A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

This is a pedagogical review on ■ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to ■ deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the ■ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of ■ deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.     

Semi-infinite cohomology in conformal field theory and 2D gravity

We discuss various techniques for computing the semi-infinite cohomology of highest weight modules which arise in the BRST quantization of two dimensional field theories. In particular, we concentrate on two such theories - the G/H coset models and 2D gravity coupled to c ≤ 1 conformal matter.     

Ab initio study of the electronic and transport properties of waved graphene nanoribbons

We apply the nonequilibrium Green's function method based on density functional theory to investigate the electronic and transport properties of waved zigzag and armchair graphene nanoribbons. Our calculations show that out-of-plane mechanical deformations have a strong influence on the band structures and transport characteristics of graphene nanoribbons. The computed I-V curves demonstrate that the electrical conductance of graphene nanoribbons is significantly affected by deformations. The relationship between the conductance and the compression ratio is found to be sensitive to the type of the nanoribbon. The results of our study indicate the possibility of mechanical control of the electronic and transport properties of graphene nanoribbons.     

Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium

In the present paper, the sinusoidal shear deformation plate theory (SDPT) is reformulated using the nonlocal differential constitutive relations of Eringen to analyze the bending and vibration of the nanoplates, such as single-layered graphene sheets, resting on two-parameter elastic foundations. The present SDPT is compared with other plate theories. The nanoplates are assumed to be subjected to mechanical and thermal loads. The equations of motion of the nonlocal model are derived including the plate foundation interaction and thermal effects. The governing equations are solved analytically for various boundary conditions. Nonlocal theory is employed to bring out the effect of the nonlocal parameter on the bending and natural frequencies of the nanoplates. The influences of nonlocal parameter, side-to-thickness ratio and elastic foundation moduli on the displacements and vibration frequencies are investigated.     

The field theory two-body problem in acoustics

We address the problem of determining effective equations of motion for sources in field theories, where finite propagation speeds lead to radiation reaction and runaway solutions. Acoustics is used to illustrate a solution of this problem: The effective equation of motion is obtained by reduction to an inertial manifold. This equation can be approximated to any desired accuracy by expansion (and truncation) in powers of the reciprocal of the wave propagation speed and reduction to a slow manifold of a singular perturbation problem. This research is supported by a grant from the National Science Foundation NSF DMS-0604331.     

石墨烯与二氧化氮的吸附特性研究

由于石墨烯的二维结构以及其超高的比表面积,因此石墨烯可以感应到一个分子量级的变化,这使得其在气体传感方面具有很大的优势。文章通过计算和分析了石墨烯与二氧化氮的系统的能带结构,态密度和电荷分布情况来说明石墨烯吸附二氧化氮后的特性变化。这有助于进一步了解了石墨烯的特性,同时进一步推动石墨烯传感的发展。     

Unit cell dependence of optical matrix elements in tight-binding theory: The case of zigzag graphene nanoribbons

In the tight-binding theory, momentum matrix elements (MMEs) needed to calculate the optical properties are normally computed using a formulation based on the gradient of the Hamiltonian in the k space. We demonstrate the inadequacy of this formulation by considering the case of zigzag graphene nanoribbons. We show that one obtains wrong values of MMEs, in violation of the well-known selection rules, if the unit cell chosen in the calculations does not incorporate the symmetries of the bulk. This is in spite of the fact that the band structure is insensitive to the choice of the unit cell. We substantiate our results based on group-theoretic arguments. Our observations will open an avenue for proper formulation of MMEs.     

石墨烯与二氧化氮的吸附特性研究

由于石墨烯的二维结构以及其超高的比表面积,因此石墨烯可以感应到一个分子量级的变化,这使得其在气体传感方面具有很大的优势.文章通过计算和分析了石墨烯与二氧化氮的系统的能带结构,态密度和电荷分布情况来说明石墨烯吸附二氧化氮后的特性变化.这有助于进一步了解了石墨烯的特性,同时进一步推动石墨烯传感的发展.     

Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.     

Stable electron field emission from carbon nanotubes emitter transferred on graphene films

Carbon nanotubes (CNTs) arrays grown by microwave plasma enhanced chemical vapor deposition (MPCVD) method was transferred onto the substrate covered with graphene layer obtained by thermal chemical vapor deposition (CVD) technology. The graphene buffer layer provides good electrical and thermal contact to the CNTs. The field emission characteristics of this hybrid structure were investigated in this study. Compared with the CNTs arrays directly grown on the silicon substrate, the hybrid emitter shows better field emission performance, such as high emission current and long-term emission stability. The presence of this graphene layer was shown to improve the field emission behavior of CNTs. This work provides an effective way to realize stable field emission from CNTs emitter and similar hybrid structures.     

