Ferromagnetic transition in a one-dimensional spin-orbit-coupled metal and its mapping to a critical point in smectic liquid crystals

Abstract

We study the quantum phase transition between a paramagnetic and ferromagnetic metal in the presence of Rashba spin-orbit coupling in one dimension. Using bosonization, we analyze the transition by means of renormalization group, controlled by an $\epsilon$-expansion around the upper critical dimension of two. We show that the presence of Rashba spin-orbit coupling allows for a new nonlinear term in the bosonized action, which generically leads to a fluctuation driven first-order transition. We further demonstrate that the Euclidean action of this system maps onto a classical smectic-A -- C phase transition in a magnetic field in two dimensions. We show that the smectic transition is second-order and is controlled by a new critical point.

16 pages, 4 figures, 1 table

References in corpus (9)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Epitaxy of Semiconductor-Superconductor nanowires
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• A controlled expansion for certain non-Fermi liquid metals
• Ferromagnetic and Nematic Non-Fermi Liquids in Spin-Orbit Coupled Two-Dimensional Fermi Gases
• Odd-parity superconductivity near inversion breaking quantum critical point in one dimension

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• Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition
• Constrained motions and slow dynamics in one-dimensional bosons with double-well dispersion