We construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states and sub-diffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique "unfreezing" transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy density of states develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.
Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold-atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral l…
We theoretically study the excitation spectrum of a two-dimensional Dirac semimetal in the presence of an incommensurate potential. Such models have been shown to possess magic-angle critical points in the single particle wavefunctions, signalled by a momentum space delocalization of plane wave eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the kernel polynomial method, we compute the single particle Green's function to extract the nature of the single particle excitation energy, damping rate, and quasiparticle residue. As a result, we are able to clearly demonstrate …
We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moiré flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, includin…
Distinguishing Mott and strain-induced anisotropic semimetals in magic-angle twisted bilayer graphene using Landau level spectroscopy
National High Magnetic Field Laboratory（国家强磁场实验室）；Florida State University（佛罗里达州立大学）；Princeton University（普林斯顿大学）；Weizmann Institute of Science（魏茨曼科学研究所）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克，巴斯克科学基金会）；University of Minnesota（明尼苏达大学）
Weyl semimetals are one kind of three-dimensional gapless semimetal with nontrivial topology in the momentum space. The chiral anomaly in Weyl semimetals manifests as a charge imbalance between the Weyl nodes of opposite chiralities induced by parallel electric and magnetic fields. We investigate the chiral anomaly effect on the plasmon mode in both intrinsic and doped Weyl semimetals within the random phase approximation. We prove that the chiral anomaly gives rise to a different plasmon mode in intrinsic Weyl semimetals. We also find the chiral anomaly leads to some exotic properties in the …
In this paper we study how dynamical chiral symmetry breaking is affected by nonzero chiral chemical potential in Dirac semimetals. To perform this study we applied lattice quantum Monte Carlo simulations of Dirac semimetals. Within lattice simulation we calculated the chiral condensate for various fermion masses, the chiral chemical potentials and effective coupling constants. For all parameters under consideration we have found that the chiral condensate is enhanced by chiral chemical potential. Thus our results confirms that in Dirac semimetals the chiral chemical potential plays a role of …
We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormaliz…
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 study dynamical instability and chiral symmetry breaking in three dimensional Weyl semimetals, which turns Weyl semimetals into "axion insulators". Charge density waves (CDW) is found to be the natural consequence of the chiral symmetry breaking. The phase mode of this charge density wave state is identified as the axion, which couples to electromagnetic field in the topological $θ{\bf E}\cdot{\bf B}$ term. One of our main results is that the "axion strings" can be realized as the (screw or edge) dislocations in the charge density wave, which provides a simple physical picture for the elusi…
The chiral anomaly is a phenomenon characteristic of Weyl fermions, which has condensed matter realizations in Weyl semimetals. Efforts to observe smoking gun signatures of the chiral anomaly in Weyl semimetals have mostly focused on a negative longitudinal magnetoresistance in electronic transport. Unfortunately, disentangling the chiral anomaly contribution in transport or optical measurements has proven non-trivial. Recent works have proposed an alternative approach of probing pseudoscalar phonon dynamics for signatures of the chiral anomaly in non-mirror-symmetric crystals. Here, we show t…
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties.A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs.In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied.It is shown that the chiral symmetry is restored in the nonlinear sigma model describin…
Weyl semimetals are a three dimensional gapless topological phase in which bands intersect at arbitrary points -- the Weyl nodes -- in the Brillouin zone. These points carry a topological quantum number known as the \emph{chirality} and always appear in pairs of opposite chiralities. The notion of chirality leads to anomalous non-conservation of chiral charge, known as the \emph{chiral anomaly}, according to which charge can be pumped between Weyl nodes of opposite chiralities by an electromagnetic field with non-zero $\boldsymbol{E}\cdot\boldsymbol{B}$. Here, we propose probing the chiral ano…
We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $ρ$ that depends on the current $\boldsymbol{I}$ and the magnetic field $\boldsymbol{B}$ as $ρ=ρ_0 (1 + γ\boldsymbol{I} \cdot \boldsymbol{B})$, and can be applied to rectifier devices controlled by $\boldsymbol{B}$. We derive the formula for the coefficient $γ$ in noncentrosymmetric Weyl semimetals. The obtained formula for $γ$ shows that the magnetochiral anisotropy…
