Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session W3: Topological Aspects of Electron Transport in Solids |
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Sponsoring Units: DCMP Chair: Shoucheng Zhang, Stanford University Room: Baltimore Convention Center Ballroom I |
Thursday, March 16, 2006 2:30PM - 3:06PM |
W3.00001: Berry Phase and Dissipationless Currents in Solids Invited Speaker: It is now recognized that the electronic band structures in solids are characterized by nontrivial quantum topological nature associated with Berry phase. This situation is analogous to the quantum Hall system under the strong magnetic field, but occurs in almost every material even without the magnetic field. Anomalous Hall effect in ferromagnets is a representative example, where the anomalous velocity induced by Berry phase leads to the transverse motion of the electrons to the applied electric field. In paramagnetic materials, on the other hand, the Kramers degeneracy makes the Berry connection non-Abelian. The spin dependent anomalous velocity leads to the spin Hall effect in semiconductors such as GaAs. These charge and spin currents are distinct from the usual transport current since it is not due to the deviation from the equilibrium electron distribution in momentum space, but is driven by the anomalous velocity of all the occupied states in equilibrium. Therefore it is essentially dissipationless. However, in real situation, the disorder effect and contact to the leads introduces the dissipation. This aspect is discussed in detail using the Keldysh formalism for each problem. Ideas of anomalous Hall insulator and spin Hall insulator are also proposed to avoid this dissipation. Applications to optical phenomena are also discussed. This work has been done in collaboration with Z. Fang, S. Murakami, K. Ohgushi, M.Onoda, S.Onoda, K. Sawada, R.Shindou, N. Sugimoto, K. Terakura, and S.C.Zhang. [Preview Abstract] |
Thursday, March 16, 2006 3:06PM - 3:42PM |
W3.00002: Fermi Liquid Berry Phase Theory of the Anomalous Hall Effect Invited Speaker: Charged Fermi liquids with broken time-reversal symmetry have an intrinsic anomalous Hall effect that derives from the Berry phases accumulated by accelerated quasiparticles that move on the Fermi surface. The intrinsic Hall conductivity is given by a new fundamental geometric Fermi liquid formula that can be regarded as the derivative with respect to magnetic flux density of the Luttinger fomula relating the density of mobile charge carriers to the k-space volume enclosed by the Fermi surface. This formula can be derived by an integration-by-parts of the Karplus-Luttinger free-electron band-structure formula to yield a topological (QHE) part plus a geometrical part expressed completely at the Fermi surface, and which has a natural generalization to interacting Fermi liquid quasiparticles (QP's). The QP Berry phases are properties of the {\it eigenstates} of the (exact) single-particle Green's function at the Fermi surface, which is a Hermitian matrix with Bloch-state eigenvectors; the Berry phases derive from the variation on the Fermi surface of the spatially-periodic factor of the QP Bloch state that characterizes how the total QP amplitude is distributed among the different electronic orbitals in the unit cell. In the case of 3D ferromagnetic metals, the Berry phases derive from the interplay of exchange splitting with spin-orbit coupling (both must be present). Remarkably, the new formula also applies to Fermi-liquid analogs such as the 2D composite fermion (CF) fluid in the half-filled lowest Landau level: in this case, the QP is a bound electron+vortex composite and not a Bloch state. This QP structure varies on the CF Fermi surface in a way that exactly gives the expected result $\sigma^{xy}$ = $e^2/2h$, unaffected by any Fermi surface anisotropy, thus explaining how a quantized value of $\sigma^{xy}$ persists even though the CF Fermi liquid is {\it not} an incompressible FQHE state. The geometric anomalous Hall effect formula suggests a more intrinsic geometric description of the Fermi surface, where the Fermi vector ${\boldmath k}_F({\bf s})$ is only one of a number of properties that vary on a curved $(D-1)$-dimensional Fermi surface manifold parametrized by curvilinear coordinates ${\bf s}$; other properties include the Berry curvature field ${\cal F}({\bf s})$, quasiparticle mean free path $\ell({\bf s})$,{\it etc}. The new formula also naturally takes into account non-trivial (multiply-connected) Fermi surface topology and open orbits. [Preview Abstract] |
Thursday, March 16, 2006 3:42PM - 4:18PM |
W3.00003: The Quantum Spin Hall Effect Invited Speaker: We show that the intrinsic spin orbit interaction in a single plane of graphene converts the ideal two dimensional semi metallic groundstate of graphene into a quantum spin Hall (QSH) state [1]. This novel electronic phase shares many similarities with the quantum Hall effect. It has a bulk excitation gap, but supports the transport of spin and charge in gapless ``spin filtered" edge states on the sample boundary. We show that the QSH phase is associated with a $Z_2$ topological invariant, which distinguishes it from an ordinary insulator [2]. The $Z_2$ classification, which is defined for any time reversal invariant Hamiltonian with a bulk excitation gap, is analogous to the Chern number classification of the quantum Hall effect. We argue that the QSH phase is topologically stable with respect to weak interactions and disorder. The QSH phase exhibits a finite (though not quantized) dissipationless spin Hall conductance even in the presence of weak disorder, providing a new direction for realizing dissipationless spin transport.\\ \\ 1. C.L. Kane and E.J. Mele, Phys. Rev. Lett. {\bf 95}, 226801 (2005). \\ 2. C.L. Kane and E.J. Mele, Phys. Rev. Lett. {\bf 95}, 146802 (2005). [Preview Abstract] |
Thursday, March 16, 2006 4:18PM - 4:54PM |
W3.00004: Spintronics, propagating mode, (quantum) spin transport, and new electron liquids Invited Speaker: The field of spintronics deals with the physics of the electron-spin in semiconductors, metals, insulators and other materials. Among these, the systems which are characterized by strong spin-orbit coupling hold a special place and exhibit a plethora of new phenomena. In classical transport in semiconductors, a propagating spin-charge collective mode appears that is qualitatively different from the diffusive charge transport. The propagating spin-charge mode is the hallmark of spin-orbit coupled systems with a Fermi surface. The Boltzmann transport equations are qualitatively different from the diffusive normal behavior. Three dimensional bulk transport will be analyzed for the first time. In semiconductors without spin-orbit coupling, an orbital Hall effect (similar to the spin-Hall effect) is present in which electrons selectively occupy different orbitals depending on their direction of motion. In quantum transport, a spatially varying spin-orbit coupling is equivalent to a Landau level problem in which electrons of opposite spin feel opposite magnetic fields, thereby exhibiting a quantum Spin-Hall effect. Time-reversal symmetry is unbroken. In these spin Hall insulators, the quantum spin transport takes place through edge states that cross the bulk gap and the Fermi level. The electron liquid on the edges is a helical liquid, in which spin is correlated with chirality, and represents a new class of one-dimensional liquids different from the Luttinger spinless, spinful or chiral liquids. I will also briefly discuss the possibility of three-dimensional quantization in systems with spin-orbit coupling. New experiments are needed and proposed to verify these predictions. [Preview Abstract] |
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