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AIP conference proceedings

On the Existence of Stoner Instability in a Semiconductor Electron Quantum Wire

Vinayak Garg, Rajinder Kumar Moudgil, Alka B. Garg, R. Mittal, R. Mukhopadhyay

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Motivated by the recent experimental evidence of the Stoner instability in a semiconductor quantum wire, we have theoretically examined the spin phase diagram of such a wire by comparing the ground‐state energy in the states of different spin polarization. To this endeavour, the self‐consistent mean‐field approximation of Singwi et al. has been used. The transverse motion of electrons is assumed to be confined by a cylindrically symmetric harmonic potential. Our study predicts a transition to the ferromagnetic phase at a sufficiently low electron density, thus corroborating the experimental scenario. Further, the partially spin‐polarized phases are found to be unstable‐ a prediction in agreement with the recent quantum Monte Carlo simulations.

DOI
10.1063/1.3606270

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Motivated by the recent experimental evidence of the Stoner instability in a semiconductor quantum wire, we have theoretically examined the spin phase diagram of such a wire by comparing the ground‐state energy in the states of different spin polarization. To this endeavour, the self‐consistent mean‐field approximation of Singwi et al. has been used. The transverse motion of electrons is assumed to be confined by a cylindrically symmetric harmonic potential. Our study predicts a transition to the ferromagnetic phase at a sufficiently low electron density, thus corroborating the experimental scenario. Further, the partially spin‐polarized phases are found to be unstable‐ a prediction in agreement with the recent quantum Monte Carlo simulations.
Stoner instabilities for fermions with repulsive interaction have been well studied within the mean-field (ladder) approximation. In this study, we consider two-dimensional electronic systems with one or two valleys and discuss a Stoner transition beyond the ladder approximation. At weak coupling, the corrections to the ladder approximation come predominantly from the renormalization of the particle-hole vertex in the particle-particle channel, and the lowest-order corrections are logarithmically singular in the low-density limit. To investigate the problem beyond the lowest order, we apply the diagrammatic Monte Carlo algorithm and treat ladder and non-ladder renormalizations on equal footing. We find that in a one-valley system, a Stoner transition to a ferromagnetism occurs at low density only if there is a cutoff on the momentum transfer carried by the interaction. In a two-valley system, the restriction is less severe. Here we find either a direct Stoner transition into a spin- and valley-polarized state, or a set of two Stoner transitions via an intermediate valley-polarized state. The pathway is controlled by the anisotropy of the fermionic dispersion.
We explore theoretically the feasibility of a spin‐polarized ground state in a symmetric electron‐electron bilayer by comparing the ground‐state energy in states of different spin polarization. Both the intra‐ and inter‐layer interactions are dealt within the framework of random‐phase approximation. We find that there occurs in the bilayer an abrupt paramagnetic‐ferromagnetic phase transition with the decreasing electron density irrespective of the magnitude of inter‐layer separation. Interestingly, the critical transition density is found to decrease with the diminishing layer spacing, implying therefore a suppression of spin polarization by interlayer interaction effects.
When the Fermi surface and the Brillouin zone boundary touch at a Van Hove point, mean-field analysis predicts a ferromagnetic (Stoner) instability at finite TMFT_{MF}TMF​ for any coupling strength due to the divergent density of states. However, the predicted effect has not been observed experimentally. Several qualitative theoretical proposals have been put forward to explain why the mean-field prediction fails. Based on numerically exact results for the two-dimensional Hubbard model with an ordinary Van Hove singularity, we uncover the mechanisms behind the suppression of the ferromagnetic instability. We employ two diagrammatic Monte Carlo approaches: (i) the four-channel self-consistent approximation and (ii) numerically exact method of combinatorial summation of diagrams with controlled resummation of the truncated expansion. We find that the system avoids the Stoner instability down to temperatures an order of magnitude below TMFT_{MF}TMF​ due to the combination of the downward renormalization of the effective coupling and the suppression of the density of states by the loss of the quasiparticle residue.
Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance have brought about a number of interesting problems in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a ``quasirepulsive'' regime in the upper branch of the energy spectrum due to the rapid quench is currently being debated, and the Stoner transition has mainly been investigated theoretically by using perturbation theory or at high polarization due to the limited theoretical approaches in the strongly repulsive regime. In this work, we present a nonperturbative theoretical approach to the quasirepulsive upper branch of a Fermi gas near a broad Feshbach resonance, and we determine the finite-temperature phase diagram for the Stoner instability. Our results agree well with the known quantum Monte Carlo simulations at zero temperature, and we recover the known virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the Stoner transition temperature becomes of the order of the Fermi temperature, around which the molecule formation rate becomes vanishingly small. This suggests a feasible way to observe Stoner ferromagnetism in the nondegenerate temperature regime.
We compute the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions, using two complementary methods: the random-phase approximation and self-consistent Hartree-Fock theory. We show that the spin-dependent interactions, which break the (pseudo-) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis (easy-plane) ferromagnet for sufficiently strong repulsive (attractive) interspecies interactions, respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of interspecies attraction, we also discuss the possibility of a bosonic analog of the Cooper-paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations, however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji et al. [Ji et al., Nat. Phys. 10, 314 (2014)].
We present a numerical study of magnetic phases of the 2D electron gas near freezing. The calculations are performed by diffusion Monte Carlo in the fixed-node approximation. At variance with the 3D case we find no evidence for the stability of a partially polarized phase. With plane wave nodes in the trial function, the polarization transition takes place at r s = 20, whereas the best available estimates locate Wigner crystallization around r s = 35. Using an improved nodal structure, featuring optimized backflow correlations, we confirm the existence of a stability range for the polarized phase, although somewhat shrunk, at densities achievable nowadays in 2-dimensional hole gases in semiconductor heterostructures. The spin susceptibility of the unpolarized phase at the magnetic transition is approximately 30 times the Pauli susceptibility.