Chiral Charge Research Articles

Chirality in Self-Assembling Rod-Coil Copolymers: Macroscopic Homochirality Versus Local Chirality

We study chiral mesophases arising as a result of the interplay between microphase separation and orientational ordering in diblock rod-coil copolymers. It is shown that nearly compositionally symmetric copolymers form a columnar structure with twisted rod-rich domains, whereas there is a suppression of the lamellar morphologies with respect to the columnar one. Using high-resolution three-dimensional self-consistent field simulations, we show that chirality in the unit cell of the hexagonal phase develops in two different ways, leading to either homochiral state or heterochiral (locally chiral) state. Thus, chiral polarization, which occurs when the rigid and flexible blocks are segregated, causes a transition to two degenerate chiral states. In a system with many twisted domains, the magnitude of the chirality charge obeys the binomial distribution with random selection of the twist direction for each of the rod-rich domains. We suggest a model of pseudodynamical structural evolution aimed at understanding of how chirality arises from the achiral state and how it evolves. At the initial stage of the evolutionary process, there exists some waiting time for the onset of irreversible changes in chirality; during this time the system flips between the two chirality states.

Nonlinear chiral transport in Dirac semimetals

We study the current of chiral charge density in a Dirac semimetal with two Dirac points in momentum space, subjected to an externally applied time dependent electric field and in the presence of a magnetic field. Based on the kinetic equation approach, we find contributions to the chiral charge current, that are proportional to the second power of the electric field and to the first and second powers of the magnetic field, describing the interplay of the chiral anomaly and the drift motion of electrons moving under the action of electric and magnetic fields.

A parallel magnetic field driven confinement versus separation of charges in GaAs quantum well investigated by magneto-photovoltage and magneto-photoluminescence spectroscopy

Opto-electronic properties of excitons under parallel and perpendicular magnetic field are investigated on various thickness of GaAs/AlGaAs quantum well. An analytical expression of diamagnetic energy under a parallel magnetic field is derived by solving the Schrödinger equation of exciton in quantum wells. The transformation underlying the solution of Schrödinger equation suggests that an in-plane separation between electron and hole may increase with an increasing parallel magnetic field, leading to a reduced coulomb interaction and slow radiative recombination rate. As a consequence of this, even in the absence of an external electrical bias, parallel magnetic field induces a chiral charge transportation across the hetero-interfaces of a quantum well, which gives rise to an increasing in-plane magneto-photovoltage signal. The present investigation provides a unique method to control the recombination and transportation of charges by the strength and orientation of a magnetic field.

Dynamical density response and optical conductivity in topological metals

Topological metals continue to attract attention as novel gapless states of matter. While there by now exists an exhaustive classification of possible topologically nontrivial metallic states, their observable properties, that follow from the electronic structure topology, are less well understood. Here we present a study of the electromagnetic response of three-dimensional topological metals with Weyl or Dirac nodes in the spectrum, which systematizes and extends earlier pioneering studies. In particular, we argue that a smoking-gun feature of the chiral anomaly in topological metals is the existence of propagating chiral density modes even in the regime of weak magnetic fields. We also demonstrate that the optical conductivity of such metals exhibits an extra peak, which exists on top of the standard metallic Drude peak. The spectral weight of this peak is transferred from high frequencies and its width is proportional to the chiral charge relaxation rate.

Probing the chiral anomaly by planar Hall effect in Dirac semimetal Cd3As2 nanoplates

Searching for exotic transport properties in new topological state of matters is an active topic. One of the most fascinating achievements is the chiral anomaly in recently discovered Weyl semimetals (WSMs), which is manifested as a negative longitudinal magnetoresistance (LMR) in the presence of a magnetic field B parallel to an electric field E. Another predicted key effect closely related to the chiral anomaly is the planar Hall effect (PHE), which has not been identified in WSMs so far. Here we carried out the planar Hall measurements on Cd3As2 nanoplates, and found that, accompanied by the large negative LMR, a PHE with non-zero transverse voltage can be developed while tilting the in-plane magnetic field B away from the electric field E. Further experiments reveal that both the PHE and the negative LMR can be suppressed synchronously by increasing the temperature, but still visible at room temperature, indicating the same origin of these two effects. The observation of PHE in Cd3As2 nanoplates gives another transport evidence for the chiral anomaly and provides a deep insight into the chiral charge pumping in Weyl Fermions system.

