The original, classical Hall e ect was discovered in 1879 by Edwin Hall. The discovery of the quantum hall effect has proven that topology is an imperative element of the quantum description of condensed matter systems. In this Viewpoint, physicists reflect on how the QHE has influenced their research. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have ...Read More. von Klitzing, K., Chakraborty, T., Kim, P. von Klitzing, Klaus ; Chakraborty, Tapash ; Kim, Philip. Daria smirnova received her Ph.D. in Physics in 2016 from the australian National university, where she currently holds a prestigious Discovery early Career research Fellow position supported by the australian research Council. T1 - 40 years of the quantum Hall effect. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. Figure 5: Bulk Fermi surfaces (FSs) constructed by quantum oscillations and calculations. For example, what can such deep networks compute? The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. Abstract. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. Quantum Hall effect in a bulk antiferromagnet EuMnBi 2 with magnetically confined two-dimensional Dirac fermions Hidetoshi Masuda,1* Hideaki Sakai,1,2*† Masashi Tokunaga,3 Yuichi Yamasaki,4,5 Atsushi Miyake,3 Junichi Shiogai,6 Shintaro Nakamura,6 Satoshi Awaji,6 Atsushi Tsukazaki,6 Hironori Nakao,7 Youichi Murakami,7 Taka-hisa Arima,5,8 The quantum Hall effect The discovery of the quantised Hall effect in 1980 won von Klitzing the 1985 Nobel prize.. Graphene samples whose lateral size ∼10 μm were fabricated into mesoscopic devices for electrical transport measurement in magnetic fields. (a) Existence of Fermi arcs in the Fermi surface of the surface band structure. 2005-03-01. The groundbreaking discovery of an optical version of quantum hall effect (QHE), published today in Physical Review X, demonstrates the leadership of Rensselaer in this vital research field. Over the past 40 years, the QHE has inspired new theories and led to experimental discoveries in a range of fields going beyond solid-state electronics to photonics and quantum entanglement. Adapted from Reference 54 with permission. (a) Consider a finite data set of P points (black dots) drawn from a ground truth linear function f* plus noise. The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. Two years after von Klitzing’s discovery, Störmer and Tsui were studying the quantum Hall effect, using extremely high-quality gallium arsenide-based samples that were made by Bell Labs scientist Arthur Gossard. The main conditions for this phenomenon to be observed are extremely low temperatures and the presence of a s… Topological Dirac or Weyl semimetals show linear dispersion around ...Read More. In 1980 at the Grenoble High Magnetic Field Laboratory in France, Klaus von Klitzing was studying the Hall conductance of a two-dimensional electron gas at very low temperatures. NASA Astrophysics Data System (ADS) Jimenez, Edward; Moya, Douglas. The superconducting qubit modality has been used to demonstrate prototype algorithms in the ...Read More. This remarkable fact requires some explanation. Based on ab initio calculations, here, we propose an intrinsic QAH phase in the Mn–dicyanoanthracene (DCA) Kagome lattice. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. Wang, Simon Gustavsson, William D. OliverVol. Figure 2: Schematics of Fermi arcs and the chiral anomaly effect. Figure 7: The global phase diagram of conductance tensor is constructed by (a) varying gate voltage for different magnetic fields (29) and (b) tilting magnetic fields (32). Quantum Hall Effect Emergence in the Fractional Quantum Hall Effect Abstract Student Luis Ramirez The experimental discovery of the fractional quantum hall effect (FQHE) in 1980 was followed by attempts to explain it in terms of the emergence of a novel type of quantum liquid. a quantized mixed-electro-spin Hall conductance). Figure 1: Two-terminal resistance of a silicon field-effect transistor at low temperatures (T=1.6 K) and fixed magnetic field B=10 Tesla. Her research interests include topological photonics, nonlinear nanophotonics and multipolar electrodynamics. semiconductor, magnetoresistance, two-dimensional electron system, quantum Hall effect, metrology, autobiography, Yasaman Bahri, Jonathan Kadmon, Jeffrey Pennington, Sam S. Schoenholz, Jascha Sohl-Dickstein, Surya GanguliVol. This remarkable fact requires some explanation. The discovery of the QSHE spurred active searches for the QAHE. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. / von Klitzing, Klaus; Chakraborty, Tapash; Kim, Philip; Madhavan, Vidya; Dai, Xi; McIver, James; Tokura, Yoshinori; Savary, Lucile; Smirnova, Daria; Rey, Ana Maria; Felser, Claudia; Gooth, Johannes; Qi, Xiaoliang. This means that electronics and technology using quantum mechanics in the future will be more energy-efficient and powerful. This site requires the use of cookies to function. Figure 3: Schematic representation of a quantum simulation system. We observed Shubnikov–de Haas oscillation and the quantum Hall effect in a high-mobility two-dimensional electron gas in polar ZnO/Mg x Zn1– x O heterostructures grown by laser molecular beam epitaxy. By continuing you agree to the use of cookies, University of Illinois at Urbana-Champaign data protection policy, University of Illinois at Urbana-Champaign contact form. The realizations of the QAH effect, however, are experimentally challengeable. These surface states are protected by topological invariants and host spin-momentum locked A new type of quantum fluid A year after the discovery of the fractional quantum Hall effect, Laughlin offered a theoretical explanation. In this Viewpoint, physicists reflect on how the QHE has influenced their research. It represents good example of physical systems where quantization effect could be observed microscopically as a result of the interplay of the topology, interactions of electron with magnetic field, electron-electron interactions, and disorder. The Hall resistance in ferromagnetic conductors is composed of the ordinary Hall effect proportional to the magnetic field and the anomalous Hall effect (AHE) proportional to the magnetization of the sample; the QAHE is the quantized version of this AHE. Investigating the conductance properties of two-dimensional electron gases at very low temperature and high magnetic fields, his group obtained curious results: The Hall conductance of such a system plotted as a function of the ratio The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. Please see our Privacy Policy. The Hall effect had been known since 1879, but in 1980 the German physicist Klaus von Klitzing, while observing the effect at very low temperatures and under extremely strong magnetic fields, discovered that as the strength of the applied magnetic field is increased, the corresponding change in the voltage of the deflected current (the Hall resistance) occurs in a series of steps or jumps that are proportional to … Observation of Quantum Hall effect in an ultra-thin (Bi 0.53Sb 0.47) 2Te 3 film Wenqin Zou,1,a) Wei Wang,2,a) Xufeng Kou,3 Murong Lang,3 Yabin Fan,3 Eun Sang Choi,4 Alexei V. Fedorov,5 Kejie Wang,2 Liang He,2,3,b) Yongbing Xu,2,b) and Kang. 11, 2020, Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. Klaus von Klitzing, Tapash Chakraborty, Philip Kim, Vidya Madhavan, Xi Dai, James McIver, Yoshinori Tokura, Lucile Savary, Daria Smirnova, Ana Maria Rey, Claudia Felser, Johannes Gooth, Xiaoliang Qi, Research output: Contribution to journal › Article › peer-review. Quantum Hall effect is a quantum mechanical concept that occurs in a 2D electron system that is subjected to a low temperature and a strong magnetic field. This project seeks to articulate a notion of emergence that is In 1998, Robert Laughlin, Horst Störmer, and Daniel Tsui won the physics Nobel prize for the discovery of the fractional quantum Hall effect [64]. Figure 4: Fermi arcs from angle-resolved photoemission spectroscopy (ARPES) and theoretical calculations. The discovery of the quantized and fractional Quantum Hall Effect phenomena is among the most important physics findings in the latter half of this century. A century later, the Hall effect was revived as a source of astonishing new physics. The electron density could be controlled in a range of 0.7 × 1012 to 3.7 × 1012 per square centimeter by tuning the magnesium content in the barriers and the growth polarity. N1 - Funding Information: A quantum Hall effect in three dimensions is a long-sought phase of matter and has inspired many efforts and claims. Figure 6: (a) The Hall resistance and (b) longitudinal resistance are measured as functions of magnetic fields for different gate voltages in Cr-doped (Bi,Sb)2Te3 films (28). The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. The Quantum Hall effect (QHE) is the observation of the Hall effect in a two-dimensional electron gas system (2DEG) such as graphene and MOSFETs. Figure 3: Copy of my notes from the night of February 5, 1980. Figure 3: Crystal structure and bulk band structure. The quantum theory of atomic structure, which is the concept that energy is available in discrete, whole packets at the subatomic level, had predicted the quantum Hall effect as early as 1975. 2. title = "40 years of the quantum Hall effect". The fractional quantum Hall effect is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e 2 / h {\displaystyle e^{2}/h}. Over the past 40 years, the QHE has inspired new theories and led to experimental discoveries in a range of fields going beyond solid-state electronics to photonics and quantum entanglement. The Fermi surface (FS) of TaP by (a) ARPES and (b) calculations agree very well. Today, more than 20 years after the discovery of the quantum Hall effect, the number of publications in this field, at more than one paper per day, is still increasing. The discovery of the quantum Hall effect (QHE) 1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. The last decade has seen the discovery of topological insulators, materials that insulate in bulk yet feature conductive surface states. The 