The interplay between quantum Hall ordering and spontaneously broken "internal" symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. Here we develop a theory of broken-symmetry quantum Hall states, applicable to a class of multi-valley systems, where the symmetry at issue is a point group element that combines a spatial rotation with a permutation of valley indices. The anisotropy of the dispersion relation, generally present in such systems, favors states where all electrons reside in one of the valleys. In a clean system, the valley "pseudo-spin" ordering, or spatial nematic ordering, occurs via a finite temperature transition. In weakly disordered systems, domains of pseudo-spin polarization are formed, which prevents macroscopic valley and nematic ordering; however, the resulting state still asymptotically exhibits the QHE. We discuss the transport properties in the ordered and disordered regimes, and the relation of our results to recent experiments in AlAs.
We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin polarized, $C_{3z}$-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin polarized, nematic insulator states are in the quantum valley Hall phase by virtue of the nontrivial…
Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantu…
The interplay between strong correlations and non-trivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of t…
We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moiré flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, includin…
We study the the interplay between spontaneously broken valley symmetry and spatial disorder in multivalley semiconductors in the quantum Hall regime. In cases where valleys have anisotropic electron dispersion a previous long-wavelength analysis [Phys. Rev. B 82, 035428 (2010)] identified two new phases exhibiting the QHE. The first is the quantum Hall Ising nematic (QHIN), a phase with long-range orientational order manifested in macroscopic transport anisotropies. The second is the quantum Hall random-field paramagnet (QHRFPM) that emerges when the Ising ordering is disrupted by quenched di…
Spontaneous Breaking of the SU(3) Flavor Symmetry in a Quantum Hall Valley Nematic
ENS, Université PSL, CNRS, Sorbonne Université（巴黎高等师范学院，巴黎文理研究大学，法国国家科学研究中心，索邦大学）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Chungnam National University（忠南国立大学）；National Technical University “KhPI”（哈尔科夫国立理工大学）；Johannes Kepler Universität（约翰内斯·开普林大学）；Université Paris-Saclay, CNRS, CEA（巴黎萨克雷大学，法国国家科学研究中心，法国原子能和替代能源委员会）
Modeling and simulation studies using a high-order Landau-de Gennes type model for the direct isotropic/smectic-A liquid crystal transition are presented showing the existence of meta-stable nematic pre-ordering under certain conditions, in agreement with experimental observations (Tokita, M. et al. Macromolecules 2006, 39, 2021-2023)
We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors $ν_G=-2+n/3$ $(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $SU(4)$ symmetric limit. For all the fractions we study there are two-component states for which the competing phases are generalizations of those occurring at neutrality $ν_G=0$. They…
Nematic quantum fluids with wavefunctions that break the underlying crystalline symmetry can form in interacting electronic systems. We examine the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope shows that a combination of local strain and many-body Coulomb interactions lift the six-fold Landau level (LL) degeneracy to form three valley-polarized quantum Hall states. We image the resulting anisotropic LL wavefunctions and show that they have a different orientation for each…
We study a cluster of quantum dots defined within silicene that host confined electron states with spin and valley degrees of freedom. Atomistic tight-binding and continuum Dirac approximation are applied for few-electron system in quest for spontaneous valley polarization driven by inter-dot tunneling and electron-electron interaction, i.e. a valley counterpart of itinerary Nagaoka ferromagnetic ordering recently identified in GaAs square cluster of quantum dots with three excess electrons [P. Dehollain, {\it et al.}, Nature {\bf 579}, 528 (2020)]. We find that for Hamiltonian without intrins…
We explore the optical birefringence of the nematic binary mixtures 6CB$_{1-x}$7CB$_x$ ($0~\le~x~\le~1$) imbibed into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of $3.4~\le~R~\le 21.0$ nm. The results are compared with the bulk behavior and analyzed with a Landau-de-Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field $σ<1/2$) or continuously (overcritical regime, $σ>1/2$), but in both cases with a characteristic paranematic pr…
Two-dimensional multi-valley electronic systems in which the dispersion of individual pockets has low symmetry give rise to quantum Hall ferroelectric and nematic states in the presence of strong quantising magnetic fields. We investigate local signatures of these states arising near impurities that can be probed via Scanning Tunnelling Microscopy (STM) spectroscopy. For quantum Hall ferroelectrics, we demonstrate a direct relation between the dipole moment measured at impurity bound states and the ideal bulk dipole moment obtained from the modern theory of polarisation. We also study the many…
A number of strongly correlated heavy fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions near certain (three) points of the surface Brillouin zone, hereafter referred to as the valleys. In strong perpendicular magnetic fields, the conical Dirac dispersions of these surface states quench onto three sets of Landau levels and we predict various possible hierarchies of incompressible quantum Hall states on the surface of hexaborides. In addition, we ad…
Recent magneto-transport experiments have provided compelling evidence for the presence of an energetically isolated threefold Q-valley degeneracy in few-layer transition metal dichalcogenides. We study the flavor SU(3) symmetry breaking when each Landau level triplet is one-third filled or empty and predict that a pure flavor nematic phase and a flavorless charge-density-wave phase will occur respectively below and above a critical magnetic field. Surprisingly, electrons carry flavor-dependent electric dipole moments even at zero magnetic field, rendering the nematics ferroelectric, allowing …
Valley-polarized quantum Hall states in graphene are described by a Heisenberg O(3) ferromagnet model, with the ordering type controlled by the strength and sign of valley anisotropy. A mechanism resulting from electron coupling to strain-induced gauge field, giving leading contribution to the anisotropy, is described in terms of an effective random magnetic field aligned with the ferromagnet z axis. We argue that such random field stabilizes the XY ferromagnet state, which is a coherent equal-weight mixture of the $K$ and $K'$ valley states. Other implications such as the Berezinskii-Kosterli…
Electrons are offered a valley degree of freedom in presence of particular lattice structures. Manipulating valley degeneracy is the subject matter of an emerging field of investigation, mostly focused on charge transport in graphene. In bulk bismuth, electrons are known to present a threefold valley degeneracy and a Dirac dispersion in each valley. Here we show that because of their huge in-plane mass anisotropy, a flow of Dirac electrons along the trigonal axis is extremely sensitive to the orientation of in-plane magnetic field. Thus, a rotatable magnetic field can be used as a valley valve…
We explore the nematic ordering of the rod-like liquid crystals 5CB and 6CB, embedded into parallel-aligned nanochannels in mesoporous silicon and silica membranes as a function of mean channel radius (4.7<=R <=8.3 nm), and thus geometrical confinement strength, by optical birefringence measurements in the infrared region. The orientational order inside the nanochannels results in an excess birefringence, which is proportional to the nematic order parameter. It evolves continuously upon cooling with a precursor behavior, typical of a paranematic state at high temperatures. These observations a…
A high-resolution dielectric and calorimetric study of the isotropic (I) to nematic (N) phase transition of carbon nanotube (CNT) dispersed liquid crystal (LC) functional composites as a function of CNT concentration is reported. The evolution of the I-N phase transition, the temperature dependence of local nematic ordering formed by dispersed CNTs in the LC media and the transition enthalpy were coherently monitored. Anisotropic CNTs induce local deformation to the nematic director of LC and form lyotropic pseudo-nematic phase in the LC media. Results clearly indicate the dramatic impact of d…
The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using first-principles calculations, we show that a 2D hexagonal triphenyl-lead lattice composed of only main group elements is susceptible to a magnetic instability, characterized by a considerably more stable antiferromagnetic (AFM) insulating state rather than the topologically nontrivial quantum spin Hall state proposed recently. Even though this AFM phase is …
