated by these numerical results, I will then focus on the easy-axis kagome spin system, and reformulate it as a lattice gauge model. Such formulation enables us to achieve a controlled theoretical description for the spin liquid phase, and we show that the chiral spin liquid is indeed a gauged U(1) symmetry protected topological (SPT) phase. [1] Yin-Chen He, Subhro Bhattacharjee, Frank Pollmann, and R. Moessner, arXiv:1509.03070 [2] Yin-Chen He, Subhro Bhattacharjee, R. Moessner, and Frank Pollmann, PRL 115, 116803 (2015) [3] Yin-Chen He and Yan Chen, PRL 114, 037201 (2015). [4] Yin-Chen He, D. N. Sheng and Yan Chen, PRL 112, 137202 (2014).

Hisano Natori, Willian Massashi

Quantum spin liquids (QSLs) are strongly correlated spin systems that remain magnetically disordered down to 0K. Although they are known to be the ground state of many model Hamiltonians, its experimental discovery is still debated, underlining the importance of research on spin liquid states arising from realistic Hamiltonian models. This work deals with a spin-orbital model in double ordered perovskites that considers antiferromagnetic interactions and strong spin-orbit coupling. The Hamiltonian features a global SU(2) and compass models symmetries, which are made explicit through the use of pseudospin and pseudoorbital operators. The Hamiltonian is rewritten in terms of Majorana fermion operators plus a Z2 gauge field. We proposed a mean-field decoupling preserving the model symmetries. By choosing translationally invariant Ansätze, we found that two of them (connected to each other by time-reversal) are quantum spin-orbital liquids characterized by degenerated gapless Fermi lines. The consistency of these Ansätze was verified through a PSG analysis. We were also able to show that this phase presents non-trivial topological features: energetically separated surface states and topological invariants associated with the nodal lines. Finally, comparison between experimental data and some predicted physical properties are made and improvements of this study are indicated.

Hofmann, Johannes

I shall present the properties of the interacting Dirac liquid, a novel three-dimensional many-body system which was recently experimentally realized and in which the electrons have a chiral linear relativistic dispersion and a mutual Coulomb interaction. I establish that the "intrinsic" Dirac liquid, where the Fermi energy lies exactly at the nodes of the band dispersion, displays unusual Fermi liquid properties similar to graphene, whereas the "extrinsic" system with finite detuning or doping behaves as a standard Landau Fermi liquid. In addition, I present analytical and numerical results for the self-energy and spectral function based on both Hartree-Fock and the random phase approximation (RPA) theories and compute the quasiparticle lifetime, residue, and renormalized Fermi velocity of the extrinsic Dirac liquid. A full numerical calculation of the extrinsic RPA spectral function indicates that the Fermi liquid description breaks down for large-energy excitations. Furthermore, I find an additional plasmaron quasiparticle sideband in the spectral function which is discontinuous around the Fermi energy. All of these predictions should be observable in ARPES and STM measurements.

Kelley, Paula

The physics of the spin-1/2 Kitaev model on a honeycomb lattice have generated enormous interest in recent years due to the potential for fractionalized excitations and topological degeneracy, supported by an exact Z$_2$ quantum spin liquid (QSL) ground state. The J$_{eff}$ = $1/2$ Mott insulator $\alpha$-RuCl$_3$ is a prime candidate for dominate Kitaev interactions due to a network of regular edge-sharing RuCl$_6$ octahedra that form a layered honeycomb structure. Experimentally, RuCl$_3$ exhibits a magnetically ordered zig-zag ground state proximate to the QSL phase below T$_N = 7$ K with a small moment ($ \sim 0.4 \mu_B$) indicating a fragile magnetic order. To perturb the system via electron doping, single crystals of Ru$_{1-x}$Ir$_x$Cl$_3$ ($0 \leq x \leq 0.5$) were prepared using a modified vapor transport technique. Single crystal x-ray diffraction studies confirm that the undistorted octahedral environment and monoclinic C-2m symmetry of the parent structure is preserved in Ir-substituted crystals due to the identical ionic radii of Ir$^{3+}$ and Ru$^{3+}$. With increasing Ir content, a gradual suppression of T$_N$ is observed in magnetic susceptibility measurements, with no indication of a long-range ordering temperature down to 2 K for $x \sim 0.3$. The $x$-T-H phase diagram of Ru$_{1-x}$Ir$_x$Cl$_3$ is established through magnetization, heat capacity, and transport measurements, laying the groundwork for further studies to pinpoint the proximity of doped $\alpha$-RuCl3 to the Kitaev QSL.

