At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous interlayer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry ±e/2 electrical charge and vortexantivortex pairs can be neutral or carry charge ±e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the LandauGinzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation.
Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as characteristic for two-dimensional (2D) electronic systems, and its many aspects can be understood without invoking electron-electron interaction. The intriguing possibility of generalizing QHE to three-dimensional (3D) systems was proposed decades ago, yet it remains elusive experimentally. Here, we report for the first time clear experimental evidence for the 3D QHE, observed in bulk ZrTe5 crystals. Owing to the extremely high sample quality, the extreme quantum limit with only the lowest Landau level occupied can be achieved by an applied magnetic field as low as 1.5 T. Remarkably, in this regime, we observe a dissipationless longitudinal resistivity ≅ accompanied with a well-developed Hall resistivity plateau = ( ± . ) ( , ) , where , is the Fermi wavelength along the field direction ( axis). This striking result strongly suggests a Fermi surface instability driven by the enhanced interaction effects in the extreme quantum limit. In addition, with further increasing magnetic field, both and increase dramatically and display an interesting metal-insulator transition, representing another magnetic field driven quantum phase transition. Our findings not only unambiguously reveal a novel quantum state of matter resulting from an intricate interplay among dimensionality, interaction, and symmetry breaking, but also provide a promising platform for further exploration of more exotic quantum phases and transitions in 3D systems.Since its discovery in 1980, the QHE has been established and well understood in a variety of 2D electron systems, including the traditional 2D electron gas 1,2 , and 2D materials like graphene 3,4 , etc. The hallmark of QHE is that the Hall conductivity takes precisely quantized values as 2 /ℎ while the longitudinal conductivity vanishes 1,2 . Here, the prefactor is the filling factor which counts the number of filled Landau levels, is the elementary charge, and ℎ is Plank's constant. Soon after its
Graphene exhibits quantum Hall ferromagnetism in which an approximate SU (4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU (4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU (4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge ±1 for any integer filling, and that skyrmions are the lowest energy charged excitations for graphene Landau level index |n| ≤ 3. We also show that the skyrmion lattice states which occur near integer filling factors support four gapless collective mode branches in the presence of full SU (4) symmetry. Comparisons are made with the more familiar SU (2) quantum Hall ferromagnets studied previously.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.