We study effects of disorder on the integer quantized Hall effect within the screening theory, systematically. The disorder potential is analyzed considering the range of the potential fluctuations. Short range part of the single impurity potential is used to define the conductivity tensor elements within the self-consistent Born approximation, whereas the long range part is treated self-consistently at the Hartree level. Using the simple, however, fundamental Thomas-Fermi screening, we find that the long range disorder potential is well screened. While, the short range part is approximately unaffected by screening and is suitable to define the mobility at vanishing magnetic fields. In light of these range dependencies we discuss the extend of the quantized Hall plateaus considering the "mobility" of the wafer and the width of the sample, by re-formulating the Ohm's law at low temperatures and high magnetic fields. We find that, the plateau widths mainly depend on the long range fluctuations of the disorder, whereas the importance of density of states broadening is less pronounced and even is predominantly suppressed. These results are in strong contrast with the conventional single particle pictures. We show that the widths of the quantized Hall plateaus increase with increasing disorder, whereas the level broadening is negligible.
We show that an energy gap is induced in graphene by light-matter coupling to a circularly polarized photon mode in a cavity. Using many-body perturbation theory we compute the electronic spectra which exhibit photon-dressed sidebands akin to Floquet sidebands for laser-driven materials. In contrast with Floquet topological insulators, in which a strictly quantized Hall response is induced by light only for off-resonant driving in the high-frequency limit, the photon-dressed Dirac fermions in the cavity show a quantized Hall response characterized by an integer Chern number. Specifically for g…
We present precision measurements of the fractional quantized Hall effect where the quantized resistance $R^{[1/3]}$ in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance $R^{[2]}$, represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of $1 - (5.3 \pm 6.3) 10^{-8}$ (95% confidence level) was obtained for the ratio $(R^{[1/3]}/6R^{[2]})$. Thi…
Recently,a half-quantized Hall conductance (HQHC) plateau is experimentally observed in a semi-magnetic topological insulator heterostructure. However,the heterostructure is metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators.In this work,we systematically study the surface transport of the semi-magnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process.In particular, we reveal that the HQHC is directly related to the half-quantized chiral cur…
The quantum Hall effect (QHE) is a topologically protected phenomenon which has been observed in various systems. In experiments, the size of Hall bar device to realize the QHE is generally much larger than the phase coherence length, in which the quantum coherence of electrons is destroyed. Here, we theoretically study the influence of dephasing effect on the quantized Hall (QH) plateaus. We find that the QH plateau disappears in perfectly quantum coherent systems if the coupling between leads and central region is imperfect. The Hall resistance is very large and strongly oscillates instead o…
The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the Hofstadter or TKNN problem and in the weak field limit the tight binding energy eigenvalue equation is indeed given by Harper Hofstadter hamiltonian. We show that due to its magnetic translational symmetry the Hall conductivity can be identified as a topological invariant and hence quantized. We thus extend the idea of Quantum Hall Effect to magnetically modulate…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
In condensed matter physics, one of the major topics is to find out and classify interesting novel topological matters and phenomena. Topologically nontrivial systems can also be achieved by using periodical driving fields. On the other hand, ratchet effect can be used to collect useful work from fluctuations or realize directed transport in periodically-driven systems. Here, we promote a dimer chain by applying two mutually-perpendicular ac electric fields, and obtain an effective two-dimensional Hamiltonian in the low-frequency regime. We thereby derive quantum Floquet anomalous Hall (QFAH) …
Half-quantized anomalous Hall conductance in topological insulator/ferromagnet van der Waals heterostructures
Linnaeus University（林奈大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（北欧原子理论中心，皇家理工学院和斯德哥尔摩大学）；University of Connecticut（康涅狄格大学）；University of Texas at El Paso（德克萨斯大学埃尔帕索分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
In this paper we propose that, quantized and nearly half-quantized intrinsic anomalous Hall effect can be induced by in-plane external magnetic field through the Zeeman coupling in non-magnetic 2D systems with sizeable spin-orbital coupling but without two-fold rotational symmetry. An analytical result is derived for 2D electron gas model with $C_{3v}$ symmetry. Based on the $\boldsymbol{k\cdot p}$ Hamiltonian derived from first principle calculations, we find that quantized and nearly half-quantized conductance can be observed in $\mathrm{Sb_2Te_3}$ thin film in the clean limit with strong in…
Half-quantized Hall Plateaus in the Confined Geometry of Graphene
Aalto University（阿尔托大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；National Institute for Materials Science（国立材料研究所）
A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of …
In this work, limiting factors for developing metrologically useful arrays from epitaxial graphene on SiC are lifted with a combination of centimeter-scale, high-quality material growth and the implementation of superconducting contacts. Standard devices for metrology have been restricted to having a single quantized value output based on the $ν$ = 2 Landau level. With the demonstrations herein of devices having multiple outputs of quantized values available simultaneously, these versatile devices can be used to disseminate the ohm globally. Such devices are designed to give access to quantize…
