Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

/pdf/berry-phase-effects-on-electronic-properties-53dkbbi2er.pdf

Berry phase effects on electronic properties

The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.

/pdf/dual-electromagnetism-helicity-spin-momentum-and-angular-2lhckmwq6h.pdf

Dual electromagnetism: Helicity, spin, momentum, and angular momentum

Dirac and Weyl materials refer to a class of solid materials which host low-energy quasiparticle excitations that can be described by the Dirac and Weyl equations in relativistic quantum mechanics. Starting with the advent of graphene as the first prominent example, these materials have been attracting tremendous interest owing to their novel fundamental properties as well as the great potential for applications. Here we introduce the basic concepts and notions related to Dirac and Weyl materials and briefly review some recent works in this field, particularly on the conceptual development and the possible spintronics/pseudospintronics applications.

Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications

Using first principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the direction of the spin quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit interaction the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distribution in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

Anisotropy of spin relaxation and transverse transport in metals

Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

/pdf/anisotropy-of-spin-relaxation-and-transverse-transport-in-3lc2dk7ggi.pdf

Anisotropy of spin relaxation and transverse transport in metals.

https://phy.ntnu.edu.tw/~changmc/Paper/Chuu_2009.pdf

Semiclassical dynamics and transport of the Dirac spin

Two-dimensional (2D) layered materials hold tremendous promise for post-Si nanoelectronics due to their unique optical and electrical properties. Significant advances have been achieved in device fabrication and synthesis routes for 2D nanoelectronics over the past decade; however, one major bottleneck preventing their immediate applications has been the lack of a reproducible approach for growing wafer-scale single-crystal films despite tremendous progress in recent experimental demonstrations. In this tutorial review, we provide a systematic summary of the critical factors-including crystal/substrate symmetry and energy consideration-necessary for synthesizing single-orientation 2D layers. In particular, we focus on the discussions of the atomic edge-guided epitaxial growth, which assists in unidirectional nucleation for the wafer-scale growth of single-crystal 2D layers.

Wafer-scale single-orientation 2D layers by atomic edge-guided epitaxial growth.

A novel wafer-scale semi-automated dry transfer process for monolayer (1L) CVD WS2 was developed utilizing the weakly coupled interface between semimetal (Bi) and two-dimensional (2D) semiconductor (WS2). Bi semimetal serves as a gently adhesive transfer template for 2D materials, introducing minimal additional defects during the transfer process. Based on 2D materials processed using this new transfer method, semimetal-contacted (Bi and Sb) monolayer CVD WS2 nFETs were further demonstrated at wafer scale. Our CVD 1L WS2 nFETs fabricated using semimetal-assisted transfer with semimetal (Bi and Sb) contacts show record high on-current of 250 µA/µm and 243 µA/µm at VDS = 1 V, and record low contact resistance of 0.63 kΩ•µm and 0.73 kΩ•µm, respectively.

Wafer-Scale Bi-Assisted Semi-Auto Dry Transfer and Fabrication of High-Performance Monolayer CVD WS2 Transistor

A moiré superlattice formed in twisted van der Waals bilayers has emerged as a new tuning knob for creating new electronic states in two-dimensional materials. Excitonic properties can also be altered drastically due to the presence of moiré potential. However, quantifying the moiré potential for excitons is nontrivial. By creating a large ensemble of MoSe2/MoS2 heterobilayers with a systematic variation of twist angles, we map out the minibands of interlayer and intralayer excitons as a function of twist angles, from which we determine the moiré potential for excitons. Surprisingly, the moiré potential depth for intralayer excitons is up to ∼130 meV, comparable to that for interlayer excitons. This result is markedly different from theoretical calculations based on density functional theory, which show an order of magnitude smaller moiré potential for intralayer excitons. The remarkably deep intralayer moiré potential is understood within the framework of structural reconstruction within the moiré unit cell.

Remarkably Deep Moiré Potential for Intralayer Excitons in MoSe2/MoS2 Twisted Heterobilayers.

For the first time, we demonstrate Ferroelectric Tunneling Junctions (FTJs) with both (a) 10-year retention time projected from measured data and (b) robust endurance (> 108 cycles) with the on-off ratio >10× by inserting a 1.8nm Al2O3 interfacial layer (IL) into the FTJs. Compared with Metal-Ferroelectric-Metal (MFM) FTJs, higher orthorhombic phase (~6×) was verified by physical analyses and first-principles calculations in our proposed Metal-Ferroelectric-IL-Metal (MFIM) FTJs, resulting in the remanent polarization (2Pr) which improves the retention and the on-off ratio significantly.

Chih Piao Chuu

Papers

Semiclassical dynamics and transport of the Dirac spin

Wafer-scale single-orientation 2D layers by atomic edge-guided epitaxial growth.

Wafer-Scale Bi-Assisted Semi-Auto Dry Transfer and Fabrication of High-Performance Monolayer CVD WS2 Transistor

Remarkably Deep Moiré Potential for Intralayer Excitons in MoSe2/MoS2 Twisted Heterobilayers.

Interfacial-Layer Design for Hf1-xZrxO2-Based FTJ Devices: From Atom to Array