Topological vortices in chiral gauge theory of graphene

Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently, Chamon, Jackiw et al. proposed a mechanism of using a Kekulé distortion background field φ and its induced gauge potential A_i to generate energy gaps. In this paper, various vortex structures inhering in this model are studied. Regarding φ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface—the velocity field vortices and the monopole-motion induced vortices—from the inner structure of the potential A_i. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.     

Ultrasound assisted reduction of graphene oxide to graphene in l-ascorbic acid aqueous solutions: Kinetics and effects of various factors on the rate of graphene formation

The reduction of graphene oxide (GO) to graphene (rGO) was achieved by using 20 kHz ultrasound in l-ascorbic acid (l-AA, reducing agent) aqueous solutions under various experimental conditions. The effects of ultrasound power, ultrasound pulse mode, reaction temperature, pH value and l-AA amount on the rates of rGO formation from GO reduction were investigated. The rates of rGO formation were found to be enhanced under the following conditions: high ultrasound power, long pulse mode, high temperature, high pH value and large amount of l-AA. It was also found that the rGO formation under ultrasound treatment was accelerated in comparison with a conventional mechanical mixing treatment. The pseudo rate and pseudo activation energy (E_a) of rGO formation were determined to discuss the reaction kinetics under both treatment. The E_a value of rGO formation under ultrasound treatment was clearly lower than that obtained under mechanical mixing treatment at the same condition. We proposed that physical effects such as shear forces, microjets and shock waves during acoustic cavitation enhanced the mass transfer and reaction of l-AA with GO to form rGO as well as the change in the surface morphology of GO. In addition, the rates of rGO formation were suggested to be affected by local high temperatures of cavitation bubbles.     

Holomorphic Chern-Simons-Witten theory: From 2D to 4D conformal field theories

It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebras, the local action of which on fields of holomorphic analogues of Chern-Simons theories becomes non-local after pushing down to the action on fields of integrable 4D conformal field theories. Quantization of integrable 4D conformal field theories and relations to string theories are briefly discussed.     

Radiation from electrons in graphene in strong electric field

We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the Dirac equation in the electric background, and amplitudes of first-order Feynman diagrams describing the interaction with the photon field are calculated for massive Dirac particles in both valleys. Photon emission probabilities from a single electron and from a many-electron system at the charge neutrality point are derived, including the angular and frequency dependence, and several limiting cases are analyzed. The pattern of photon emission at the Dirac point in a strong field is determined by an interplay between the nonperturbative creation of electron–hole pairs and spontaneous emission, allowing for the possibility of observing the Schwinger effect in measurements of the radiation emitted by pristine graphene under DC voltage.     

Shot noise in magnetic field modulated graphene superlattice

We investigate the shot noise properties in a monolayer graphene superlattice modulated by N parallel ferromagnets deposited on a dielectric layer. It is found that for the antiparallel magnetization configuration or when magnetic field is zero the new Dirac-like point appears in graphene superlattice. The transport is almost forbidden at this new Dirac-like point, and the Fano factor reaches its maximum value 1/3. In the parallel magnetization configuration as the number of magnetic barriers increases, the shot noise increases. In this case, the transmission can be blocked by the magnetic–electric barrier and the Fano factor approaches 1, which is dramatically distinguishable from that in antiparallel alignment. The results may be helpful to control the electron transport in graphene-based electronic devices.     

Gauge symmetries in 2D field theory

A simple algorithm is proposed for constructing generators of gauge symmetry as well as reducibility relations for arbitrary systems of partial differential equations in two dimensions.     

Rippling and the external electric field on conductance in corrugated graphene nanoribbons molecular device

Molecular devices constructed using corrugated graphene nanoribbons (GNRs) are proposed in the paper. Recursive Green's function calculations show that the intrinsic ripples in graphene and the external electric field energy play important roles on the electron transport properties. Negative differential resistance is observed in zigzag corrugated GNRs. With the wavelength of the ripples decreasing, both the zigzag and armchair corrugated GNRs exhibit ON/OFF characteristics. On applying external electric field, current decreases dramatically in zigzag corrugated GNRs. These findings show that corrugated GNRs can be used to design functional nanoscale devices.     

Tailoring atomic structure to control the electronic transport in zigzag graphene nanoribbon

We have performed ab initio   density functional theory calculation to study the electronic transport properties of the tailored zigzag-edged graphene nanoribbon (ZGNR) with particular electronic transport channels. Our results demonstrated that tailoring the atomic structure had significantly influenced the electronic transport of the defective nanostructures, and could lead to the metal-semiconducting transition when sufficient atoms are tailored. The asymmetric I–V$I\text{–}V$ characteristics as a result of symmetry breaking have been exhibited, which indicates the route to utilize GNR as a basic component for novel nanoelectronics.