1980 discovery of the quantum version was a surprise whose theoretical basis still contains some puzzles. The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of /.It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. Their surprising discovery … Abstract - Figures Preview. The Quantum Hall Effects: Discovery, basic theory and open problems. N2 - The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The topologies of a TI and that of a WSM/DSM originate from similar inverted band structures. Quantum Hall Effect Emergence in the Fractional Quantum Hall Effect Abstract Student Luis Ramirez The experimental discovery of the fractional quantum hall effect (FQHE) in 1980 was followed by attempts to explain it in terms of the emergence of a novel type of quantum liquid. abstract = "The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The mathematical expression for quantum hall effect is as follows: The last decade has seen the discovery of topological insulators, materials that insulate in bulk yet feature conductive surface states. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. The birthday of the quantum Hall effect (QHE) can be fixed very accurately. Figure 2: (a) The honeycomb lattice with complex next-nearest-neighbor hopping. Quantum Hall effect 2.1. K. Das Gupta IIT Bombay Nanoscale Transport 2016, HRI (Feb 24 & 25, 2016) Topics. ... Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. The 1998 Nobel … In 1980, Klaus von Klitzing received the Nobel Prize in Physics for his discovery that the quantum Hall effect was indeed exactly discrete, meaning that the electrons could exist only in sharply defined levels of … It also poses, but perhaps also answers, the question of why a new monograph entitled 'The Quantum Hall Effect' is a highly desirable addition to the literature. This will provide a useful background for our discussion of the quantum Hall e ect. The 1980 discovery of the quantum Hall effect kicked off the study of topological orders, electronic states with “protected” patterns of long-range quantum entanglement that … The Quantum Hall effect has been discovered by von Klitzing in Germany and by Tsui, Stormer and Gossard in U.S.A. Robert Laughlin also in U.S.A. explained the quantization of Hall current by using “flux quantization” and introduced incompressibility to obtain (a) Cubic unit cell of LnPtBi (Ln=Y, Gd, or Nd). The groundbreaking discovery of an optical version of quantum hall effect (QHE), published today in Physical Review X, demonstrates the leadership of Rensselaer in this vital research field. AB - The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The discovery of the quantum Hall effect (QHE) was the result of systematic measurements on the two-dimensional electron gas (2DEG) systems, where the electrons are free to propagate in the x-y plane but are confined by some potential U(z) along the z-direction. INTRODUCTION. The discovery of the quantum Hall effect was enabled by the invention of the MOSFET (metal-oxide-semiconductor field-effect transistor) by Mohamed Atalla and Dawon Kahng in 1959. note = "Funding Information: Daria smirnova received her Ph.D. in Physics in 2016 from the australian National university, where she currently holds a prestigious Discovery early Career research Fellow position supported by the australian research Council. The upper part is a sketch of the sample holder with the contacts for source S, drain D, gate G, and substrate bias VSB. It was the night of the 4th to the 5th of February 1980 at around 2 a.m. during an experiment at the High Magnetic Field Laboratory in Grenoble. The quantum theory of atomic structure, which is the concept that energy is available in discrete, whole packets at the subatomic level, had predicted the quantum Hall effect as early as 1975. QHE is a difference in mechanical voltage that is created when a two-dimensional semiconductor is placed in a large magnetic field. Some of the successful explanations of the effect are summarized in … Figure 7: Crystal and band structures of Heusler Weyl semimetals. L. Wang3,b) 1National Lab of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China 40 years of the quantum Hall effect. This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed matter science. According to his theory the low temperature and the powerful magnetic field compel the electron gas to condense to form a new type of quantum fluid. The discovery and the explanation of the fractional quantum Hall effect in 1982-83 may be said to represent an indirect demonstration of the new quantum fluid and its fractionally charged quasiparticles. Together they form a unique fingerprint. It also uses cookies for the purposes of performance measurement. The 2+1D topological insulator is defined by Kane-Mele This allows researchers to explore quantum effects by operating high-purity MOSFETs at liquid helium temperatures. Similar to the quantum Hall effect, the QAH effect harbors dissipationless chiral edge states, thus providing an energy-efficient platform for state-of-the-art applications in