Biscalar Integrable Conformal Field Theories in Any Dimension.

We propose a D-dimensional generalization of 4D biscalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a particular strong-twist limit of γ-deformed N=4 supersymmetric Yang-Mills theory. Similar to the 4D case, the planar correlators of this D-dimensional theory are conformal and dominated by "fishnet" Feynman graphs. The dynamics of these graphs is described by the integrable conformal SO(1,D+1) spin chain. In 2D, it is the analogue of Lipatov's SL(2,C) spin chain for the Regge limit of QCD but with the spins s=1/4 instead of s=0. Generalizing recent 4D results of Grabner, Gromov, Korchemsky, and one of the authors to any D, we compute exactly at any coupling a four-point correlation function dominated by the simplest fishnet graphs of cylindric topology and extract from it exact dimensions of operators with chiral charge 2 and any spin together with some of their operator product expansion structure constants.

Magnetic field induced Weyl semimetal from Wannier-function-based tight-binding model

Weyl semimetals (WSMs) have Weyl nodes where conduction and valence bands meet in the absence of inversion or time-reversal symmetry (TRS), or both. Interesting phenomena are expected in WSMs such as the chiral magnetic effect, anomalous Hall conductivity or Nernst effect, and unique quantum oscillations. The TRS-broken WSM phase can be driven from a topological Dirac semimetal (DSM) by magnetic field or magnetic dopants, considering that DSMs have degenerate Weyl nodes stabilized by rotational symmetry, i.e. Dirac nodes. Here we develop a Wannier-function-based tight-binding (WF-TB) model to investigate the formation of Weyl nodes and nodal rings induced by B field in the topological DSM Na$_3$Bi. The field is applied along the rotational axis. Remarkably, our study based on the WF-TB model shows that upon B field each Dirac node is split into four separate Weyl nodes along the rotational axis near the Fermi level; two nodes with single chiral charge (single Weyl nodes) and two with double chiral charge (double Weyl nodes). This result is in contrast to the common belief that each Dirac node splits into two Weyl nodes. In the effective models, the existence of double Weyl nodes ensures nonzero cubic terms in momentum. We further examine the evolution of Fermi arcs at a side surface as a function of chemical potential. The number of Fermi arcs is consistent with the corresponding Fermi surface Chern numbers, corroborating our finding of the double Weyl nodes. Furthermore, our study reveals the existence of nodal rings in the mirror plane below the Fermi level upon B field. These nodal rings persist with spin-orbit coupling, in contrast to typical nodal ring semimetals. Our WF-TB model can be used to compute interesting features arising from Berry curvature such as anomalous Hall and thermal conductivities, and our findings can be applied to other topological DSMs like Cd$_3$As$_2$.

Coupled wire model of Z4 orbifold quantum Hall states

We introduce a coupled wire model for a sequence of non-Abelian quantum Hall states that generalize the Z4 parafermion Read Rezayi state. The Z4 orbifold quantum Hall states occur at filling factors \nu = 2/(2m-p) for odd integers $m$ and $p$, and have a topological order with a neutral sector characterized by the orbifold conformal field theory with central charge $c=1$ at radius $R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the $Z_4$ Read Rezayi state, and the series of $p\ge 3$ defines a sequence of non-Abelian states that resembles the Laughlin sequence. Our model is based on clustering of electrons in groups of four, and is formulated as a two fluid model in which each wire exhibits two phases: a weak clustered phase, where charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered phase where the electrons are strongly bound in groups of 4. The transition between these two phases on a wire is mapped to the critical point of the 4 state clock model, which in turn is described by the orbifold conformal field theory. For an array of wires coupled in the presence of a perpendicular magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin state with a chiral charge mode at the edge, but no neutral mode and a gap for single electrons. Coupled wires near the critical state form quantum Hall states with a gapless neutral mode described by the orbifold theory. The coupled wire approach allows us to employ the Abelian bosonization technique to fully analyze the physics of single wire, and then to extract most topological properties of the resulting non-Abelian quantum Hall states. These include the list of quasiparticles, their fusion rules, the correspondence between bulk quasiparticles and edge topological sectors, and most of the phases associated with quasiparticles winding one another.

Engineering of robust topological quantum phases in graphene nanoribbons.

Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin-momentum locked transport channels or Majorana fermions1-3. The idea of using such states in spintronic devices or as qubits in quantum information technology is a strong driver of current research in condensed matter physics4-6. The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states7-9. In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model10,11. Because the SSH model describes chiral topological insulators, charge fractionalization and spin-charge separation in one dimension, numerous efforts have been made to realize the SSH Hamiltonian in cold-atom, photonic and acoustic experimental configurations12-14. It is, however, desirable to rationally engineer topological electronic phases into stable and processable materials to exploit the corresponding quantum states. Here we present a flexible strategy based on atomically precise graphene nanoribbons to design robust nanomaterials exhibiting the valence electronic structures described by the SSH Hamiltonian15-17. We demonstrate the controlled periodic coupling of topological boundary states18 at junctions ofgraphene nanoribbons with armchair edges to create quasi-one-dimensional trivial and non-trivial electronic quantum phases. This strategy has the potential to tune the bandwidth of the topological electronic bands close to the energy scale of proximity-induced spin-orbit coupling19 or superconductivity20, and may allow the realization of Kitaev-like Hamiltonians3 and Majorana-type end states21.

Planar Hall effect in the type-II Weyl semimetal Td−MoTe2

Topological Weyl semimetals (WSMs), a new quantum state of matter, provide the realization of relativistic Weyl fermions in solid-state physics. The appearance of the Weyl nodes will demonstrate novel transport phenomena related to the chiral anomaly. Theoretical prediction hints that the giant planar Hall effect (PHE) can be induced by the chiral anomaly in the WSMs. In this work, we performed PHE measurements to probe chiral charge in type-II WSM ${T}_{d}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$. Robust transverse voltage can be acquired when the magnetic field and electric current is coplanar. Subsequently, the amplitude of intrinsic PHE increased sharply at $T=50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ with the decreasing temperature. The increasing trend in the temperature dependence is attributed to coupling effect between the chiral charge and the electric one, which drives the system into intermediate-coupling states at higher field. Our work confirms that the PHE measurement is a practical transport tool to probe chiral charge pumping effect in the WSMs systems.

Chiral Organization and Charge Redistribution in Chloroaluminum Phthalocyanine on Au(111) Beyond the Monolayer

The nontrivial effect of molecular dipoles on the surface work function of metals is explored for the unidirectional ordered arrays forming the first and second layers of chloroaluminum phthalocyanine on Au(111). This phthalocyanine is a nonplanar molecule with permanent electric dipole perpendicular to its molecular π-plane that can adopt two distinct configurations (Cl-up and Cl-down) when adsorbed on surfaces. The ordered array forming the first layer is known to consist of all Cl-up molecules, whereas the less-studied second layer is formed by molecules in the Cl-down configuration. The inverted orientation of the molecules in these two layers constitutes our benchmark system to investigate the influence of the dipole array orientation on the surface work function. The present study includes an experimental and theoretical approach that combines diverse imaging and spectroscopic scanning probe microscopies, in ultrahigh vacuum, with first-principles density functional theory-based atomistic simulation...

Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle $\omega_4 \in \mathcal H^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.

Negative magnetoresistance suppressed through a topological phase transition in (Cd1−xZnx)3As2 thin films

The newly discovered topological Dirac semimetals host the possibilities of various topological phase transitions through the control of spin-orbit coupling as well as symmetries and dimensionalities. Here, we report a magnetotransport study of high-mobility (Cd1-xZnx)3As2 films, where the topological Dirac semimetal phase can be turned into a trivial insulator via chemical substitution. By high-field measurements with a Hall-bar geometry, magnetoresistance components ascribed to the chiral charge pumping have been distinguished from other extrinsic effects. The negative magnetoresistance exhibits a clear suppression upon Zn doping, reflecting decreasing Berry curvature of the band structure as the topological phase transition is induced by reducing the spin-orbit coupling.

Non-Abelian S=1 chiral spin liquid on the kagome lattice

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.

Elemental chalcogens as a minimal model for combined charge and orbital order

Helices of increased electron density can spontaneously form in materials containing multiple, interacting density waves. Although a macroscopic order parameter theory describing this behaviour has been proposed and experimentally tested, a detailed microscopic understanding of spiral electronic order in any particular material is still lacking. Here, we present the elemental chalcogens Selenium and Tellurium as model materials for the development of chiral charge and orbital order. We formulate minimal models capturing the formation of spiral structures both in terms of a macroscopic Landau theory and a microscopic Hamiltonian. Both reproduce the known chiral crystal structure and are consistent with its observed thermal evolution and behaviour under applied pressure. The combination of microscopic and macroscopic frameworks allows us to distil the essential ingredients in the emergence of helical charge order, and may serve as a guide to understanding spontaneous chirality both in other specific materials and throughout materials classes.

