Regensburg 2016 – scientific programme
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SYES: Symposium Frontiers of Electronic Structure Theory: Focus on Topology and Transport
SYES 6: Frontiers of Electronic Structure Theory: Focus on Topology and Transport IV
SYES 6.6: Talk
Thursday, March 10, 2016, 12:15–12:30, H24
Anomalous Hall conductivity and orbital magnetization as local quantities — •Antimo Marrazzo1 and Raffaele Resta2 — 1THEOS, EPF Lausanne, Switzerland — 2Dipartimento di Fisica, Univ. Trieste, Italy
Anomalous Hall conductivity (AHC) and orbital magnetization (OM) are—from a theorist’s viewpoint—closely related: both have an expression as k-space integrals of the appropriate geometrical quantity. The k space is an artificial construct: all bulk properties are embedded in the ground state density matrix in r space, independently of the boundary conditions. Is it possible to address AHC and OM as local properties, directly in r space? For insulators, two recent papers have proved that the answer is affirmative: both AHC (quantized in insulators) and OM can be evaluated from a local formula over bounded samples. A rationale can be found in the “nearsightedness” of the density matrix: but since this is qualitatively different in insulators and metals (exponential vs. power law) it is not obvious that the same successful approach can be extended to metals. Using model Hamiltonians, we have performed simulations over 2D bounded metallic flakes, where the T-invariance is broken in two alternative ways: either à la Haldane, or by a macroscopic B field. In both cases, our simulations show that the relevant quantity can be extracted from a knowledge of the electron distribution in the bulk region of the sample only. This looks counterintuitive because the OM of a magnetized sample owes to currents localized near its surface; but the key reason for the success of the local approach to AHC and OM is that the formulas are not based on currents.