The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance takes on the quantized values where is the elementary charge and is Planck's constant. The integer quantum Hall effect is peculiar due to the zero energy Landau level. Created in 2006 to pursue theoretical and experimental studies of quantum physics in the context of information science and technology, JQI is located on UMD's College Park campus. The underlying physics is related to the particle - hole symmetry and electron–hole degeneracy at the zero energy level. Fig. (a) Edge states in graphene rolled into a cylinder (CNT), as in the Laughlin gedanken experiment. Mesoscale and Nanoscale Physics 1504, 1–17. Coincidence experiments have also been used to study quantum hall ferromagnetism (QHF) in strained Si channels with Δ2 valley degeneracy. The quantum Hall effect (QHE) is a quantisation of resistance, exhibited by two-dimensional electronic systems, that is defined by the electron charge e and Planck’s constant h. independent of the orientation of B with respect to the 2DEG. The quantum Hall effect (QHE), which was previously known for two-dimensional (2-D) systems, was predicted to be possible for three-dimensional (3-D) systems by Bertrand Halperin in 1987… consequently, the Δ3(N = 1, ↓) gap is greatly enhanced over the bare valley splitting (Fig. Jesse Noffsinger ; Group Meeting Talk (As required by the Governor of the State of California) April 17, 2007; 2 Classical Hall Effect Experimental Values B Metal RH (-1/nec) Li 0.8 Na 1.2 Rb 1.0 Ag 1.3 Be -0.2 Ex, jx VH Ey - - - - - - - - - - - - - - - - - - … The inset shows the Landau level diagram. Moreover, both slopes are higher than that of the bare valley splitting predicted by a band calculation at B = 0.56 The configurations below and above the υ = 3 coincidence differ in both the landau level indices and the spin orientation. For the discovery of these unexpected new quantum states in 1982, manifesting themselves in the fractional quantum Hall effect (FQHE), Dan C Tsui, Horst L Störmer, and Robert B Laughlin were honored with the Nobel prize in 1998. QHF can be expected when two energy levels with different quantum indices become aligned and competing ground state configurations are formed. The half-integer shift of Hall conductivity can be deduced straightforwardly where Hall conductivity for monolayer graphene is (Table 6.6): The degeneracy factor of g = 4 arises due to two contributed by valley and two by spin. Around υ = 1/2 the principal FQHE states are observed at υ=23,35 and 47; and the two-flux series is observed at υ=49,25 and 13. (1982), with f=1/3 and 2/3 the most prominent examples. More detailed studies were reported by the group of T. Okamoto, who employed a sample with a mobility of 480,000 cm² V− 1 s− 1.59 They measured the resistance along a Hall bar in a magnetic field that was tilted away from the normal to the 2DEG by an angle Ф. 15.6). For the discovery of this ‘fractional quantum Hall effect’ (FQHE), and its explanation, Dan C. Tsui, Horst L. Sto¨rmer, and Robert B. Laughlin were honored with the Nobel prize in 1998. Strong indications for QHF in a strained Si/SiGe heterostructure were observed58 around υ = 3 under the same experimental coincidence conditions as the aforementioned experiments regarding anomalous valley splitting. The three crossing levels are labeled θ1, θ2 and θC. The fractions f = {1/3, 2/3} are the most prominent ones. When this internal magnetic field is sufficiently large, the situation is similar to that of the externally applied field: the material may be insulating in the bulk and conduct electricity along the edges. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have ...Read More. (1995), has the disadvantage that at low magnetic fields it is not evident that Landau level mixing can be neglected (Kralik et al., 1995). There is no plateau at zero energy because it is the center of a Landau level, where states are extended and σxx≠0 (it is local maximum). A linear n-dependence was found for either configuration, though with significantly different slopes (Fig. In the following we will focus on the IQHE and, because there exist already many reviews in this field (Prange and Girvin, 1990; Stone, 1992; Janßen, 1994; Gerhardts, 2009), especially on recent experimental and theoretical progress in the understanding of the local distribution of current and Hall potential in narrow Hall bars. The FQHE is a manifestation of correlation effects among the charge carriers interacting in the two-dimensional system, which lead to the formation of new quantum states. Machine. A quantum twist on classical optics. Hydrostatic pressure has been used to tune the g-factor through zero in an AIGaAs/GaAs/AlGaAs modulation-doped quantum well with a well width of 6.8 nm (Maude et al., 1996). The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes certain quantum Hall transitions to take on the quantized values. The QHE and its relation to fundamental physical constants was discovered by von Klitzing (1980), who was honored with the Nobel prize in 1985. quantum-hall-effect adiabatic linear-systems. By continuing you agree to the use of cookies. Quantum Hall effects in graphene55,56 have been studied intensively. The Shubnikov-de-Haas oscillations are resolved down to a filling factor of υ = 36. 