Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems

TL;DR

This paper investigates the phase diagram and collective excitations of double-layer quantum Hall systems at total filling factor  2, revealing canted antiferromagnetic and spin singlet states, with detailed theoretical analysis and experimental relevance.

Contribution

It provides a detailed Hartree-Fock and continuum quantum field theory analysis of canted and singlet quantum Hall states, including phase transitions and collective modes.

Findings

Identification of canted antiferromagnetic and spin singlet phases

Continuous quantum phase transitions with softening collective excitations

Presence of Goldstone mode and Kosterlitz-Thouless transition in the canted phase

Abstract

We present details of earlier studies (Zheng et al, Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al, ibid 79, 917 (1997)) and additional new results on double-layer quantum Hall systems at a total filling \nu = 2 \nu_1, where a single layer at filling \nu_1 forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case \nu_1 = 1, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well separated layers, we find two double-layer quantum Hall phases: one with a finite interlayer antiferromagnetic spin ordering in the plane orthogonal to the applied field (the `canted' state), and the other a spin singlet. The quantum transitions between the various quantum Hall states are continuous, and are signaled by the softening of collective intersubband spin density excitations. For the case of general \nu_1, closely related results are obtained by a semi-phenomenological continuum quantum field theory description of the low-lying spin excitations using a non-linear sigma model. Because of its broken symmetry, the canted phase supports a linearly dispersing Goldstone mode and has a finite temperature Kosterlitz-Thouless transition. We present results on the form of the phase diagram, the magnitude of the canted order parameter, the collective excitation dispersions, the specific heat, the form of the dynamic light scattering spectrum at finite temperature, and the Kosterlitz-Thouless critical temperature. Our findings are consistent with recent experimental results.