Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.Comment: 18 pages, 8 figure

Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer

Let $G$ be an $n$-node planar graph. In a visibility representation of $G$, each node of $G$ is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of $G$ are vertically visible to each other. In the present paper we give the best known compact visibility representation of $G$. Given a canonical ordering of the triangulated $G$, our algorithm draws the graph incrementally in a greedy manner. We show that one of three canonical orderings obtained from Schnyder's realizer for the triangulated $G$ yields a visibility representation of $G$ no wider than $\frac{22n-40}{15}$. Our easy-to-implement O(n)-time algorithm bypasses the complicated subroutines for four-connected components and four-block trees required by the best previously known algorithm of Kant. Our result provides a negative answer to Kant's open question about whether $\frac{3n-6}{2}$ is a worst-case lower bound on the required width. Also, if $G$ has no degree-three (respectively, degree-five) internal node, then our visibility representation for $G$ is no wider than $\frac{4n-9}{3}$ (respectively, $\frac{4n-7}{3}$). Moreover, if $G$ is four-connected, then our visibility representation for $G$ is no wider than $n-1$, matching the best known result of Kant and He. As a by-product, we obtain a much simpler proof for a corollary of Wagner's Theorem on realizers, due to Bonichon, Sa\"{e}c, and Mosbah.Comment: 11 pages, 6 figures, the preliminary version of this paper is to appear in Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science (STACS), Berlin, Germany, 200

Surface constraints on the depth of the Atlantic meridional overturning circulation: Southern Ocean versus North Atlantic

Paleoclimate proxy evidence suggests that the Atlantic meridional overturning circulation (AMOC) was about 1000 m shallower at the Last Glacial Maximum (LGM) compared to the present. Yet it remains unresolved what caused this glacial shoaling of the AMOC, and many climate models instead simulate a deeper AMOC under LGM forcing. While some studies suggest that Southern Ocean surface buoyancy forcing controls the AMOC depth, others have suggested alternatively that North Atlantic surface forcing or interior diabatic mixing plays the dominant role. To investigate the key processes that set the AMOC depth, here we carry out a number of MITgcm ocean-only simulations with surface forcing fields specified from the simulation results of three coupled climate models that span much of the range of glacial AMOC depth changes in phase 3 of the Paleoclimate Model Intercomparison Project (PMIP3). We find that the MITgcm simulations successfully reproduce the changes in AMOC depth between glacial and modern conditions simulated in these three PMIP3 models. By varying the restoring time scale in the surface forcing, we show that the AMOC depth is more strongly constrained by the surface density field than the surface buoyancy flux field. Based on these results, we propose a mechanism by which the surface density fields in the high latitudes of both hemispheres are connected to the AMOC depth. We illustrate the mechanism using MITgcm simulations with idealized surface forcing perturbations as well as an idealized conceptual geometric model. These results suggest that the AMOC depth is largely determined by the surface density fields in both the North Atlantic and the Southern Ocean

Persistent spin current in spin-orbit coupling systems in the absence of an external magnetic field

The spin-orbit coupling systems with a zero magnetic field is studied under the equilibrium situation, {\it i.e.}, without a voltage bias. A persistent spin current is predicted to exist under most circumstances, although the persistent charge current and the spin accumulation are identically zero. In particular, a two-dimensional quantum wire is investigated in detail. Surprisingly, a persistent spin current is found to flow along the confined direction, due to the spin precession in accompany with the particle motion. This provides an interesting example of constant spin flowing without inducing a spin accumulation, contrary to common intuition.Comment: 4 pages, 5 figure

Nature of Spin Hall Effect in a finite Ballistic Two-Dimensional System with Rashba and Dresselhaus spin-orbit interaction

The spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction is studied numerically. We find that the spin Hall conductance is very sensitive to the transverse measuring location, the shape and size of the device, and the strength of the spin-orbit interaction. Not only the amplitude of spin Hall conductance but also its sign can change. This non-universal behavior of the spin Hall effect is essentially different from that of the charge Hall effect, in which the Hall voltage is almost invariant with the transverse measuring site and is a monotonic function of the strength of the magnetic field. These surprise behavior of the spin Hall conductance are attributed to the fact that the eigenstates of the spin Hall system is extended in the transverse direction and do not form the edge states.Comment: 5 pages, 5 figure

Bias-controllable intrinsic spin polarization in a quantum dot

We propose a novel scheme to efficiently polarize and manipulate the electron spin in a quantum dot. This scheme is based on the spin-orbit interaction and it possesses following advantages: (1) The direction and the strength of the spin polarization is well controllable and manipulatable by simply varying the bias or the gate voltage. (2) The spin polarization is quite large even with a weak spin-orbit interaction. (3) Both electron-electron interaction and multi-energy levels do not weaken but strengthen the spin polarization. (4) It has the short spin flip time. (5) The device is free of a magnetic field or a ferromagnetic material. (6) It can be easily realized with present technology.Comment: 9 pages, 5 figure

Spin relaxation in nn-type (111) GaAs quantum wells

We investigate the spin relaxation limited by the D'yakonov-Perel' mechanism in $n$-type (111) GaAs quantum wells, by means of the kinetic spin Bloch equation approach. In (111) GaAs quantum wells, the in-plane effective magnetic field from the D'yakonov-Perel' term can be suppressed to zero on a special momentum circle under the proper gate voltage, by the cancellation between the Dresselhaus and Rashba spin-orbit coupling terms. When the spin-polarized electrons mainly distribute around this special circle, the in-plane inhomogeneous broadening is small and the spin relaxation can be suppressed, especially for that along the growth direction of quantum well. This cancellation effect may cause a peak (the cancellation peak) in the density or temperature dependence of the spin relaxation time. In the density (temperature) dependence, the interplay between the cancellation peak and the ordinary density (Coulomb) peak leads to rich features of the density (temperature) dependence of the spin relaxation time. The effect of impurities, with its different weights on the cancellation peak and the Coulomb peak in the temperature dependence of the spin relaxation, is revealed. We also show the anisotropy of the spin relaxation with respect to the spin-polarization direction.Comment: 8 pages, 6 figure

Direct images of bundles under Frobenius morphisms

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded by instability of $W\otimes{\rm T}^{\ell}(\Omega^1_X)$ ($0\le \ell\le n(p-1)$)(Corollary \ref{cor3.8}). When $X$ is a smooth projective curve of genus $g\ge 2$, it implies $F_*W$ being stable whenever $W$ is stable.Comment: the final version to appear in Invent. math. (2008

Fourier transform and rigidity of certain distributions

Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces.Comment: 10 page