Knolle, Johannes

Motivated by recent synthesis of the hyper-honeycomb material $\beta$-Li2IrO3, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalised degrees of freedom are Majorana fermions and emergent flux-loops. Properties of this 3D model are known to differ in important ways from those of its 2D counterpart -- it has finite-temperature phase transition, as well as distinct features in Raman response. We show, however, that the qualitative behaviour of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.

Liu, Tianhan

We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. This picture is also supported by exact diagonalizations on finite clusters.

Lundgren, Rex

We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landau parameters for a conventional spin-degenerate Fermi liquid. We project quasiparticle states onto the Fermi surface and obtain an effectively spinless, projected Landau theory with a single projected Landau parameter per angular momentum channel that captures the spin-momentum locking or nontrivial Berry phase of the Fermi surface. As a result of this nontrivial Berry phase, projection to the Fermi surface can increase or lower the angular momentum of the quasiparticle interactions. We derive equilibrium properties, criteria for Fermi surface instabilities, and collective mode dispersions in terms of the projected Landau parameters. We briefly discuss experimental means of measuring projected Landau parameters.

Mahler, David

Three dimensional Dirac semi-metals can be seen as a “3D graphene” hosting a linear dispersion in all three momentum directions. By breaking either the inversion symmetry or the time reversal symmetry the Dirac points are split into two Weyl points where the spin degeneracy is lifted. It is predicted that the surface of Weyl materials host unconventional surface states characterized by so called Fermi arcs [1]. In this work we focus on HgTe based materials. The band structure of HgTe consists of two degenerate $\Gamma_{8}$- band above the $\Gamma_{6}$- band and therefore an inverted band structure. The degeneracy of the two $\Gamma_{8}$- bands can be lifted by strain. Tensile strained HgTe has been shown to be a three dimensional topological insulator [2]. Compressive strain leads to symmetry protected linear touching points of the two $\Gamma_{8}$- bands [3]. These two combressive strain induced Dirac points are expected to split into degenerate Weyl points due to the broken inversion symmetry. Here we report on magneto-transport measurements in compressively strained bulk HgTe. We find unusual magneto-resistance effects which are expected for a Weyl semi metal state. [1] X. Wan, A. M. Turner, A. Vishwanath and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, PRB 83, 205101 (2011). [2] C. Brüne, et. al., Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe, PRL 106, 126803 (2011). [3] L. Liu and W. Leung, Transport property of zero-gap semiconductors und tensile stress*, PRB 12, 6 (1975).

Morampudi, Siddhardh

Characterizing topologically ordered phases of matter involves identifying the statistics of their emergent anyonic excitations. We show that the exchange statistics of excitations show characteristic signatures in experimentally relevant spectral functions. Drawing motivation from models of gapped quantum spin liquids and fractional Chern insulators which possess fractionalized anyonic excitations, we consider a model with gapped two particle and three particle abelian anyonic excitations. We show that the low energy part of spectral functions can show a robust behaviour from which the statistics of the excitations can be obtained.

Morawetz, Klaus

The quantum kinetic equation for SU(2) symmetric systems is derived with special consideration of spin-orbit coupling in magnetic and electric fields. The theory is applicable for linear and nonlinear intrinsic and extrinsic spin-orbit coupling as well as graphene. The RPA response functions to an electric field are derived for arbitrary magnetic fields and spin-orbit coupling. The coupled density and spin response functions allow to describe dynamical classical, quantum, and anomalous Hall effect as well as spin-Hall effects and its inverse. The collective modes show a splitting due to polarization and/or spin-orbit coupling for neutral impurity scattering. The long-range Coulomb potential of charged impurities are considered and the spin-orbit coupling leads to characteristic modifications of the screening parameter. New high-frequency modes out-of-plane are found. Explicit expressions for the dynamical response and conductivity for relativistic Fermions, Dirac particles and graphene are presented.

