Chern-Simons Theory and Dynamics of Composite Fermions

We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from microscopic wave functions, we further show that the momentum manifold has a uniformly distributed Berry curvature. As a result, composite fermions do not follow the ordinary Newtonian dynamics as commonly believed, but the more general symplectic one. For a Landau level with the particle-hole symmetry, the theory correctly predicts its Hall conductance at half-filling as well as the symmetry between an electron filling fraction and its hole counterpart.Comment: 5 pages, no figur

Asymmetry of the Geometrical Resonances of Composite Fermions

We propose an experiment to test the uniform-Berry-curvature picture of composite fermions. We show that the asymmetry of geometrical resonances observed in a periodically modulated composite fermion system can be explained with the uniform-Berry-curvature picture. Moreover, we show that an alternative way of modulating the system, i.e., modulating the external magnetic field, will induce an asymmetry opposite to that of the usual periodic grating modulation which effectively modulates the Chern-Simons field. The experiment can serve as a critical test of the uniform-Berry-curvature picture, and probe the dipole structure of composite fermions proposed by Read.Comment: 6 pages, 2 figure

Critical velocities for a superfluid in a periodic potential

In contrast to the homogeneous superfluid which has only one critical velocity, there exist two critical velocities for a superfluid in a periodic potential. The first one, which we call inside critical velocity, is for a macroscopic impurity to move frictionlessly in the periodic superfluid system; the second, which is called trawler critical velocity, is the largest velocity of the lattice relative to the lab frame for the superfluidity to maintain. The results are relevant to the superfluidity observed in the Bose-Einstein condensate in an optical lattice and supersolid helium.Comment: extensive revision, 4 pages and 4 figure

Attractive electron-electron interaction induced by geometric phase in a Bloch band

We investigate electron pairing in the presence of the Berry curvature field that ubiquitously exists in ferromagnetic metals with spin-orbit coupling. We show that a sufficiently strong Berry curvature field on the Fermi surface can transform a repulsive interaction between electrons into an attractive one in the p-wave channel. We also reveal a topological possibility for turning an attractive s-wave interaction into one in the p-wave channel, even if the Berry curvature field only exists inside the Fermi surface (circle). We speculate that these novel mechanism might be relevant to the recently discovered ferromagnetic superconductors such as UGe$_{2}$ and URhGe.Comment: 4 pages, 3 figure

Mapping a fractional quantum Hall state to a fractional Chern insulator

We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized \emph{two-dimensional} projected Wannier functions of a Landau level.Comment: 8 pages, 5 figure

Quantum Anomalous Hall Insulator of Composite Fermions

We show that a weak hexagonal periodic potential could transform a two-dimensional electron gas with an even-denominator magnetic filling factor to a quantum anomalous Hall insulator of composite fermions, giving rise to fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.Comment: 5 pages, 4 figures, 2 tables, detailed supplementary file adde

Self-consistent Single-band Approximation for Interacting Boson Systems

Traditionally, the single-band approximation for interacting many-body systems is done with pre-determined single-particle Wannier functions, ignoring the dependence of the Wannier function on interaction. We show that the single-band approximation has to be done self-consistently to properly account the interaction effect on the Wannier functions. This self-consistent single-band approximation leads to a nonlinear equation for Wannier functions, which can be recast into a set of nonlinear equations for Bloch functions. These equations are simplified for two special cases, the superfluid regime and deep in the Mott insulator regime. A simple example with double-well potential is used to illustrate our results.Comment: 4 pages, 2 figure

Heat Superconductivity

Electrons/atoms can flow without dissipation at low temperature in superconductors/superfluids. The phenomenon known as superconductivity/superfluidity is one of the most important discoveries of modern physics, and is not only fundamentally important, but also essential for many real applications. An interesting question is: can we have a superconductor for heat current, in which energy can flow without dissipation? Here we show that heat superconductivity is indeed possible. We will show how the possibility of the heat superconductivity emerges in theory, and how the heat superconductor can be constructed using recently proposed time crystals. The underlying simple physics is also illustrated. If the possibility could be realized, it would not be difficult to speculate various potential applications, from energy tele-transportation to cooling of information devices.Comment: 12 pages, 2 figures. Correct an issue pointed out by Jing-ning Zhang. Figures and text update

Reply to Comment on: "Radiation-Induced 'Zero-Resistance State' and the Photon Assisted Transport"

We show that the comment by A.F. Volkov ignores a delicate issue in the conductance measurement for a hall bar system. In such system, $\rho _{xx}\approx \rho_{xy}^{2}\sigma_{xx}$ while $\sigma_{xy}\gg \sigma_{xx}$, as correctly pointed out in Ref.3. We clarify that the so called "zero resistance state" is actually a "zero conductance state". A discussion concerning the phase transition induced by the negative conductance is presented.Comment: 1 pag

Reply to Comment on "Berry phase correction to electron density of states in solids"

The Comment by Duval et al. [PRL 96, 099701 (2006)] addresses an important, but not the main, result of our Letter [PRL 95, 137204 (2005)]. It does not contradict our results in substance, and the only objection is really on the style of approach