Ching Hua Lee

Pseudopotential formalism for fractional Chern insulators

Recently, generalizations of fractional quantum Hall (FQH) states known as fractional quantum anomalous Hall or, equivalently, fractional Chern insulators states, have been realized in lattice models. Ideal wave functions such as the Laughlin wave function, as well as their corresponding trial Hamiltonians, have been vital to characterizing FQH phases. The Wannier function representation of fractional Chern insulators recently proposed [X.-L. Qi, Phys. Rev. Lett. 107, 126803 (2011)] defines an approach to generalize these concepts to fractional Chern insulators. In this paper, we apply the Wannier function representation to develop a systematic pseudopotential formalism for fractional Chern insulators. The family of pseudopotential Hamiltonians is defined as the set of projectors onto asymptotic relative angular momentum components which forms an orthogonal basis of two-body Hamiltonians with magnetic translation symmetry. This approach serves both as an expansion tool for interactions and as a definition of positive-semidefinite Hamiltonians for which the ideal fractional Chern insulator wave functions are exact null-space modes. We compare the short-range two-body pseudopotential expansion of various fractional Chern insulator models at filling mu = 1/3 in phase regimes where a Laughlin-type ground state is expected to be realized. We also discuss the effect of inhomogeneous Berry curvature which leads to components of the Hamiltonian that can not be expanded into pseudopotentials, and elaborate on their role in determining low-energy theories for fractional Chern insulators. Finally, we generalize our Chern pseudopotential approach to interactions involving more than two bodies with the goal of facilitating the identification of non-Abelian fractional Chern insulators.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and nontrivial quantum geometry.

Negative differential resistance and characteristic nonlinear electromagnetic response of a Topological Insulator.

Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. GaAs employed in the Gunn diode. In this work, we show that negative differential resistance also generically arise in Dirac ring systems, an example of which has been experimentally observed in the surface states of Topological Insulators. This novel realization of negative differential resistance is based on a completely different physical mechanism from that of the Gunn effect, relying on the characteristic non-monotonicity of the response curve that remains robust in the presence of nonzero temperature, chemical potential, mass gap and impurity scattering. As such, it opens up new possibilities for engineering applications, such as frequency upconversion devices which are highly sought for terahertz signal generation. Our results may be tested with thin films of Bi2Se3 Topological Insulators, and are expected to hold qualitatively even in the absence of a strictly linear Dirac dispersion, as will be the case in more generic samples of Bi2Se3 and other materials with topologically nontrivial Fermi sea regions.

Exact holographic mapping in free fermion systems

In this paper, we perform a detailed analysis of the exact holographic mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. These analytic results allow us to study the asymptotic properties that are difficult to probe numerically, such as the near-horizon regime of the black-hole geometry. We shall also explore a few interesting but hitherto unexplored bulk geometries, such as that corresponding to a boundary critical fermion with a nontrivial dynamical critical exponent. Our analytic framework also allows us to study the holographic mapping of some of these boundary theories in dimensions 2+1 or higher.

Line nodes, Dirac points, and Lifshitz transition in two-dimensional nonsymmorphic photonic crystals

Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple two-dimensional photonic crystal lattices with gap closures, i.e., band degeneracies protected by nonsymmorphic symmetry. Our photonic structures are relatively easy to fabricate, consisting of two inequivalent dielectric cylinders per unit cell. Along high-symmetry directions, they exhibit line degeneracies protected by glide-reflection symmetry and time-reversal symmetry, which we explicitly demonstrate for

Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect

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Anisotropic pseudopotential characterization of quantum Hall systems under a tilted magnetic field

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Band structure engineering of ideal fractional Chern insulators

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