Valley contrasting physics in graphene: magnetic moment and topological transport (0709.1274v1)

Abstract: We investigate physical properties that can be used to distinguish the valley degree of freedom in systems where inversion symmetry is broken, using graphene systems as examples. We show that the pseudospin associated with the valley index of carriers has an intrinsic magnetic moment, in close analogy with the Bohr magneton for the electron spin. There is also a valley dependent Berry phase effect that can result in a valley contrasting Hall transport, with carriers in different valleys turning into opposite directions transverse to an in-plane electric field. These effects can be used to generate and detect valley polarization by magnetic and electric means, forming the basis for the so-called valley-tronics applications.

• The paper demonstrates an intrinsic magnetic moment in graphene’s valleys analogous to the Bohr magneton, emphasizing its role in valleytronics.
• It employs semiclassical wavepacket dynamics to uncover a valley Hall effect that generates nearly quantized transverse conductivity.
• The study bridges theoretical insights and practical applications, setting the foundation for future advancements in quantum computing and nanoelectronics.

Valley Contrasting Physics in Graphene: Magnetic Moment and Topological Transport

In the paper of graphene-based systems, a critical area of focus is the exploitation of the valley degree of freedom as a means to facilitate advanced applications in nanotechnology, notably the emergent field of valleytronics. The paper "Valley Contrasting Physics in Graphene: Magnetic Moment and Topological Transport" by Xiao, Yao, and Niu rigorously examines this subject using graphene with broken inversion symmetry as a paradigmatic example. In this detailed exploration, the authors not only identify the intrinsic magnetic moment associated with the valley index of carriers but also describe a valley-dependent Berry phase effect that engenders a Hall-like transport phenomenon.

Key Findings and Numerical Results

One of the seminal findings presented in the paper is the existence of an intrinsic magnetic moment corresponding to the valley pseudospin in graphene. This magnetic moment is analogized to the Bohr magneton for electron spin, signifying its fundamental role as a measurable entity. The authors derive a clear expression for this intrinsic magnetic moment $\mathfrak{m}(\bm k)$ and establish its crucial dependence on the system's broken inversion symmetry. Graphene's valley contrasting magnetic moment is expressed as:

$$\mathfrak{m}(\bm k)= \tau_z \frac{ 3 e a^2\Delta t^2} {4\hbar (\Delta^2 + 3q^2 a^2 t^2)} \;.$$

This finding underscores the anisotropic nature of the magnetic response, which is not characteristic of typical spin-related phenomena, thus providing an insightful understanding of how valley polarization can be controlled and detected.

A related phenomenon is the prediction of a valley Hall effect in graphene systems with broken symmetry. Through the application of semiclassical wavepacket dynamics, the authors delineate how carriers from different valleys respond to external electric fields by moving in opposite transverse directions, resulting in a valley Hall conductivity that approaches a quantized value:

$$\sigma_{H} (\tau_z) = \tau_z \frac{e^2}{h}\Bigl[1 - \frac{\Delta} {2 \mu} - \frac{3\Delta t^2 q_F^2 a^2} {8 \mu^3} \Bigr].$$

This quantization, akin to the behavior observed in topological insulators, highlights an avenue for utilizing graphene's valley degree of freedom for practical applications in valleytronics.

Theoretical and Practical Implications

The implications of this paper extend into both the theoretical understanding and practical applications of graphene and other two-dimensional materials with similar properties. The intrinsic magnetic moment and valley Hall effect elucidated here establish crucial foundational aspects for the manipulation of valleys similarly to spins in spintronic applications. By mimicking the principles applied in spintronics, valleytronics aspires to offer another dimension of control in electronic devices, which could lead to more efficient information processing technologies.

The potential of these phenomena to be harnessed in semiconducting devices forms a bridge between theoretical physics and material science, providing a standard framework for exploring valley contrasting physics in a broad class of materials. Moreover, experimental demonstrations of these effects in systems such as epitaxial graphene allow the validation and refinement of the theoretical constructs proposed.

Speculation on Future Developments

As research progresses, further exploration into the manipulation and control of the valley degree of freedom in graphene could pave the way for quantum computing advancements and high-performance nanoelectronics. In the future, it is plausible that devices engineered to exploit the valley degree of freedom could fundamentally alter how electronic systems are designed, ranging from improved sensors to quantum information processors.

Additionally, the emergence of other two-dimensional materials with naturally broken inversion symmetry could expand the applicability of the concepts presented in this paper. Such advancements will necessitate collaboration across domains, integrating insights from condensed matter physics, materials science, and electronic engineering.

In summary, the paper presents a thorough investigation into the valley contrasting physics of graphene, offering both theoretical insights and practical pathways for future developments in electronic applications. The meticulous examination of valley-related phenomena reinforces graphene's role as a cornerstone in developing novel electronic systems.