Abstract
Quantum Hall ferromagnetic transitions are typically achieved by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of ~2.4 × 1010 cm−2, this ratio grows greater than 1, resulting in a ferromagnetic ground state at filling factor ν = 2. At the critical density, a resistance peak due to the formation of microscopic domains of opposite spin orientations is observed. Such gate-controlled spin-polarizations in the quantum Hall regime opens the door to realizing Majorana modes using two-dimensional systems in conventional, low-spin-orbit-coupling semiconductors.
Highlights
In a perpendicular magnetic field (Bp), two-dimensional (2D) electrons/holes execute cyclotron motion, and their energy spectrum consists of a ladder of discrete Landau levels[1]
The ordering of and the energy gaps between these spin-polarized Landau levels depend on the ratio of the Zeeman splitting to the cyclotron gap, r ≡ Ez/Ec2
The resistance peak inside the ν = 2 minimum shown in Fig. 2a is the evidence of such a density-controlled quantum Hall ferromagnetic transition in our system
Summary
In a perpendicular magnetic field (Bp), two-dimensional (2D) electrons/holes execute cyclotron motion, and their energy spectrum consists of a ladder of discrete Landau levels[1]. Each Landau level further splits into two spin-polarized levels μB = eħ/2m0 is the Bohr magneton, σ is due to the Zeeman effect with the Pauli operator, g is the Landé g a Hamiltonian HS tensor, and B is the. The g tensor can be approximately reduced to two components, gp and gip, for netic field respectively In this case, the energy splitting due the perpendicular magnetic to the Zeeman effect is Ez =. The ordering of and the energy gaps between these spin-polarized Landau levels depend on the ratio of the Zeeman splitting to the cyclotron gap, r ≡ Ez/Ec2. In this case all the Landau levels are spaced. For a 2D system with a carrier density p, the number of filled
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