spintronics9, 10 and quantum computing11, 12. Econophysics: from Game Theory and Information Theory to Quantum Mechanics. INTRODUCTION. Blue and red FSs correspond to electron and hole pockets, respectively. After a brief explanation of the quantization of a two-dimensional electron gas in high magnetic fields the background of the discovery of the quantum Hall effect is given. The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. Publication: Metrologia. ARTICLE OPEN Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions Jinbo Pan1,6, Jiabin Yu2,3,6, Yan-Fang Zhang1,4,5, Shixuan Du4, Anderson Janotti 5, Chao-Xing Liu 2 and Qimin Yan 1 Recent years have witnessed tremendous success in the discovery … The phenomenon is now called the integral quantum Hall effect For his discovery, von Klitzing received the 1985 Nobel Prize in Physics. Figure 6: Crystal structure and schematics of Fermi arcs for MoTe2. The discovery of quantum Hall effect in two-dimensional (2D) electronic systems inspired the topological classifications of electronic systems1,2. Figure 2: Analogies for the error landscape of neural networks. Dive into the research topics of '40 years of the quantum Hall effect'. (a,b) TaAs FS. Here, the “Hall conductance” undergoes quantum Hall transitions to take on the quantized values at a certain level. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The quantum anomalous Hall (QAH) phase is a topological state of matter characterized by a nonzero quantized Hall conductivity without an external magnetic field. Klaus von Klitzing discovered the integer quantum Hall effect in 1980 and won the physics Nobel prize for it in 1985 [63]. The discovery of integer Quantum Hall effect. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. Several research groups have recently succeeded in observing these new particles directly (see reference list). This personal review demonstrates that condensed matter physics ...Read More. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. National Physical Laboratory (UK) The 1980 discovery of the quantum Hall effect kicked off the study of topological orders, electronic states with “protected” patterns of long-range quantum entanglement that are remarkably robust. On the other hand, the discovery of the fractional quantum Hall effect brought along the development of the theory of strongly correlated electron systems. (a) The layered crystal structure (Td phase) with inversion symmetry breaking. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. Its practical significance, however, was immediately obvious, and today the quantum Hall effect, recognized in the 1985 Nobel Prize in physics, is the basis of the standard definition of the unit of electrical resistance, the ohm. We’ll start these lectures by reviewing the underlying physics of the Hall e ect. magnetism and exhibits quantized Hall resistance and zero longitudinal resistance. (a) A schematic picture of the typical structure of critical points of smooth random Gaussian landscapes. It also poses, but perhaps also answers, the question of why a new monograph entitled 'The Quantum Hall Effect' is a highly desirable addition to the literature. The inverse of the von Klitzing constant is equal to half that of the conductance quantum … The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc­ tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. 11, 2020, The recent striking success of deep neural networks in machine learning raises profound questions about the theoretical principles underlying their success. Figure 1: Deep neural expressivity through transient chaos. This effect is at present the subject of extensive experimental and … The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. How can we train them? Over the past 40 years, the QHE has inspired new theories and led to experimental discoveries in a range of fields going beyond solid-state electronics to photonics and quantum entanglement. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. The groundbreaking discovery of an optical version of quantum hall effect (QHE), published today in Physical Review X, demonstrates the leadership of … This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed … (b) View of the structure showing Ln-Pt-Bi–type layers stacked along the [111] axis. The Discovery of the Quantum Hall Effect Landwehr, G. Abstract. First published online as a Review in Advance on December 21, 2016 The MOSFET (metal-oxide-semiconductor field-effect transistor), invented by Mohamed Atalla and Dawon Kahng at Bell Labs in 1959, enabled physicists to study electron behavior in a nearly ideal two-dimensional gas. Highlighted is t... Chao-Xing Liu, Shou-Cheng Zhang, Xiao-Liang QiVol. Superconducting Qubits: Current State of Play, Quantum Hall Effect: Discovery and Application, The Quantum Anomalous Hall Effect: Theory and Experiment, Control, Robotics, and Autonomous Systems, Organizational Psychology and Organizational Behavior, https://doi.org/10.1146/annurev-conmatphys-031016-025148. Here’s the set-up. The discovery of the quantum