In this talk, we describe recent experimental progress in detecting the chiral anomaly in the Dirac semimetal Na$_3$Bi in the presence of a magnetic field. The chiral anomaly, which plays a fundamental role in chiral gauge theories, was predicted to be observable in crystals by Nielsen and Ninomiya in 1983 [1]. Theoretical progress in identifying and investigating Dirac and Weyl semimetals has revived strong interest in this issue [2-6]. In the Dirac semimetal, the breaking of time-reversal symmetry by a magnetic field $\bf B$ splits each Dirac node into two chiral Weyl nodes. If an electric f…
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
The planar Hall effect (PHE), the appearance of an in-plane transverse voltage in the presence of co-planar electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields, occurs in regular Weyl semimetals (WSMs) as one of the fundamental manifestations of chiral anomaly. A major issue, therefore, is whether there are alternate route to PHE, without invoking chiral anomaly. We demonstrate that PHE exists in an inhomogeneous Weyl semimetal (IWSM) even in the absence of the aforesaid anomaly. Using semiclassical Boltzmann transport theory, we show that PHE appears in an IWSM due to the strain-induce…
Weyl semimetals are a three-dimensional topological phase of matter with isolated band touchings in the Brillouin Zone. These points have an associated chirality, and many of the proposals to detect the Weyl semimetal state rely on the chiral anomaly. A consequence of the chiral anomaly is that under the application of an $\vec{E}\cdot\vec{B}$ field, charge is transferred between points of opposite chirality. In this paper we propose an optical absorption experiment that provides evidence for the chiral anomaly. We use the Kubo formula, and find that an applied $\vec{E}\cdot\vec{B}$ induces th…
Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here we predict that the chiral anomaly occurs - and has experimentally observable consequences - when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b. For ex…
We provide a review of recent experimental results on the chiral anomaly in Dirac/Weyl semimetals. After a brief introduction, we trace the steps leading to the prediction of materials that feature protected 3D bulk Dirac nodes. The chiral anomaly is presented in terms of charge pumping between the chiral Landau levels of Weyl fermions in parallel electric and magnetic fields. The related chiral magnetic effect and chiral zero sound are described. Current jetting effects, which present major complications in experiments on the longitudinal magnetoresistance, are carefully analyzed. We describe…
The transverse and longitudinal magnetoresistance (MR) of two samples of the topological chiral semimetal CoSi with different RRR was studied. It is shown that the Kohler rule works for the transverse MR. The Kohler rule is also fulfilled in the case of longitudinal MR at a low reduced magnetic field. A sharp deviation of longitudinal MR curve for sample with low RRR from the Kohler prediction at high fields reveals its tendency to a sign change at higher magnetic fields. The Shubnikov de Haas quantum oscillations were observed and analyzed in both perpendicular and parallel configurations of …
We report on the mean-field study of the Chiral Magnetic Effect (CME) in static magnetic fields within a simple model of a parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from re-summed ladder diagrams with arbitrary number of loops. We find that on-site repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. …
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 calculate the magnetoconductivity of the Weyl semimetal with $\mathbb{Z}_2$ symmetry and chiral anomaly utilizing the recently developed hydrodynamic theory. The system in question will be influenced by magnetic fields connected with ordinary Maxwell and the second $U(1)$-gauge field, which is responsible for anomalous topological charge. The presence of chiral anomaly and $\mathbb{Z}_2$ anomalous charge endow the system with new transport coefficients. We start with the linear perturbations of the hydrodynamic equations and calculate the magnetoconductivity of this system. The holographic …
In this paper Chiral Magnetic Effect (CME) in Dirac semimetals is studied by means of lattice Monte Carlo simulation. We measure conductivity of Dirac semimetals as a function of external magnetic field in parallel $σ_{\parallel}$ and perpendicular $σ_{\perp}$ to the external field directions. The simulations are carried out in three regimes: semimetal phase, onset of the insulator phase and deep in the insulator phase. In the semimetal phase $σ_{\parallel}$ grows whereas $σ_{\perp}$ drops with magnetic field. Similar behaviour was observed in the onset of the insulator phase but conductivity …
We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat…
Formulating consistent theories describing strongly correlated metallic topological phases is an outstanding problem in condensed matter physics. In this work we derive a theory defining a fractionalized analogue of the Weyl semimetal state: the fractional chiral metal. Our approach is to construct a 4+1D quantum Hall insulator by stacking 3+1D Weyl semimetals in a magnetic field. In a strong enough field the low-energy physics is determined by the lowest Landau level of each Weyl semimetal, which is highly degenerate and chiral, motivating us to use a coupled-wire approach. The one-dimensiona…
