Dynamical current–current correlation in two-dimensional parabolic Dirac systems

2019 ◽  
Vol 383 (6) ◽  
pp. 550-557 ◽  
Author(s):  
Chen-Huan Wu
Keyword(s):  
Two Dimensional ◽  
Dirac Systems ◽  
Current Correlation

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

Closed-form representations of iterated Darboux transformations for the massless Dirac equation

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150064
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Closed Form ◽  
Scalar Potential ◽  
Higher Order ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
First Order ◽  
Dirac Systems ◽  
Form Representation ◽  
Exactly Solvable

It is shown that first-order Darboux transformations for the two-dimensional massless Dirac equation with scalar potential and for the Schrödinger equation are the same up to a change of coordinates. As a consequence, we obtain a closed-form representation of iterated, higher-order Darboux transformations for our Dirac equation. We use the formalism to generate several new exactly-solvable Dirac systems through higher-order Darboux transformations.

scholarly journals Dominant role of two-photon vertex in nonlinear response in two-dimensional Dirac systems

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Habib Rostami ◽  
Emmanuele Cappelluti
Keyword(s):  
Nonlinear Response ◽  
Dominant Role ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Nonlinear Transport ◽  
Many Body Theory ◽  
Clean Limit ◽  
Two Photon ◽  
Dirac Systems ◽  
The Impact

AbstractWe show that the standard concepts of nonlinear response to electromagnetic fields break down in two-dimensional Dirac systems, like graphene, in the quantum regime close to the Dirac point. We present a compelling many-body theory for nonlinear transport focusing on disorder scattering as a benchmark example. We show that, although the diamagnetic two-photon vertex is absent at the non-interacting level, disorder effects give rise to a self-generation of such two-photon vertex surviving even in the clean limit. We predict that the two-photon vertex self-generation is present only in two dimensions. The impact of such a striking scenario on the nonlinear quantum transport is discussed, predicting a huge enhancement of third-order dc conductivity comparing to the common models.

scholarly journals The rare two-dimensional materials with Dirac cones

2015 ◽  
Vol 2 (1) ◽  
pp. 22-39 ◽  
Author(s):  
Jinying Wang ◽  
Shibin Deng ◽  
Zhongfan Liu ◽  
Zhirong Liu
Keyword(s):  
Transition Metal Oxides ◽  
2D Materials ◽  
Structural Features ◽  
Two Dimensional ◽  
Electron Gases ◽  
Von Neumann ◽  
Dirac Systems ◽  
Two Dimensional Materials ◽  
Dirac Materials ◽  
Structural And Electronic Properties

Abstract Inspired by the great development of graphene, more and more research has been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition-metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann–Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.

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