Quantum Transport in Graphene and Phosphorene Junctions

石墨烯與黑燐烯導電結的量子輸運研究

Student thesis: Doctoral Thesis

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Award date31 May 2021

Abstract

With the development of semiconductor and engineering manufacturing technology, electronic devices become smaller, faster and highly integrated. Nowadays, building more transistors on the chip by reducing the sizes of devices can effectively reduce the manufacturing cost and improve their performance. The trend of electronic device development is to realize devices with smaller dimensions in order to lower the manufacturing cost, and improve integration rate, and the working efficiency.

At the moment, people have the ability to engineer materials on an atomic scale and can routinely make nano-structures. As a result, nano-structures have been actively studied recently to explore the exploitation of nano-structures in device applications. When the dimensions of the electronic device are smaller than certain thresholds, the classical theory is no longer suitable for describing the transport characteristics of the device. For these cases, the physical properties, especially the transport properties, should be understood using quantum mechanics. This has led to a large number of research studies of interesting phenomena recently in quantum transport as well as the application of quantum transport in device applications.

Apart from these recent developments in the device technology, there is also a strong focus on the study of new materials, particularly the low-dimensional materials, for the development of high performance devices. Among them, single-element two-dimensional materials, which include graphene and phosphorene, are currently attracting a lot of research interest. These two-dimensional materials have outstanding properties, which make them promising candidates for new applications in electronic, optoelectronic, and nano-mechanical devices. This thesis presents our theoretical studies of the transport properties of some nano-structures of the following two-dimensional materials: graphene and phosphorene. The thesis consists of seven chapters.

In Chapter 1, we first review the research background of quantum transport in two-dimensional materials and the required conditions for quantum transport. After that is a review the fabrication method and the electronic properties of graphene and phosphorene.

In Chapter 2, there is a review of the basics of quantum transport, such as transmission, reflection and the Landaur-Buttiker formalism, as well as the calculation methods for some useful physical quantities. There is a discussion of the following two numerical methods for calculating the quantum transport properties: the mode matching method and the Green's function method. Although the original ideas of the two calculation methods are different, there are no essential difference in the way in which they deal with the Schrödinger's equation.

In Chapter 3, we study the valley transport and valley polarization phenomenon in graphene nanoribbon cross junctions. The cross-shaped junction has two single-layer armchair nanoribbon leads and two single-layer zigzag nanoribbon leads with bilayer graphene as the central device region. Electrons injected into the bilayer region from one of the armchair leads are scattered into the other leads. In the zigzag leads, valley polarized currents are formed as a result of quantum interference and the Fano effect. We also study the effects of the device dimensions and an external electric field. It is found that the valley polarized current can be controlled by the applied a vertical electric field.

In Chapter 4, we report our study of the valley-dependent transport of the graphene-based monolayer-bilayer-monolayer nanoribbon junction. The Fano resonance effect is found to play an important role in the transport characteristics of the structure. The Fano resonance effect can make the inter-valley scattering much larger than the intra-valley scattering at some Fermi energies. As a result, this kind of graphene junctions can be used to build valley converters.

In Chapter 5, we study the transport properties of phosphorene along different transport directions. The Goos-Hanchen shift along different transport directions in phospherene is also studied. Since the electron behaviors along the armchair and zigzag directions resemble the behaviors of Dirac quasiparticles and Schrödinger quasiparticles respectively, the properties of phosphorene junctions depend strongly on the transport direction.

In Chapter 6, we firstly review the BCS theory, Andreev reflection and the pseudo-parity properties of hexagonal two-dimensional materials. After the review, we study the Andreev reflection in the normal-superconducting junction based on phosphorene nanoribbons. We consider both the nearest neighbor and the next nearest neighbor models in our study. The relation between pseudo-parity and Andreev reflection is explored. The effect of an external electric is considered and it is shown to have significant effect on the Andreev reflection.

In Chapter 7, we summarize the main results of the thesis.

    Research areas

  • Quantum transport, Graphene, Phosphorene, Valleytronics, Goos-Hanchen shift, Andreev reflection