The Ohio State University
Topological Phases with Crystalline Symmetries.
Degree: PhD, Physics, 2018, The Ohio State University
In this dissertation, we focus on topological phases
protected or enforced by crystalline symmetries. The topological
phase can appear in the ground state of fermion and interacting
boson or in the excitation bands of the free boson such as phonon
and magnon. Those topics are covered in three parts. In the second
chapter, we study the Glide Symmetry Protected Topological (GSPT)
phases of interacting bosons and fermions in three spatial
dimensions with certain on-site symmetries. They are crystalline
Symmetry Protected Topological (SPT) phases, which are
distinguished from a trivial product state only in the presence of
non-symmorphic glide symmetry. We classify these GSPT phases with
various on-site symmetries such as U(1) and time reversal, and
show that they can all be understood by stacking and coupling
two-dimensional short-range-entangled phases in a glide-invariant
way. Using such a coupled layer construction we study the anomalous
surface topological orders of these GSPT phases, which gap out the
two-dimensional surface states without breaking any symmetries.
While this framework can be applied to any non-symmorphic SPT
phase, we demonstrate it in many examples of GSPT phases including
the non-symmorphic topological insulator with "hourglass fermion"
surface states.In the third chapter, we discuss the non-symmorphic
crystalline symmetry enforced Quantum Spin Hall effect (QSHE). In
the generic classification frame of SPT phases, the classification
for the ground state of fermion in 2D with charge
conservation and time-reversal (TR) symmetry. The ground state can
be in either trivial state or QSHE state, which depends on the
specific model. However, we prove that the gapped ground state must
be QSHE other than trivial as long as given non-symmorphic symmetry
present. We also propose a crystal structure as one realization,
and make an effort on material searching based on the space group.
This work can supply a new principle of QSHE materials searching,
which is purely depending on the symmetry instead of electronic
details.Last but not least, in the fourth chapter, we discuss the
topological phases of the bands of magnon. The crystalline
symmetries or its combination with TR symmetry are proved to play a
crucial role in magnon bands topology classification. In spite of
flourishing studies on the topology of spin waves, a generic
framework to classify and compute magnon band topology in
non-collinear magnets is still missing. We provide such a theory
framework, by mapping an arbitrary linear spin wave into a local
free-fermion Hamiltonian with exactly the same spectrum, symmetry
implementation and band topology, which allows for a full
classification and calculation on any topological properties of
magnon bands under different symmetry groups. We apply this
fermionization approach to honeycomb Kitaev magnet
. The crystalline symmetry protected band
touchings will be discussed in detail and the evolution of its
magnon band topology is also investigated under an external
Advisors/Committee Members: Lu, Yuan-Ming (Advisor).
Subjects/Keywords: Physics; Theoretical Physics; Symmetry Protected Topological Phases; Topological Magnon
to Zotero / EndNote / Reference
APA (6th Edition):
Lu, F. (2018). Topological Phases with Crystalline Symmetries. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1524790822570583
Chicago Manual of Style (16th Edition):
Lu, Fuyan. “Topological Phases with Crystalline Symmetries.” 2018. Doctoral Dissertation, The Ohio State University. Accessed December 18, 2018.
MLA Handbook (7th Edition):
Lu, Fuyan. “Topological Phases with Crystalline Symmetries.” 2018. Web. 18 Dec 2018.
Lu F. Topological Phases with Crystalline Symmetries. [Internet] [Doctoral dissertation]. The Ohio State University; 2018. [cited 2018 Dec 18].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1524790822570583.
Council of Science Editors:
Lu F. Topological Phases with Crystalline Symmetries. [Doctoral Dissertation]. The Ohio State University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1524790822570583