조길영 교수

We study superconducting states of doped inversion-symmetric Weyl semimetals. Specifically, we consider a lattice model realizing a Weyl semimetal with an inversion symmetry and study the superconducting instability in the presence of a short-ranged attractive interaction. With a phonon-mediated attractive interaction, we find two competing states: a fully gapped finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov pairing state and a nodal even-parity pairing state. We show that, in a BCS-type appr

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum ano

We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e., the Hall viscosity, and the Wen-Zee term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally

We study the ${\mathbb{Z}}_{2}$ topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries ${\mathrm{G}}_{1}\ifmmode\times\else\texttimes\fi{}{\mathrm{G}}_{2}$. It has been argued that the topologically ordered state cannot be realized on a purely two-dimensional lattice model. We carefully examine the statement and show that the surface state should break ${\mathrm{G}}_{2}$ if the symmetry ${\mathrm{G}}_{1}$ is gauged on the surface. This manifests

We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the ``scaling limit'' (correlation length $\ensuremath{\xi}$ much larger than microscopic ``lattice'' scale ``$a$''), and can be thought of as a CFT perturbed by a relevant perturbation.

Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented space-time, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature o

A bstract We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction, the topological phases emerge as macroscopic world-volume theories of M5-branes wrapped around certain types of non-hyperbolic 3-manifolds. We devise a systematic algorithm for identifying the emergent topological phases from topological data of the i

We study the zero-temperature phase diagram and fractional excitations when a thin film of 3D topological insulator has two competing masses: $T$-symmetric exciton condensation and the $T$-breaking Zeeman effect. Two topologically distinct phases are identified: in one, the quasiparticles can be viewed as in a quantum spin Hall phase and in the other a quantum anomalous Hall phase. The vortices of the exciton order parameter can carry fractional charge and statistics of electrons in both phases.

We study possible gapless edge states of translation-symmetric ${\mathbb{Z}}_{2}$ spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of ${\mathbb{Z}}_{2}$ spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these ${\mathbb{Z}}_{2}$ spin liquids and find their effective background field

We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2e field with finite momentum. However, the order parameter here is a quart

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a

Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of weak quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice de

We discuss the possibility of realizing Weyl semimetal phase in the magnetically doped topological band insulators. When the magnetic moments are ferromagnetically polarized, we show that there are three phases in the system upon the competition between topological mass and magnetic mass: topological band insulator phase, Weyl semimetal phase, and trivial phase. We explicitly derive the low energy theory of Weyl points from the general continuum Hamiltonian of topological insulators near the Dir

Two-dimensional topologically ordered states such as fractional quantum Hall fluids host anyonic excitations, which are relevant for realizing fault-tolerant topological quantum computers. Classification and characterization of topological orders have been intensely pursued in both the condensed matter and mathematics literature. These topological orders can be bosonic or fermionic depending on whether the system hosts fundamental fermionic excitations or not. In particular, emergent topological