Anomalous transport properties of Dirac and Weyl semimetals (Review Article)

In this review we discuss a wide range of topological properties of electron quasiparticles in Dirac and Weyl semimetals. Their nontrivial topology is quantified by a monopole-like Berry curvature in the vicinity of Weyl nodes, as well as by the energy and momentum space separations between the nodes. The momentum separation, which is also known as the chiral shift, is one of the key elements of this review. We show that it can be dynamically generated in Dirac materials in a background magnetic field. We also pay a special attention to various forms of interplay between the background electromagnetic fields and the topological characteristics of Dirac and Weyl semimetals. In particular, we discuss their signature features in the transport of the electric and chiral charges, heat, as well as the quantum oscillations associated with the Fermi arc states. The origin of the dissipative transport of the Fermi arc states is critically examined. Finally, a consistent chiral kinetic theory for the description of Weyl semimetals is reviewed and its applications are demonstrated.

The dp type π-bond and chiral charge density waves in 1T-TiSe2.

Based on the atomic electronic configuration and Ti-Se coordination, a valence bond model for the layered transition metal dichalcogenide (TMDC) 1T-TiSe2 is proposed. 1T-TiSe2 is viewed as being composed of edge-sharing TiSe4-plaquettes as TiSe2-ribbon chains in each layer via a directional valence shell electron distribution as chemical bonds, in contrast to the conventional layer view of face-sharing TiSe6-octahedra. The four valence electrons per Ti in the hybridized dsp2-orbitals of square coordination form σ-bonds with the four nearest neighbor Se atoms in the chain. The electrons in the lone pair of the Se-4pz orbital are proposed to form a dp type π-bond via side-to-side orbital overlap with the empty Ti-3dxz/3dyz orbitals within each chain, which is positively supported by quantum chemistry calculations. A study of electron energy loss spectroscopy (EELS) with transmission electron microscopy (TEM) for 1T-TiSe2 is presented to show an energy loss near ∼7 and ∼20 eV, which confirms the existence of collective plasmon oscillations with the predicted effective electron numbers for the π- and (π + σ)-bond electrons, respectively.

Breakdown of the Chiral Anomaly in Weyl Semimetals in a Strong Magnetic Field.

The low-energy quasiparticles of Weyl semimetals are a condensed-matter realization of the Weyl fermions introduced in relativistic field theory. Chiral anomaly, the nonconservation of the chiral charge under parallel electric and magnetic fields, is arguably the most important phenomenon of Weyl semimetals and has been explained as an imbalance between the occupancies of the gapless, zeroth Landau levels with opposite chiralities. This widely accepted picture has served as the basis for subsequent studies. Here we report the breakdown of the chiral anomaly in Weyl semimetals in a strong magnetic field based on abinitio calculations. A sizable energy gap that depends sensitively on the direction of the magnetic field may open up due to the mixing of the zeroth Landau levels associated with the opposite-chirality Weyl points that are away from each other in the Brillouin zone. Our study provides a theoretical framework for understanding a wide range of phenomena closely related to the chiral anomaly in topological semimetals, such as magnetotransport, thermoelectric responses, and plasmons, to name a few.

Chiral effects in gauge theories and the chiral chemical potential

The chiral balance is broken as a result of an anomaly relation for the axial current in a strongly magnetized electron–positron gas in QED. The pair creation process, due to the decay of longitudinal axial photons (out of light cone), induces an imbalanced chirality and contributes to a chiral current along the external magnetic field B. In our case, a pseudo‐vector longitudinal mode generates the chiral charge density. A chiral chemical potential is not necessary. Only an electromagnetic chemical potential is introduced, but the chiral effect is valid even when it vanishes. A nonzero fermion mass is assumed, which is usually considered vanishing. The introduction of a chiral chemical potential in the frame of electroweak theory at finite temperature and density is discussed. It is not compatible with the Standard Model, since the spontaneous symmetry breaking prevents the conservation of the weak neutral charge.

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime**Supported by National Science Foundation of China (NSFC) (11690022, 11475237, 11121064) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100) as well as the CAS Center for Excellence in Particle Physics (CCEPP)

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincaré symmetry P(1,5)=SO(1,5)⋉P1,5 as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.