We investigate the unconventional quantum phase transitions in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $Θ$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in order: (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition in $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics.
We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence b…
Disordered non-interacting systems in sufficiently high dimensions have been predicted to display a non-Anderson disorder-driven transition that manifests itself in the critical behaviour of the density of states and other physical observables. Recently the critical properties of this transition have been extensively studied for the specific case of Weyl semimetals by means of numerical and renormalisation-group approaches. Despite this, the values of the critical exponents at such a transition in a Weyl semimetal are currently under debate. We present an independent calculation of the critica…
Quantum oscillations in magnetoconductance of a material at low temperatures and in presence of an intense magnetic field are described by the Shubnikov de Haas (SdH) effect. It is widely assumed to be the hallmark of the Fermi surface of a given metal. In contrast to the canonical situation, we identify an exotic oscillation in nonlinear responses of three-dimensional nodal line semimetals (NLSMs) which persist even at temperatures where the typical SdH-like oscillations vanish. This oscillation occurs due to the periodic gap-closing of a pair of Landau levels at zero Fermi energy with the va…
As exemplified by the growing interest in the quantum anomalous Hall effect, the research on topology as an organizing principle of quantum matter is greatly enriched from the interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study on the magnetic Weyl semimetal EuCd$_2$As$_2$. Unconventional contribution to the anomalous Hall and anomalous Nernst effects were observed both above and below the magnetic transition temperature of EuCd$_2$As$_2$, indicating the existence of significant Berry curvature. EuCd$_2$As$_2$ represents a rare case in …
Weyl semimetals are well known for their anomalous transport effects caused by a large fictitious magnetic field generated by the non-zero Berry curvature. We performed the analysis of the electrical transport measurements of the magnetic Weyl semimetal Mn$_{3}$Ge in the a-b and a-c plane. We have observed negative longitudinal magneto-resistance (LMR) at a low magnetic field ($B<1.5$ T) along all the axes. The high field LMR shows different behavior along x and z axes. A similar trend has been observed in the case of planar Hall effect (PHE) measurements as well. The nature of high field LMR …
Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin-orbit coupling and electron-electron interactions are believed to induce a time-reversal symmetry broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy. However, the emergent properties in these materials are far from clear, and exotic new states of matter have been conjectured. Here we demonstrate optically that at low temperatures the free carrier spectral weight is proportional to T^2 where T is the temperature, as expected for massless Dirac ele…
We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg--Landau free energy and apply these concepts to the case of an isotropic band touching point. For vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features…
The topological properties of fermions arise from their low-energy Dirac-like band dispersion and associated chiralities. Initially confined to points, extensions of the Dirac dispersion to lines and even loops have now been uncovered and semimetals hosting such features have been identified. However, experimental evidence for the enhanced correlation effects predicted to occur in these topological semimetals has been lacking. Here, we report a quantum oscillation study of the nodal loop semimetal ZrSiS in high magnetic fields that reveals significant enhancement in the effective mass of the q…
We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us…
A symmetry-protected topological phase has nontrivial surface states in the presence of certain symmetries, which can either be gapless or be degenerate. In this work, we study the physical consequence of such gapless surface states at the bulk quantum phase transition (QPT) that spontaneously breaks these symmetries. The two-dimensional Affleck-Kennedy-Lieb-Tasaki phase on a square lattice and its QPTs to Néel ordered phases are realized with the spin-$1/2$ Heisenberg model on a decorated square lattice. With large-scale quantum Monte Carlo simulations, we show that even though the bulk QPTs …
The Weyl semimetal, due to a non-zero energy difference in the pair of Weyl nodes shows chiral magnetic effect(CME). This leads to a flow of dissipationless electric current along an applied magnetic field. Such a chiral magnetic effect in Weyl semimetals has been studied using the laws of classical electrodynamics. It has been shown that the CME in a such a semimetal changes the properties namely, frequency dependent skin depth, capacitive transport, plasma frequency etc. in an unconventional way as compared to the conventional metals. In the low frequency regime, the properties are controlle…
We propose the metallic and weakly dispersive surface states of half-Heusler semimetals as a possible domain for the onset of unconventional surface superconductivity ahead of the bulk transition. Using density functional theory (DFT) calculations and the random phase approximation (RPA), we analyse the surface band structure of LuPtBi and its propensity towards Cooper pair formation induced by screened electron-electron interactions in the presence of strong spin-orbit coupling. Over a wide range of model parameters, we find an energetically favoured chiral superconducting condensate featurin…
We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This correspondence has potential implications in both directions. We illustrate the proposal by investigating its consequences for the spectral and transport properties of Dirac and Weyl semimetals. Particular realizations of this framework give rise to Dirac nodal spectra with nodal lines and rings. We demonstrate a bulk-boundary correspondence between bulk topolog…
We study possible Weyl semimetals of strongly-correlated electrons by investigating magnetotransport properties in pyrochlore R2Ir2O7 (R=rare-earth ions), choosing three types of R ions to design the exchange coupling scheme between R 4f and Ir 5d moments; non-magnetic Eu (4f6), isotropic Gd (4f7), and anisotropic Tb (4f8). In the doping-induced semimetallic state, distinctive features of magnetoresistance and Hall effect are observed in R=Gd and Tb compounds due to the effects of the exchange-enhanced isotropic and anisotropic Zeeman fields, respectively, exemplifying the double Weyl semimeta…
Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin…
We investigate the low-energy scaling behavior of an interacting 3D Weyl semimetal in the presence of disorder. In order to achieve a renormalization group analysis of the theory, we focus on the effects of a short-ranged-correlated disorder potential, checking nevertheless that this choice is not essential to locate the different phases of the Weyl semimetal. We show that there is a line of fixed-points in the renormalization group flow of the interacting theory, corresponding to the disorder-driven transition to a diffusive metal phase. Along that boundary, the critical disorder strength und…
Pezzini et al. reported an unconventional mass enhancement in topological nodal line semimetal ZrSiS (Nat. Phys. 14, 178 (2018), whose origin remains puzzling. In this material, strong short-range interactions might induce excitonic particle-hole pairs. Here we study the renormalization of fermion velocities and find that the mass enhancement in ZrSiS can be well understood if we suppose that ZrSiS is close to the quantum critical point between semimetal and excitonic insulator. Near this quantum critical point, the fermion velocities are considerably reduced by excitonic quantum fluctuation, …
We present a systematic investigation of the magnetoresponses of the Weyl points (WPs) with a topological charge of n = 2, 3 and 4, and with both linear and quadratic energy tilt. The linear tilt always tends to squeeze the Landau levels (LLs) of both conduction and valence bands of all the WPs, and eventually leads to LL collapse in the type-II phase. However, the quadratic energy tilt has more complex influences on the LLs of the unconventional WPs. For charge-n (n = 2, 4) WP, the influence of the quadratic tilt on the LLs of conduction and valence bands are opposite, i.e. if the LLs of cond…
Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in semimetallic and metallic phases,…
Interplay between magnetism and electronic band topology is of central current interest in topological matter research. We use quantum oscillations as powerful tool to probe the evolution of band topology in the Dirac semimetal EuMnSb$_2$. The Eu local 4f magnetic moments display different antiferromagnetic states below 25 K and a field-polarized phase above 16 T. Upon cooling from 65 K into the field-polarized state, an exotic temperature dependent shift of oscillation peaks arises, accompanied by the development of non-zero Berry phase and a huge unconventional splitting of the oscillations.…
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and…
The emergent Weyl fermions in condensed matter generally break the Lorentz invariance resulting in a tilted (type-I) or over-tilted (type-II) energy dispersion. The tilting energy spectrums can lead to exotic quantum interference effects in a junction set up. Here, we theoretically investigate the Josephson current in a Weyl superconductor-Weyl (semi)metal-Weyl superconductor junction of a time-reversal (TR) broken type-I Weyl semimetal. We demonstrate that the Cooper pairs of BCS-like pairing acquire a finite momentum in case of inversion symmetric tilt. Consequently, the system exhibits tilt…
The origins of hydrodynamic transport in strongly interacting Dirac and Weyl semimetals have remained elusive in theoretical descriptions and experimental measurements. We investigate the structure and microscopic properties of transport in WP$_2$, a type-II Weyl semimetal, to probe the emergence of hydrodynamic phenomena. We characterize the quantum behavior underlying the hydrodynamic transport regime as a function of temperature through ab initio calculations of the relevant microscopic scattering processes, including electron-phonon, electron-electron, and phonon-mediated electron-electron…
Topological semimetals are three dimensional materials with symmetry-protected massless bulk excitations. As a special case, Weyl nodal-line semimetals are realized in materials either having no inversion or broken time-reversal symmetry and feature bulk nodal lines. The 111-family of materials, LaNiSi, LaPtSi and LaPtGe (all lacking inversion symmetry), belong to this class. Here, by combining muon-spin rotation and relaxation with thermodynamic measurements, we find that these materials exhibit a fully-gapped superconducting ground state, while spontaneously breaking time-reversal symmetry a…
Rapid progress of quantum transport study in topological Dirac semimetal, including observations of quantum Hall effect in two-dimensional (2D) Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ samples, has uncovered even more interesting quantum transport properties in high-quality and three-dimensional (3D) samples. However, such 3D Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ films with low carrier density and high electron mobility have been hardly obtained. Here we report the growth and characterization of 3D thick Cd$_{\mathrm{3}}$As$_{\mathrm{2}}$ films adopting molecular beam epitaxy. The highest electron mobi…
We present a real-space view of one-dimensional (1D) to three-dimensional (3D) topological materials with 13 representative samples selected from each class, including 1D trans-polyacetylene, two-dimensional (2D) graphene, and 3D topological insulators, Dirac semimetals, Weyl semimetals, and nodal-line semimetals. This review is not intended to present a complete up-to-date list of publications on topological materials, nor to provide a progress report on the theoretical concepts and experimental advances, but rather to focus on an analysis based on the valence-bond model to help the readers g…
Although strong electronic correlations are known to be responsible for some highly unusual behaviors of solids such as, metal--insulator transitions, magnetism and even high--temperature superconductivity, their interplay with recently discovered topological states of matter awaits full exploration. Here we use a modern electronic structure method combining density functional theory of band electrons with dynamical self-energies of strongly correlated states to predict that two well-known phases of actinide compound UNiSn, a paramagnetic semiconducting and antiferromagnetic metallic, correspo…
Fermi liquid theory works very well in most normal metals, but is found violated in many strongly correlated electron systems, such as cuprate and heavy-fermion superconductors. A widely accepted criterion is that, the Fermi liquid theory is valid when the interaction-induced fermion damping rate approaches zero more rapidly than the energy. Otherwise, it is invalid. Here, we demonstrate that this criterion breaks down in topological double-and triple-Weyl semimetals. Renormalization group analysis reveals that, although the damping rate of double- and triple-Weyl fermions induced by the Coulo…