Nakamura, Masaaki

We discuss dynamic spin susceptibility (DSS) in two-dimensional (2D) Dirac electrons with spin-orbit interactions to characterize topological insulators. The imaginary part of the DSS appears as an absorption rate in response to a transverse AC magnetic field, just like an electron spin resonance experiment for localized spin systems. We found that when the system is in a static magnetic field, the topological state can be identified by an anomalous resonant peak of the imaginary part of the DSS as a function of the frequency of the transverse magnetic field $\omega$. This anomalous peak is related to a transition between two Landau levels close to the Fermi level, which is not allowed in the trivial state. In the absence of the static magnetic field, the imaginary part of the DSS becomes a continuous function of $\omega$ with a threshold frequency $\omega_{\rm c}$. In this case, the topological and the trivial phases can also be distinguished by the values of $\omega_{\rm c}$ and by the line shapes. Thus the DSS is an essential and an experimentally observable physical quantity to characterize the topological insulators. arXiv:1506.04691

Niu, Chengwang

Here we predict, based on first-principles calculations, that monolayers of SnTe, PbTe, TlS, and TlSe can be characterized as two-dimensional (2D) topological crystalline insulators (TCIs), confirmed by the calculated mirror Chern number $n_M = -2$ and the emergence of two pairs of gapless edge states in one-dimensional nanoribbon [1,2]. Sandwiched between NaCl or NaBr films, both the electronic and topological characteristics can be tuned via the thickness of cladding NaCl (NaBr) layers and the topological characteristics survive even when the middle layers of the quantum wells are trivial insulators as free standing films [3]. Remarkably, the electrostatic, i.e. Madelung, potential of cladding-layer NaCl (NaBr) acts on the middle layers and leads to the band inversion, resulting in the phase transition from trivial insulator to 2D TCIs. In addition, under uniaxial strain, a topological phase transition between 2D TCI and 2D topological insulator (TI) is revealed with the calculated spin Chern number $C_S = -1$ for the 2D TI [2]. Financial support of the DFG (SPP 1666) and the Virtual Institute for Topological Insulators (VITI) are gratefully acknowledged. [1] C. Niu, P. M. Buhl, G. Bihlmayer, D.Wortmann, S. Blügel, and Y. Mokrousov, Phys. Rev. B {\bf 91}, 201401(R) (2015). [2] C. Niu, P. M. Buhl, G. Bihlmayer, D.Wortmann, S. Blügel, and Y. Mokrousov, Nano Lett. {\bf 15}, 6071 (2015). [3] C. Niu, P. M. Buhl, G. Bihlmayer, D. Wortmann, S. Blügel, and Y. Mokrousov, submitted (2015).

Qi, Yang

Quantum spin liquid states with intrinsic topological orders supports fractionalized anyons excitations, and they can carry fractional quantum numbers of spin rotational symmetry, time reversal symmetry and crystal symmetries. This symmetry fractionalization distinguishes different topologically ordered spin liquid states. Different ways of fractionalizing symmetries can be classified through enumerating different combinations of fractional quantum numbers of each type of anyons, but some combinations are anomalous and can only be realized on the surfaceof a 3D topological crystalline insulator instead of a true 2D system. For $\mathbb Z_2$ and chiral spin liquids realized in systems with an odd number of spin-$\frac12$ per unit cell, we fully classify the anomaly-free combinations of symmetry fractionalization. Furthermore, we propose ways to detect the fractional quantum numbers in numerical simulations.

Rachel, Stephan

Majorana fermions, originally proposed as elementary particles acting as their own antiparticles, can 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.

Rhim, Jun Won

We investigate the static and dynamic properties of the nodal line semimetal to the external fields such as the uniform magnetic field and the electromagnetic field. Under the uniform magnetic field parallel to the plane where the nodal line resides, we show that there exist almost nondispersive Landau levels at the Fermi level (EF=0) as a function of the momentum along the field direction inside the ring. We expect the 3D quantum Hall effect from the unusual Landau levels. We analyze the origin of the almost flat Landau levels by introducing the Hamiltonian for the graphene bilayer with fictitious interlayer couplings under a tilted magnetic field which is equivalent to the original one. We also study the dynamic responses of the nodal line semimetal by calculating the poalrizability. From the dynamical polarizability, we obtain the plasmon modes in the doped case, which show anisotropic dispersions and angle-dependent plasma frequencies. In the doped case, the Fermi surface has a torus shape and two independent processes of the momentum transfer contribute to the singular features of the polarizability even though we only have a single Fermi surface. In the static limit, we have the highly anisotropic Friedel oscillations which show the angle-dependent algebratic power law and the beat phenomena in the oscillatory electron density near a charged impurity.

