Research & Selected Publications

Fractional Quantum Hall Effect

Ground state wave functions and topology

Fractional quantum Hall effect (FQHE) is a collective phenomenon of strongly correlated electrons under magnetic field which shows precisely quantized Hall conductance along with other novel topological and geometrical properties. The unique difficulty to understand FQHE mainly comes from its true strong-correlation nature, which means the interaction between electrons cannot be treated perturbatively. In 1989, J. K. Jain proposed that FQHE can be "viewed" as the integer quantum Hall effect of emergent quasiparticles named composite fermions (CFs), which are bound states of electrons and quantized vortices, and the residue interaction between CFs is weak and can be treated as higher order perturbations. Since then, the CF wave functions become a very powerful tool to explain various phenomenon and properties observed in FQHE and CF liquid.  The original CF wave functions are mainly written in disk geometry or spherical geometry, which bring the inconvenience of open boundaries, "shift" of magnetic flux,  or incompatibility with perfect crystal structure.  To avoid these inconveniences, one obvious option is do the study in the torus geometry. In [1], we construct the CF wave functions in the torus geometry through developing a tricky projection technique. CF wave functions in the torus geometry also allow direct evaluations of topological invariants such as Chern number, Berry phase and Hall viscosity by twisting boundary phases or geometries [2-5].  We also constructed toroidal wave functions for composite anyons, which are imaginary intermediate particles between electrons and CFs with different number of vortices attached, and show the adiabatic approach originally proposed by Greiter and Wilczek is valid in numerics [5].

[1] S. Pu, Y.-H. Wu, and J. K. Jain “Composite Fermions on a Torus”, Phys. Rev. B 96, 195302, (2017)

[2] S. Pu, M. Fremling, and J. K. Jain “Berry phase of the Composite-Fermion Fermi Sea: Effect of Landau-level mixing”, Phys. Rev. B 98, 075304, (2018)

[3] S. Pu, M. Fremling, and J. K. Jain “Hall Viscosity of Composite Fermions”, Phys. Rev. Research 2, 013139, (2020)

[4] S. Pu, “Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons”, Phys. Rev. B 102, 165101 (2020)

[5] S. Pu, J. K. Jain, “Composite anyons on a torus”, Phys. Rev. B 104, 115135 (2021)

Vortex lattice in superconductors

We show that a three-dimensional (3D) fully gapped type-II superconductor can feature emergent in-gap Fermi surfaces of Caroli-de Gennes Matricon (CdGM) quasiparticles in the presence of an Abrikosov vortex lattice. In particular, these CdGM Fermi surfaces manifest in the emergent 3D band structure enabled by the intervortex tunneling physics, and their stability is guaranteed by a Z2 topological index. By developing an effective analytical theory, we find that each vortex line carrying a 1D nodal dispersion is a sufficient condition for the vortex lattice to form CdGM Fermi surfaces. Following this prediction, in-gap CdGM Fermi surfaces are numerically confirmed in a microscopic vortex-lattice simulation of a superconducting Dirac semimetal with an s-wave spin-singlet pairing, which is directly applicable to a large class of type-II superconductors such as LiFeAs. Remarkably, the CdGM Fermi surfaces persist even when the normal state is deformed to a doped insulator of trivial band topology. Our work establishes the vortex lattice as a new experimentally feasible control knob for emergent topological phenomena in conventional superconductors. 

[11] S. Pu, J. D. Sau, R. -X. Zhang, "Topologically protected emergent Fermi surface in an Abrikosov vortex lattice ", arXiv:2402.18627

(2024)