Magnetic polarons beyond linear spin-wave theory: Mesons dressed by magnons
Physical Review B(2024)
摘要
When a mobile hole is doped into an antiferromagnet, its movement will
distort the surrounding magnetic order and yield a magnetic polaron. The
resulting complex interplay of spin and charge degrees of freedom gives rise to
very rich physics and is widely believed to be at the heart of high-temperature
superconductivity in cuprates. In this paper, we develop a quantitative
theoretical formalism, based on the phenomenological parton description, to
describe magnetic polarons in the strong coupling regime. We construct an
effective Hamiltonian with weak coupling to the spin-wave excitations in the
background, making the use of standard polaronic methods possible. Our starting
point is a single hole doped into an AFM described by a 'geometric string'
capturing the strongly correlated hopping processes of charge and spin degrees
of freedom, beyond linear spin-wave approximation. Subsequently, we introduce
magnon excitations through a generalized 1/S expansion and derive an effective
coupling of these spin-waves to the hole plus the string (the meson) to arrive
at an effective polaron Hamiltonian with density-density type interactions.
After making a Born-Oppenheimer-type approximation, this system is solved using
the self-consistent Born approximation to extract the renormalized polaron
properties. We apply our formalism (i) to calculate beyond linear spin-wave
ARPES spectra, (ii) to reveal the interplay of ro-vibrational meson
excitations, and (ii) to analyze the pseudogap expected at low doping.
Moreover, our work paves the way for exploring magnetic polarons out-of
equilibrium or in frustrated systems, where weak-coupling approaches are
desirable and going beyond linear spin-wave theory becomes necessary.
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