Romhanyi, Judit

The celebrated Shastry Sutherland model has a gapped dimer singlet ground state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this model, upto small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. DM interactions admix a triplet component into the singlet ground state and give rise to weakly dispersing triplon bands. We show that an applied magnetic field splits the triplon modes and opens band gaps. Surprisingly, we are left with topological bands with Chern numbers $\pm 2$. SrCu$_2$(BO$_3$)$_2$ thus supports topologically protected triplonic edge modes and is a magnetic analogue of the integer quantum Hall effect. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch once again in a spin-1 generalization of a Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

Schmitz, Peter Christian

We investigate the topological, spectral and structural properties of Sb$_2$Te$_3$$_x$GeTe$_y$ compounds, some of which are interfacial phase-change materials (IPCMs), as a function of strain and stacking sequence using density functional theory. Induced by electric fields and heat, IPCMs can perform fast reversible transitions between crystalline states of different stacking. Since they possess strong SOC and a TI+NI layering, they are a promising platform for nontrivial interface states and switching between topological phases. So far they were shown to exhibit TIs and unstable TI/NI transition points [1], yet no consistent classification exists. We analyze if the novel 3D topological Dirac semimetal (TDSM) phase [2] is relevant to these $C_3$ systems: Under parameter variation, 2 cones move through the bulk spectrum, gapped due to symmetry breaking potentials between the blocks which enables nonzero 3D $Z_2$ invariants. We show that corresponding states are localized at the interfaces of iPCMs and the effective topological phase is controlled by their van der Waals interaction. [1] J. Tominaga et al, Adv. Mat. Inter. 1 (2014) [2] B. Yang and N. Nagaosa, Nature Commun. 5, 4898 (2014)

Seradjeh, Babak

As understood recently, a topological state may be generated dynamically in an otherwise normal combination of materials by a periodic driving force. These states can only occur when the system is driven out of equilibrium. For example, a Floquet topological insulator can be realized in a two-dimensional system of Dirac fermions, such as graphene, irradiated by a circularly polarized laser. It is characterized by steady states at the edge of the systems. In this talk I present some of our recent theoretical work on the realization and interesting physics of these Floquet topological phases. Specfically, an effective theory of Floquet topological insulators is formulated and usedto study their transport signature. Remarkably, we find that disorder can enhance transport at certain Floquet topological transitions by several orders of magnitude. Moreover, the bulk current at a Floquet topological transition can be engineered by the laser profile to be valley polarized, thus realizing a valley switch.

Shimura, Yasuyuki

Novel phenomena induced by strong hybridization between quadrupolar moments and conduction electrons have attracted recent intensive attention. The cubic Pr-based compound PrV$_2$Al$_20$ with $\Gamma_3$ non-magnetic doublet ground state is one of the most promising compounds. The degeneracy of the doublet is lifted by the antiferro-quadrupole (AFQ) ordering at $T_Q =$ 0.6 K. Below $T_Q$, PrV$_2$Al$_20$ exhibits the heavy-fermion superconductivity with a strongly enhanced effective mass $(m* ~ 140 m_0)$ at $T_{\rm SC} =$ 0.05 K. Recently, we have measured the magnetoresistance in PrV$_2$Al$_20$ down to 0.4 K up to 31 T for $H$ [111]. The AFQ phase is found to be suppressed by the strong magnetic field at $H_c \sim $ 11 T. In the vicinity of the critical field, the temperature dependence of the resistivity shows sub-linear $T$-dependence, clearly deviated from the Fermi-liquid behavior. This is the first observation of the field-induced quadrupolar quantum criticality. In addition, we found the heavy-cyclotron effective mass up to $m*/m_0 \sim 10$ from the Shubnikov-de Haas Oscillation. In order to study the low temperature anisotropic transport phenomena induced by orbital ordering under high magnetic field, we further measured the magnetoresistance for $H$ [111] and [110] down to very low temperature of 0.02 K up to 18 T. We found the peak in $\rho(H)$ with a hysteresis suggesting a first-order transition at 15 T only for $H$ [110]. By sharp contrast, for $H$ [111], no hysteresis was observed down to 0.02 K around the critical field of 11 T. Near the critical field, the temperature dependence exhibits a downward curvature only in a very-narrow temperature region below $\sim $ 0.3 K. The $T^2$ coefficient $A(H)$ is evidently divergent toward the critical field, indicating the quasi-particle mass indeed diverges at the quadrupolar quantum critical point.

Shinaoka, Hiroshi

We investigate the electronic and magnetic properties of the pyrochlore oxide Cd$_2$Os$_2$O$_7$ using the density-functional theory plus on-site repulsion ($U$) method, and depict the ground-state phase diagram with respect to $U$. We conclude that the all-in–all-out noncollinear magnetic order is stable in a wide range of $U$. We also show that the easy-axis anisotropy arising from the spin-orbit coupling plays a significant role in stabilizing the all-in–all-out magnetic order. A pseudogap was observed near the transition between the antiferromagnetic metallic and insulating phases. Finally, we discuss possible origins of the peculiar low-temperature properties observed in experiments. [1] H. Shinaoka, T. Miyake, and S. Ishibashi, PRL 108, 247204 (2012).

Shitade, Atsuo

Topological superconductors (SCs) support Majorana fermions at their boundaries. In two dimensions, time-reversal broken topological SCs are charcterized by the Chern number $C$ and the presence of Majorana edge states. A typical design principle is to realize spinless chiral SCs, whose Cooper pairs carry nonzero angular momentum (AM). In the context of chiral SCs, the bulk orbital AM $L_z/N$ is believed to be a manifestation of Majorana edge states and is known to be $1/2$ for chiral $p$-wave SCs with $C = 1$ [1]. More surprisingly, it was recently found to vanish for chiral SCs with $C > 1$ [2]. However, we know only one experimental realization of chiral SCs, namely, $^3$He-A with $C = 1$. On the other hand, topological SCs are experimentally more plausible and can have high Chern number. Here we investigate the bulk orbital AM in electron-doped ($C = -1$) and hole-doped ($C = -3$) topological SCs [3,4], which consist of the Rashba spin-orbit interaction (SOI), the Zeeman interaction, and the $s$-wave pairing potential. We find crossover for $C = 0$, similarities to the corresponding chiral SCs, i.e., $L_z/N = -1/2$ for $C = -1$ and $L_z/N = 0$ for $C = -3$, for the small SOI. and suppression or recovery of the bulk orbital AM due to the large SOI. Although topological SCs are designed aiming at spinless chiral SCs with use of the SOI, they exhibit the chiral-SC behaviors only when the SOI is small. [1] A. Shitade and T. Kimura, Phys. Rev. B 90, 134510 (2014) and references therein. [2] Y. Tada, W. Nie, and M. Oshikawa, Phys. Rev. Lett. 114, 195301 (2015). [3] A. Shitade and Y. Nagai, Phys. Rev. B 92, 024502 (2015). [4] A. Shitade and Y. Nagai, in preparation.

Smith, Adam

We calculate the dynamical structure factor (DSF) for three 3D Kitaev quantum spin liquids (KQSLs), whose fractionalized degrees of freedom are Majorana fermions and emergent $\mathbb{Z}_2$ flux-loops. Recent interest in 3D QSLs has been motivated by the synthesis of the candidate hyperhoneycomb material $\beta$-Li$_2$IrO$_3$ which has lead to the extension of the Kitaev model to 3D lattices. The three lattices we consider have gapless Weyl points, nodal lines and Majorana fermi surfaces, respectively, providing us with a characteristic range of gapless 3D KQSLs. Our main findings are a remarkable insensitivity to both dimensionality and lattice structure, with the majority of the dynamical behaviour being determined by the DOS, particularly at low energies. By comparing these 3D lattices and the 2D honeycomb lattice we can go someway towards categorizing the dynamics of Kitaev quantum spin liquids.

Su, Yixi

Note: will be submitted later.

Wan, Yuan

Quantum spin ice is a novel family of spin ice magnets that possess substantial quantum fluctuations. The fractional excitations are spinons, which are quantum analog of the monopoles in classical spin ice. The spinon propagates in quantum spin ice via quantum tunnelling. As opposed to a conventional quantum particle, the spinon moves in a background of disordered spins. The orientation of background spins controls the spinon motion, whereas the spinon motion in turn alters the spin background. One may naturally ask what a suitable framework for understanding the dynamics of spinon is in quantum spin ice, and furthermore, whether the spinon propagation is coherent. In this talk, we address these issues by investigating a minimal model that captures the essential features of single spinon dynamics in quantum spin ice. We demonstrate that the spinon motion can be thought of as a quantum walk with entropy-induced memory. Our numerical simulation shows that the simple quasi-particle behaviour emerges out of the intricate interplay between the spinon and the background spins .

Yamada, Masahiko G.

Double perovskite compounds, such as $\mathrm{Sr_2FeMoO_6},$ have attracted intense interest as a spintronics device because of its room temperature ferrimagnetism and magnetoresistance as well as the possibility of half-metal. Recent progress in synthesizing atomic scale slabs by pulsed laser deposition or molecular beam epitaxy has motivated us to investigate a (001) thin film of $\mathrm{Sr_2FeMoO_6}.$ Now, we propose that this (001) thin film should realize a Wigner crystal phase of interacting electrons when its flat band is doped slightly because its spin-orbit coupling would enhance the stability of its ferrimagnetism and unusual band structure with a flat band against the electron doping.