Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$

Abstract

Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. Especially, the latter is quantum information geometry, where the quantum Fisher information naturally arises as quantum metric. We apply these results to the $X$-wave magnets, which include $d$% -wave, $g$-wave and $i$-wave altermagnets as well as $p$-wave and $f$-wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effect. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the $X$-wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of recent progress together with some original results.

51 pages, 5 figures

References in corpus (2)

• Almost half-quantized planar Hall effects in $X$-wave magnets with $X=p,d,f,g,i$
• Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets

Cited by in corpus (4)

• Nonlinear spin-Seebeck diode in $f$-wave magnets, third-order spin-Nernst effects in $g$-wave magnets and spin-Nernst effects in $i$-wave altermagnets
• Fourth-order and six-order nonlinear spin current rectifier in three-dimensional $h$-wave and $j$-wave odd-parity magnet
• Quantum geometric map of magnetotransport
• Third-order optical response in d-wave altermagnets: Analytical and numerical results from microscopic model