hall effect has proven that topology is an imperative element of the quantum description of condensed matter systems. Klitzing won the 1985 Nobel Prize in Physics because the discovery of the quantum Hall effect (QH) 100 years later [6]. The quantum Hall effect (QHE) with quantized Hall resistance plateaus of height h/νe 2 was first observed in two-dimensional (2D) electron systems in 1980 [].Here, h is Planck's constant, ν is Landau filling factor and e is electron charge. Annual Review of Condensed Matter Physics, Vol. (a) The noncentrosymmetric crystal lattice of TaAs-family compounds. Figure 1: Six members in the family of Hall effects. Figure 2: Copy of the experimental curves measured on February 5, 1980, at the High Magnetic Field Laboratory in Grenoble, which led to the discovery of the quantized Hall resistance. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. 8:13-30 (Volume publication date March 2017) It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. Figure 1: The topological insulator (TI) and Weyl semimetal (WSM) or Dirac semimetal (DSM). Electricity found in a quantum Hall system can be conducted without energy being lost. Figure 3: Signal propagation predicts trainability. In particular, it disclosed the actual existence of various concepts which had previously been merely products of theoretical imagination. (OpenGovAsia) Researchers from the Singapore University of Technology and Design (SUTD) and scientists from across the world have made a discovery on the “Quantum Hall Effect” (QHE). Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. The quantum theory of atomic structure, which is the concept that energy is available in discrete, whole packets at the subatomic level, had predicted the quantum Hall effect as early as 1975. After the discovery of the Hall effect, the German physicist K.V. This was the discovery of the fractional quantum Hall effect. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. Figure 4: (a) Evolution of band structure and edge states upon increasing the spin splitting for Mn-doped HgTe quantum wells. Here we always keep the parameter B>0. The quantum Hall effect (QHE) with quantized Hall resistance plateaus of height h/νe 2 was first observed in two-dimensional (2D) electron systems in 1980 [].Here, h is Planck's constant, ν is Landau filling factor and e is electron charge. The quantum Hall effect, discovered unexpectedly 35 years ago, is now the basis for defining the unit of electrical resistance. How does information ...Read More. Band inversion occurs for one species of spin but not for the other. 8, 2017, Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Quantum Hall Effect 'Reincarnated' in 3D Topological Materials May 18, 2020 — Physicists have found surprising evidence of a link between the 2D quantum Hall effect … The quantum anomalous Hall (QAH) phase is a topological state of matter characterized by a nonzero quantized Hall conductivity without an external magnetic field. Today, more than 20 years after the discovery of the quantum Hall effect, the number of publications in this field, at more than one paper per day, is still increasing. publisher = "Springer Nature Switzerland AG", https://doi.org/10.1038/s42254-020-0209-1. Von Klitzing has through his experiment shown that the quantised Hall effect has fundamental implications for physics. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. 8, 2017. The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall (QAH) effect, axion electrodynamics, and Majorana fermions. 7, 2016, The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. 25,812.807449(86) Ω, is named in honor of von Klitzing's discovery of the quantum Hall effect, and is listed in the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty. author = "{von Klitzing}, Klaus and Tapash Chakraborty and Philip Kim and Vidya Madhavan and Xi Dai and James McIver and Yoshinori Tokura and Lucile Savary and Daria Smirnova and Rey, {Ana Maria} and Claudia Felser and Johannes Gooth and Xiaoliang Qi". This “new discovery” further confirmed the fact that electrons existed and can only exist in discrete energy levels. The research topic included the characterization of the electronic transport of silicon field effect transistors. The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. According to Bernevig-Zhang and Kane-Mele, quantum spin Hall effect refers to quantized transverse S z -spin current induced by force acting on electric charges (i.e. Figure 3: Illustration of (a) normal band structure, (b) band structure at the critical point, and (c) inverted band structure. The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. Researchers have discovered a uniquely quantum effect in erasing information that may have significant implications for the design of quantum computing chips. It is a simple consequence of the motion of charged particles in a magnetic eld. Figure 5: Illustration of the Hall conductance in a ferromagnet–topological insulator heterostructure. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect.