Related papers: Comment on "Elementary formula for the Hall conduc…
When deriving a formula for the Hall conductivity of interacting electrons in Phys. Rev. B 86, 165133, we have relied on an unjustified implicit assumption that a certain gauge choice could be made. Only under this condition would the…
A formula for the Hall conductivity of interacting electrons is given under the assumption that the ground state manifold is N_gs-fold degenerate and discrete translation symmetry is neither explicitly nor spontaneously broken.
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
We present a concrete example of fractional Chern insulator whose fermion Hamiltonian consists of hopping and Coulomb repulsive interaction terms. Both of them are of finite range on the square lattice. In a strong coupling limit for the…
We consider the Hall effect in a system of weakly coupled Luttinger chains. We obtain the full conductivity tensor in the absence of dissipation along the chains. We show that while the dependence of the Hall and transverse conductivities…
The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to…
Using the non-commutative Kubo formula for aperiodic solids [1-3] and a recently developed numerical implementation [4], we study the conductivity $\sigma$ and resistivity $\rho$ tensors as functions of Fermi level and temperature, for…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
We present a composite fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the…
Motivated by a recent Comment by J. H\"oller and N. Read [Phys. Rev. B 93, 197401 (2016)], we revisit the problem of a chiral Luttinger liquid on a boundary of a Galilean-invariant quantum Hall fluid. After correcting the linear response…
We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a…
We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum…
Using the Kubo formula, we show explicitly that a non-interacting electron system can not behave like a Hall-insulator, {\it ie.,} a DC resistivity matrix $\rho_{xx}\rightarrow\infty$ and $\rho_{xy}=$finite in the zero temperature limit, as…
Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report…
The theory of the nonlinear Hall effect has been established by I. Sodemann and L. Fu [Phys. Rev. Lett. 115, 216806 (2015)] in a semiclassical framework: therein, the effect appears as a geometrical property of Bloch electrons, originating…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$, is calculated. We have shown that to leading order in $1/\epsilon_{F}\tau$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron…
In this letter we study the Hall conductance for a non-Hermitian Chern insulator and quantitatively describe how the Hall conductance deviates from a quantized value. We show the effects of the non-Hermitian terms on the Hall conductance…
We show that at electronic filling factor $\nu=1/2$, the lowest Landau level constraint implies that at any temperature, and in the presence of {\it any} amount of particle-hole symmetric disorder, the {\it composite fermion} Hall…
Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in…