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arXiv:2312.10791 · Physical review. B./Physical review. B

Symmetry breaking in zero-field two-dimensional electron bilayers

Tessa Cookmeyer, S. Das Sarma

Published Mar 27, 2024• 4 citations
arXivHTMLPDF

Abstract

We theoretically consider bilayers of two-dimensional (2D) electron gases as in semiconductor quantum wells, and investigate possible spontaneous symmetry breaking transitions at low carrier densities driven by interlayer Coulomb interactions. We use a self-consistent technique implementing mean-field truncations of the interacting four-fermion terms, and find a U(1) layer symmetry breaking transition at low carrier densities where the individual layer identities are lost leading to an effective pseudospin XY ferromagnet in the 2D plane. Our results validate earlier theoretical studies using simpler restricted Hartree-Fock techniques, and establish the pseudospin XY ferromagnet as a possible low-density symmetry broken phase of 2D bilayers.

DOI
10.1103/physrevb.109.115307

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We theoretically consider bilayers of two-dimensional (2D) electron gases as in semiconductor quantum wells, and investigate possible spontaneous symmetry breaking transitions at low carrier densities driven by interlayer Coulomb interactions. We use a self-consistent technique implementing mean-field truncations of the interacting four-fermion terms, and find a U(1) layer symmetry breaking transition at low carrier densities where the individual layer identities are lost leading to an effective pseudospin XY ferromagnet in the 2D plane. Our results validate earlier theoretical studies using simpler restricted Hartree-Fock techniques, and establish the pseudospin XY ferromagnet as a possible low-density symmetry broken phase of 2D bilayers.
We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall (QH) regime of wide parabolic wells and zero width double well (bilayer) systems. Spin, isospin (associated with the layer index in the bilayer systems), and orbital dynamics all play important roles in the quantum phase transitions being studied. We propose a general class of variational wave functions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. In wide well systems at odd filling factors, we find a many-body state of broken parity symmetry for weak in-plane magnetic fields and an isospin skyrmion stripe phase, which simultaneously has isospin and charge modulation, for strong in-plane fields. In wide well systems at even filling factors, we find direct first order transitions between simple (un)polarized QH states, but also several many-body states that are only slightly higher in energy (within the Hartree-Fock theory) than the ground state in strong in-plane field region. We suggest that going beyond the approximations used in this paper one may be able to stabilize such many-body phases with broken symmetries (most likely the skyrmion stripe phase). In a bilayer system at the filling factor $\ensuremath{\nu}=4N\ifmmode\pm\else\textpm\fi{}1,$ where N is an integer, we obtain an isospin spiral stripe phase in addition to the known (in)commensurate phases and the stripe phase without isospin winding. We do not find a charge or spin density wave instability in the bilayer system at $\ensuremath{\nu}=4N+2,$ except for the known commensurate canted antiferromagnetic phase. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interest. We discuss the symmetry properties of our predicted quantum phase diagrams and give a unified picture of these novel many-body phases. We point out how quantum level crossing phenomena in many situations (tuned by the applied tilted magnetic field) may lead to interesting quantum phases and transitions among them.
We revisit the physics of electron gas bilayers in the quantum Hall regime (M ac D onald A. and E isenstein J., Nature , 432 (2004) 691; E isenstein J., Science , 305 (2004) 950), where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation of a BEC of excitons in the half-filled electron bilayers, where empty states play the role of holes. We discuss the fundamental difficulties with this scenario, and propose an alternative approach based on a treatment of the system as a pseudospin magnet. We show that the experimentally observed tunneling peak can be linked to the XY ferromagnet (FM) to Ising antiferromagnet (AFM) phase transition of the S = 1/2 XXZ pseudospin model, driven by the change in total electron density. This transition is accompanied by a qualitative change in the nature of the low-energy spin wave dispersion from a gapless linear mode in the XY-FM phase to a gapped, quadratic mode in the Ising AFM phase.
Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena. In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of interaction strengths, the ν= 4 bulk is unpolarized whereas the ν= 3 bulk is fully polarized. In the parameter space spanned by the interaction strength and width of the interface, we find two phases at the interface. Phase A has spin as a good quantum number, and the long-wavelength spin edge excitations are gapped. In phase B, spin rotation symmetry is spontaneously broken at the mean-field level. Using symmetry arguments we find the effective theory near the interface of phase B. This effective theory is known to have gapless long-wavelength spin excitations. In the second project, we study the ground state of a tunnel-decoupled double-layer graphene system when both layers are undoped. We find a simple Hamiltonian in the continuum limit from symmetries of the system. Using the Hartree-Fock approximation we find a state with inter-layer coherence with broken layer U(1) symmetry. This phase becomes magnetized in presence of a non-zero Zeeman field. A first-order phase transition can be driven from the ferromagnetic phase to the magnetized inter-layer coherent phase by increasing the Zeeman field. We predict the number of gapless modes in the bulk.
Quantum materials featuring both itinerant and localized degrees of freedom exhibit numerous exotic phases and transitions that deviate from the Ginzburg-Landau paradigm. This paper uses the composite operator formalism to examine the bilayer strongly correlated Hubbard model. We observe the spontaneous breaking of layer symmetry, where the electron density in one of the layer reaches half-filling, resulting in a layer selective Mott phase (LSMP). This broken symmetry phase becomes unstable at a critical average electronic density away from half-filling. Furthermore, significant layer differentiation persists up to a moderate interlayer hopping, beyond which the system abruptly transitions to a layer uniform phase. In the LSMP phase, the electrons in the two layers are weakly hybridized, resulting in a small Fermi surface. The volume of the Fermi surface jumps at the transition from the LSMP to the uniform phase. We also discuss the physical mechanisms leading to the collapse of the LSMP phase under different perturbations.
Abstract We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of d z 2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel–Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.
We present an exact diagonalization study of bilayer quantum Hall systems at filling factor nu = 2 in the spherical geometry. We find the high-Zeeman-coupling phase boundary of the broken symmetry canted antiferromagnet is given exactly by previous Hartree-Fock mean-field theories, but that the state's stability at weak Zeeman coupling has been qualitatively overestimated. In the absence of interlayer tunneling, degeneracies occur between total spin multiplets due to the Hamiltonian's invariance under independent spin rotations in top and bottom two-dimensional electron layers.