The chiral magnetic effect is a one of the exotic bulk transport properties of the Weyl semimetals. Because of the Nielsen-Ninomiya "no-go theorem", the total chiral magnetic current is absent in the equilibrium state. One of the mechanisms for generating this current is the chiral anomaly. This phenomenon is the anomalous nonconservation of chiral charge for massless relativistic particles. It can be realized by parallel magnetic and electric fields, and it leads to such new transport phenomenon as the negative longitudinal magnetoresistance. Using a simple theory (we consider both linearized…
Magneto conductivities in Weyl semimetals (WSM) in presence of small fields are studied using quasi-classical Boltzmann transport equations (BTE). Following such formalism here we consider irradiation via circularly polarized light on a two-node time reversal breaking WSM already under a dc/static electric field and study the magneto-transport properties due to the presence of chiral anomaly. Chiral anomaly affects both longitudinal magnetoconductivity as well as planar Hall conductivity. {As our field set-up causes continuous time variation in the relative orientation between the fields, one …
Electronic transport in Weyl semimetals is quite extraordinary due to the topological property of the chiral anomaly generating the charge pumping between two distant Weyl nodes with opposite chiralities under parallel electric and magnetic fields. Here, we develop a full nonequilibrium quantum transport theory of the chiral anomaly, based on the fact that the chiral charge pumping is essentially nothing but the Bloch oscillation. Specifically, by using the Keldysh nonequilibrium Green function method, it is shown that there is a rich structure in the chiral anomaly transport, including the ne…
The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied ac electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear dc current as it is second-order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of nonzero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On exam…
We study the chiral magnetic effect (CME) in tilted multi-Weyl Semimetals (WSM) employing a two-band lattice model. We focus on the type-II phase of mWSMs, introduced by incorporating a Lorentz symmetry violating tilt term. We add to the understanding of the CME (and anomalous Hall effect) in the type-II phase of mWSMs and near the Lifshitz transition by varying tilt. Like the elementary WSM, our results also indicate that the Berry curvature drives the CME for higher monopole charges. We find a peak in the CME at the transition point and discuss its significance using the density of states. A…
We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropic behavior and is larger along the tilt direction. This striking anisotropy of DCMC which results in anisotropic optical activity and rotary power, can be experimentally observed as a topological…
We study the static electric current due to the Chiral Magnetic Effect in samples of Weyl semimetals with slab geometry, where the magnetic field is parallel to the boundaries of the slab. We use the Wilson-Dirac Hamiltonian as a simplest model of parity-breaking Weyl semimetal with two-band structure. We find that the CME current is strongly localized at the open boundaries of the slab, where the current density in the direction of the magnetic field approaches the conventional value $j = μ_5 B /2 π^2$ at sufficiently small values of the chiral chemical potential $μ_5$ and magnetic field $B$.…
We consider a configuration of three stacked graphene monolayers with equal consecutive twist angles $θ$. Remarkably, in the chiral limit when interlayer coupling terms between $\textrm{AA}$ sites of the moiré pattern are neglected we find four perfectly flat bands (for each valley) at a sequence of magic angles which are exactly equal to the twisted bilayer graphene (TBG) magic angles divided by $\sqrt{2}$. Therefore, the first magic angle for equal-twist trilayer graphene (eTTG) in the chiral limit is $θ_{*} \approx 1.05^{\circ}/\sqrt{2} \approx 0.74^{\circ}$. We prove this relation analytic…
The complete set of Maxwell's and hydrodynamic equations for the chiral electrons in Weyl semimetals is presented. The formulation of the Euler equation takes into account the explicit breaking of the Galilean invariance by the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino) contributions should be added to the electric current and charge densities in Maxwell's equations that provide the information on the separation of Weyl nodes in energy and momentum. On the other hand, these topological contributions do not directly affect the Euler equation and the energy conservation r…
We report a detailed magneto-transport study in single crystals of NbP. High quality crystals were grown by vapour transport method. An exceptionally large magnetoresistance is confirmed at low temperature which is non-saturating and is linear at high fields. Models explaining the linear magnetoresistance are discussed and it is argued that in NbP this is linked to charge carrier mobility fluctuations. Negative longitudinal magnetoresistance is not seen, unlike several other Weyl monopnictides, suggesting lack of well defined chiral anomaly in NbP. Unambiguous Shubnikov-de-Haas oscillations ar…
