Three dimensional Dirac semimetals / Saad Zaheer.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Zaheer, Saad, author.

Contributor:

Mele, E. J. (Eugene J.), degree supervisor.

Cvetic, Mirjam, degree committee member.

Kane, C. L. (Charles L.), degree committee member.

Khoury, Justin, 1975- degree committee member.

Lubensky, Tom C., degree committee member.

University of Pennsylvania. Department of Physics and Astronomy.

Language:

English

Subjects (All):

Penn dissertations--Physics and astronomy.

Physics and astronomy--Penn dissertations.

Local Subjects:

Penn dissertations--Physics and astronomy.

Physics and astronomy--Penn dissertations.

Physical Description:

xv, 131 leaves ; 29 cm

Production:

[Philadelphia, Pennsylvania] : [University of Pennsylvania], 2014.

Summary:

We extend the physics of graphene to three dimensional systems by showing that Dirac points can exist on the Fermi surface of realistic materials in three dimensions. Many of the exotic electronic properties of graphene can be ascribed to the pseudorelativistic behavior of its charge carriers due to two dimensional Dirac points on the Fermi surface. We show that certain nonsymmorphic spacegroups exhibit Dirac points among the irreducible representations of the appropriate little group at high symmetry points on the surface of the Brillouin zone. We provide a list of all Brillouin zone momenta in the 230 spacegroups that can host Dirac points. We describe microscopic considerations necessary to design materials in one of the candidate spacegroups such that the Dirac point appears at the Fermi energy without any additional non-Dirac-like Fermi pockets. We use density functional theory based methods to propose six new Dirac semimetals: BiO 2 and SbO 2 in the β -cristobalite lattice (spacegroup 227), and BiCaSiO 4, BiMgSiO 4, BiAlInO 4, and BiZnSiO 4 in the distorted spinels lattice (spacegroup 74). Additionally we derive effective Dirac Hamiltonians given group representative operators as well as tight binding models incorporating spin-orbit coupling. Finally we study the Fermi surface of zincblende (spacegroup 216) HgTe which is effectively point-like at Γ in the Brillouin zone and exhibits accidental degeneracies along a threefold rotation axis. Whereas compressive strain gaps the band structure into a topological insulator, tensile strain shifts the accidental degeneracies away from Γ and enlarges the Fermi surface. States on the Fermi surface exhibit nontrivial spin texture marked by winding of spins around the threefold rotation axis and by spin vortices indicating a change in the winding number. This is confirmed by microscopic calculations performed in tensile strained HgTe and Hg 0.5 Zn 0.5 Te as well as k.p theory. We conclude with a summary of recent work on the physics of Dirac semimetals especially after the observation of the topological Dirac semimetals Cd 3 As 2 and Na 3 Bi and outline topics for future research. Symmetry protected Dirac semimetals, on the other hand, have yet to be observed experimentally.

Notes:

Ph. D. University of Pennsylvania 2014.

Department: Physics and Astronomy.

Supervisor: Eugene J. Mele.

Includes bibliographical references.