Magnetic Multilayers: Quasiclassical Transport Via the Kubo Formula

A real‐space quantum approach, based on the Kubo formula, is used to describe the quasiclassical transport behavior of metallic multilayers. We emphasize the differences between the cases of current in the plane of the layers, for which size effects play a dominant role and current perpendicular to the planes, for which we provide several proofs that the so‐called series resistor model holds for all length scales

Linear Transport Theory of Magnetoconductance in Metallic Multilayers: A Real-space Approach

The linear transport behavior of metallic multilayers is studied by using the real-space Kubo formula, for a model Hamiltonian consisting of zero-range spin-dependent impurity-scattering potentials. The resulting theory allows a direct comparison with the Boltzmann equation approach in the quasiclassical limit, which is expected to be a good approximation for most magnetic multilayers. Furthermore, the regimes for which quantum corrections might be needed are explicitly indicated. It is explicitly shown that: (i) periodicity is not required as a mechanism for giant magnetoresistance, and (ii) the two main geometries, current in the plane of the layers and perpendicular to the plane of the layers, exhibit very different size effects, the latter yielding the so-called series resistor model

Anomaly in Conformal Quantum Mechanics: From Molecular Physics to Black Holes

A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular domain of distances, they are characterized by a long-range conformal interaction (inverse square potential), the apparent absence of dimensional scales, and an SO(2,1) symmetry algebra. Examples from molecular physics to black holes are provided and discussed within a unified treatment. When such systems are physically realized in the appropriate strong-coupling regime, the occurrence of quantum symmetry breaking is possible. This anomaly is revealed by the failure of the symmetry generators to close the algebra in a manner shown to be independent of the renormalization procedure

Anomalous Commutator Algebra for Conformal Quantum Mechanics

The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived

Electron Transport in Magnetic Inhomogeneous Media

Giant magnetoresistance has been observed in both magnetic multilayers and magnetic granular solids. We develop a framework for unifying these particular realizations of inhomogeneous magnetic media, based on the real-space Kubo formula. It constitutes a spin-dependent form of linear response theory, associated with internal spin-dependent fields arising from spin accumulation; moreover, we discuss the physical meaning of these spin dependences. For magnetic multilayers we discuss the particular cases of collinear and noncollinear configurations, and we consider limiting cases of the elastic mean-free path to inhomogeneity-scale ratio for granular solids. Furthermore, we introduce the concept of magnetically self-averaging systems, which include the current perpendicular to the plane geometry of multilayers and granular solids. In the limit of no spin-flip scattering, we show that there are no length scales associated with the magnetoresistance of self-averaging structures

Black Hole Thermodynamics From Near-horizon Conformal Quantum Mechanics

The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D≥4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their “coordinate singularity,” can be used self-consistently to describe the thermodynamics of black holes

Magnetoresistance of Multilayered Structures for Currents Perpendicular to the Plane of the Layers

While most transport measurements on multilayered structures have been done for currents in the plane of the layers, there is an emerging interest in the geometry where the currents are perpendicular to the plane of the layers. We discuss the field and current patterns in these two cases. For the latter, the elastic mean free path is not a relevant length scale; rather, it is the spin-flip mean free path that is important. In the case of currents perpendicular to the plane of the layers, one must distinguish between models which allow spin mixing of the currents and those in which the currents from the spin-up and spin-down electrons do not mix

SO(2,1) Conformal Anomaly: Beyond Contact Interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity

Effective Field Theory Program for Conformal Quantum Anomalies

The emergence of conformal states is established for any problem involving a domain of scales where the long-range SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs is in place, this renormalization mechanism is capable of producing binding in the strong-coupling regime. A realization of this phenomenon, in the form of dipole-bound anions, is discussed