Berry Phase of Nonlinear Correction

量子非线性输运及其在费米气体中的破坏

Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature

研究揭示了费米气体中 Berry 曲率对量子非线性输运的影响，并发现空间非均匀性导致量化破裂的现象。

Berry偶极跃迁中的外在和内在非线性霍尔效应

Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions

本研究揭示三维Hopf绝缘体在Berry偶极跃迁附近，非线性霍尔电导率由普适函数表征且与Hopf不变量变化成正比，建立了两者间的对应关系。

Berry Phase in Atom-Molecule Conversion Systems and Fractional Monopole

We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule conversion. The geometric phase can be viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole.

Finite-size corrections to quantized particle transport in topological charge pumps

We investigate the quantization of adiabatic charge transport in the insulating ground state of finite systems. Topological charge pumps are used in experiments as an indicator of topological order. In the thermodynamic limit the transport can be related to a topological Berry phase and is thus strictly quantized. This is no longer true for finite systems. We derive finite-size corrections to the transport both for non-interacting and interacting systems and relate them to analytic properties of the single- and many-body Berry curvature. We find that they depend on the details of experimental …

Nonlinear Dirac Cones

Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often characterized by a $π$ Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a novel type of Dirac cones that are robust to local perturbations without symmetry restrictions. Due to a different pseudo-spin texture, the Berry phase of the Dirac cone is no longer quan…