arXiv subjects

Shudan Zhong

Publications and source records attributed to Shudan Zhong.

5 recordsLinked to original sources

arXiv2021

Intrinsic anomalous Hall conductivity in a nonuniform electric field

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector $q$ to order $q^2$, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

cond-mat.mes-hall↗

arXiv2020

Learning Embeddings of Directed Networks with Text-Associated Nodes---with Applications in Software Package Dependency Networks

A network embedding consists of a vector representation for each node in the network. Its usefulness has been shown in many real-world application domains, such as social networks and web networks. Directed networks with text associated with each node, such as software package dependency networks, are commonplace. However, to the best of our knowledge, their embeddings have hitherto not been specifically studied. In this paper, we propose PCTADW-1 and PCTADW-2, two algorithms based on neural networks that learn embeddings of directed networks with text associated with each node. We create two new node-labeled such networks: The package dependency networks in two popular GNU/Linux distributions, Debian and Fedora. We experimentally demonstrate that the embeddings produced by our algorithms resulted in node classification with better quality than those of various baselines on these two networks. We observe that there exist systematic presence of analogies (similar to those in word embeddings) in the network embeddings of software package dependency networks. To the best of our knowledge, this is the first time that such systematic presence of analogies is observed in network and document embeddings. We further demonstrate that these network embeddings can be novelly used for better understanding software attributes, such as the development process and user interface of software, etc.

cs.LG↗

arXiv2016

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under magnetic field as a consequence of an anisotropic $B^2$ contribution, which may explain the low-field regime of recent experiments; (ii) predicts strong second harmonic generation proportional to $B$ that is enhanced as the Fermi energy approaches the Weyl point, leading to large nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for the circular photogalvanic effect arising from the Berry curvature dipole is reproduced by a full quantum calculation using a Floquet approach.

cond-mat.mes-hall↗

arXiv2016

Gyrotropic magnetic effect and the magnetic moment on the Fermi surface

The current density ${\bf j}^{\rm{\bf B}}$ induced in a clean metal by a slowly-varying magnetic field ${\bf B}$ is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for $α^{\rm gme}_{ij}=j^{\rm{\bf B}}_i/B_j$ in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.

cond-mat.mes-hall↗

arXiv2015

Optical gyrotropy from axion electrodynamics in momentum space

Several emergent phenomena and phases in solids arise from configurations of the electronic Berry phase in momentum space that are similar to gauge field configurations in real space such as magnetic monopoles. We show that the momentum-space analogue of the "axion electrodynamics" term $\mathbf{E}\cdot\mathbf{B}$ plays a fundamental role in a unified theory of Berry-phase contributions to optical gyrotropy in time-reversal invariant materials and the chiral magnetic effect. The Berry-phase mechanism predicts that the rotatory power along the optic axes of a crystal must sum to zero, a constraint beyond that stipulated by point group symmetry, but observed to high accuracy in classic experimental observations on $α$-quartz. Furthermore, the Berry mechanism provides a microscopic basis for the surface conductance at the interface between gyrotropic and nongyrotropic media.

cond-mat.str-el↗