Geometry and the anomalous Hall effet in ferromagnets

The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support the dominant role of the KL velocity term in ferromagnets.Comment: 6 pages, 4 figures, conference proceedings, tutorial revie

Phase fluctuations versus Gaussian fluctuations in optimally-doped YBa2_2Cu3_3O7_7

We analyze recent torque measurements of the magnetization $M_d$ vs. magnetic field $H$ in optimally doped YBa$_2$Cu$_3$O$_{7-y}$ (OPT YBCO) to argue against a recent proposal by Rey et al that the magnetization results above $T_c$ are consistent with Gaussian fluctuations. We find that, despite its strong interlayer coupling, OPT YBCO displays an anomalous non-monotonic dependence of $M_d$ on $H$ which represents direct evidence for the locking of the pair wavefunction phase $\theta_n$ at $T_c$ and the subsequent unlocking by a relatively weak $H$. These unusual features characterize the unusual nature of the transition to the Meissner state in cuprate superconductors. They are absent in low-$T_c$ superconductors to our knowledge. We also stress the importance of the vortex liquid state, as well as the profiles of the melting field $H_m(T)$ and the upper critical field curve $H_{c2}(T)$ in the $T$-$H$ plane. Contrary to the claims of Rey et al, we show that the curves of the magnetization and the Nernst signal illustrate the inaccessibility of the $H_{c2}$ line near $T_c$. The prediction of the $H_{c2}$ line by Rey et al is shown to be invalid in OPT YBCO.Comment: 6 pages, 6 figure

Phase coherence and the Nernst effect at magic angles in organic conductors

A giant Nernst signal was recently observed for fields near crystallographic directions in (TMTSF)$_2$PF$_6$. Such large Nernst signals are most naturally associated with the motion of pancake vortices. We propose a model in which phase coherence is destroyed throughout the sample except in planes closely aligned with the applied field $\bf H$. A small tilt above or below the plane changes the direction and density of the penetrating vortices and leads to a Nernst signal that varies with the tilt angle of $\bf H$ as observed. The resistance notches at magic angles are understood in terms of flux-flow dissipation from field-induced vortices.Comment: 4 pages, 4 figure

The zero-energy state in graphene in a high magnetic field

The fate of the charge-neutral Dirac point in graphene in a high magnetic field $H$ has been investigated at low temperatures ($T\sim$ 0.3 K). In samples with small $V_0$ (the gate voltage needed to access the Dirac point), the resistance $R_0$ at the Dirac point diverges steeply with $H$, signalling a crossover to an insulating state in intense field. The approach to the insulating state is highly unusual. Despite the steep divergence in $R_0$, the profile of $R_0$ vs. $T$ in fixed $H$ saturates to a $T$-independent value below 2 K, consistent with charge carrying gapless excitations.Comment: 4 pages, 4 figures. Four new sub-figures have been added. Text expanded to discuss data from more sample

The Nernst effect in high-TcT_c superconductors

The observation of a large Nernst signal $e_N$ in an extended region above the critical temperature $T_c$ in hole-doped cuprates provides evidence that vortex excitations survive above $T_c$. The results support the scenario that superfluidity vanishes because long-range phase coherence is destroyed by thermally-created vortices (in zero field), and that the pair condensate extends high into the pseudogap state in the underdoped (UD) regime. We present a series of measurements to high fields $H$ which provide strong evidence for this phase-disordering scenario.Comment: 21 pages, 28 figure