Engineering relativistic fermions in condensed matter systems

Kim, Youngseok

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https://hdl.handle.net/2142/101471 Copy

Description

Title

Engineering relativistic fermions in condensed matter systems

Author(s)

Kim, Youngseok

Issue Date

2018-05-31

Director of Research (if dissertation) or Advisor (if thesis)

Gilbert, Matthew J.

Doctoral Committee Chair(s)

Gilbert, Matthew J.

Committee Member(s)

• Lyding, Joseph W.
• Mason, Nadya
• Ravaioli, Umberto

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

relativistic fermions, graphene, topological semimetals

Abstract

When the speed of the particle is much less than the speed of light, non-relativistic classical mechanics faithfully describes the motion of the particle. Analogously, using wave-particle duality, the non-relativistic description of classical mechanics may be applied to describe the motion of a free electron governed by the Schrodinger equation. In condensed matter systems, intricate interactions between electrons and nuclei are simplified by using a concept of the quasi-particle. In such description, the electron is considered as a dressed free electron, and its motion is described by replacing the electron mass with an effective mass. This simplification successfully describes electron motion in metals and semiconductors. However, when a particle travels with a velocity close to the speed of light, relativistic quantum mechanics govern the physics. A relativistic particle, such as the neutrino in particle physics, is then governed by the Klein-Gordon equation. While most of the relativistic particles discussed in particle physics require high energy to observe and are thus accessible only in particle colliders, similar excitations may be found in condensed matter systems. For example, dressed quasi-particle excitation in certain materials obeys the same relativistic quantum mechanics without requiring high energy to observe. Taking advantage of the readily accessible relativistic particles in small solids, unique physical phenomena of relativistic particles are accessible in the lab. Our goal is to study such materials that facilitate relativistic quasi-particles. We introduce a number of concrete examples of materials to obtain better understanding of the properties of relativistic particles as well as find new opportunities to engineer the material properties. We first study two-dimensional Dirac fermions in graphene. Specifically, we explore the opportunity to artificially engineer superlattice Dirac fermions (SDF) by placing graphene on self-assembled nanospheres. We use a tight-binding model to understand the effect of the lattice deformations induced by the nanosphere substrate. The conductance is calculated using non-equilibrium Green function formalism and we find the conductance dips as a signature of SDF at commensurate fillings of charges per self-assembled superlattice unit cell. We find similar behavior in experiment confirming the strain induced superlattice transport behavior in graphene, demonstrating graphene-nanoparticle heterostructure as a promising platform to generate artificially engineered Dirac fermions with the goal of realizing band structure engineering. We then extend our understanding of relativistic quasi-particles to the three-dimensional solids and their possible unconventional superconducting states. In particular, nodal superconductivity has been theoretically predicted in doped inversion symmetric Weyl semimetals (WSM). Using a four terminal measurement configuration, we show that the nodal points may be shifted and induce a topological phase transition by an application of transverse uniform current in doped WSM. We analyze the topological phase diagram and find characteristic dips in the density of states which serve as a signature of the existence of nodal points, thereby identifying the nodal superconductivity in doped WSM. Lastly, we study Dirac fermions in three-dimensional antiferromagnetic solid and a possible mechanism to induce metal-insulator transition by manipulating the antiferromagnetic order. An antiferromagnetic semimetal has been discovered as a new type of topological semimetal which may host symmetry protected Dirac fermions. By reorienting the antiferromagnetic order, we may break the underlying symmetry and open a gap in the quasi-particle spectrum, inducing the (semi) metal-insulator transition (MIT). Here, we predict that the transition may be manipulated by controlling the chemical potential of the system. We perform both numerical and analytical evaluation on the thermodynamic potential of our model Hamiltonian. The results show that the insulating state is preferred over the semimetallic state when the chemical potential is at Dirac point. As the chemical potential moves away from the Dirac point, the system exhibits a possible transition from insulating to semimetallic phase and corresponding antiferromagnetic order may be switched. We perform the density functional theory calculation to confirm our analysis and propose two-terminal transport measurement as a possible way to identify the voltage-induced switching mechanism of the antiferromagnetic order.

Graduation Semester

2018-08

Type of Resource

text

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Copyright and License Information

Copyright 2018 Youngseok Kim

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