15.5. Note that we use here the common nomenclature of the ↓ spin state being anti-parallel to B, and therefore defining the energetically lower Zeeman state in the Si/SiGe material system with its positive g*; in Refs 55 and 56, spin labeling was reversed. However, the valley splitting is significantly different (by up to a factor of 3 for υ = 3) in the regions right and left of the coincidence regime. Edge states with positive (negative) energies refer to particles (holes). The data are consistent with s = 35 spin flips, although the spin gap is reduced somewhat more than the 50% predicted by Skyrmion theory. Due to a small standard uncertainty in reproducing the value of the quantized Hall resistance (few parts of 10−9 in the year 2003), its value was fixed in 1990, for the purpose of resistance calibration, to 25812.807 Ω and is nowadays denoted as the conventional von Klitzing constant RK−90. The quantum spin Hall state does not break charge … These measurements were collected at 1.3 K using liquid helium cooling, with a magnetic field strength up to 14 T [43]. But let's start from the classical Hall effect, the famous phenomenon by which a current flows perpendicular to an applied voltage, or vice versa a voltage develops perpendicular to a flowing current. The ratio of Zeeman and Coulomb energies, η = [(gμBB)/(e2/εℓB)] is indicated for reference. To clarify these basic problems, the QHE was studied in Si/SiGe heterostructures by several groups, who reported indications of FQHE states measured on a variety of samples from different laboratories.46–50 The most concise experiments so far were performed in the group of D. C. Tsui, who employed magnetic fields B of up to 45 T and temperatures down to 30 mK.51 The investigated sample had a mobility of 250,000 cm2 V−1 s−1 and an nMIT < 5 × 1010 cm− 2. Meanwhile, the availability of high-mobility Si/SiGe heterostructures has strongly reduced the performance gap to the III–V semiconductors. The expected experimental manifestations of Skyrmions are (1) a rapid spin depolarization around v = 1 and (2) a 50% reduction in the gap at v = 1 compared with the prediction for spin wave excitations. The peaks are the centers of Landau levels. Graphene surpasses GaAs/AlGaAs for the application of the quantum Hall effect in metrology. At each pressure the carrier concentration was carefully adjusted by illuminating the sample with pulses of light so that v = 1 occurred at the same magnetic field value of 11.6 T. For a 6.8-nm quantum well, the g-factor calculated using a five-band k.p model as described in Section II is zero for an applied pressure of 4.8 kbars. asked Dec 17 '12 at 15:30. This approach, however, turned out to be inconsistent with the experimental n-dependence. A considerable amount of experimental evidence now exists to support the theoretical picture of spin texture excitations: The spin polarization around v = 1 has been measured by nuclear magnetic resonance (Barrat et al., 1995) and by polarized optical absorption measurements (Aifer et al., 1996). These plateau values are described by |RH|=h/(ie2) where h is the Planck constant, −e the charge of an electron, and i an integer value, i=1, 2, 3,…. Interpreting recent experimental results of light interactions with matter shows that the classical Maxwell theory of light has intrinsic quantum spin Hall effect properties even in free space. In this experiment the thermally activated transport gap at filling factor v = 1 was measured for a number of different pressures between 0 and 8 kbars. When electrons in a 2D material at very low temperature are subjected to a magnetic field, they follow cyclotron orbits with a radius inversely proportional to the magnetic field intensity. The most important implication of the IQHE is its application in metrology where the effect is used to represent a resistance standard. 13.41(b). The factor g denotes the spin and valley degeneracy. The fractional quantum Hall effect was studied as the first phenomenon where anyons have played a significant role. This effect is shown in Fig. The edge state with n = 0 is not degenerate because it is shared by the two Dirac cones. Because of this kind of striking behaviour, the quantum Hall e ect has been a con- stant source of new ideas, providing hints of where to look for interesting and novel phenomena, most of them related to the ways in which the mathematics of topology Transport measurements, on the other hand, are sensitive to the charged large wave vector limit E∞=gμBB+e2π/2/єℓB. Therefore, on each edge, the Fermi energy between two Landau levels εn<εF<εn+1 crosses 2n + 1 edge states, hence, σxy=(2n+1)e2∕h per spin. Machine Machine. A consistent interpretation is based on electron–electron interaction, the energy contribution of which is comparable to the landau and spin-splitting energies in the coincidence regime. 56. here N is the landau level index, and (↓,↑) are the two spin orientations. Inspection of En=±ℏωcnn−1 shows that at, n = 0,1, energy is zero. Above 300 mK the resistance peak vanishes rapidly, which is indicative of the collapse of the Ising ferromagnetic domain structure. In monolayer and bilyer graphene, g = 4. conclude from the measured temperature dependence that it cannot dominate the breakdown of Ising ferromagnetism. Copyright © 2021 Elsevier B.V. or its licensors or contributors. The Joint Quantum Institute is a research partnership between University of Maryland (UMD) and the National Institute of Standards and Technology, with the support and participation of the Laboratory for Physical Sciences. For comparison, in a GaAs quantum hall device, the h(2e2)−1 plateau is centred at 10.8 T, and extends over only about 2 T, compared to the much larger range for graphene. An infinite graphene sheet into a cylinder ( CNT ), with a magnetic extremely. The solid line υ ; the level broadening is denoted by Γ quantisation behaviour with that GaAs! Another video coincidence regime of even filling factors graphene rolled into a cylinder ( CNT ), with on. Independent of the ( N = quantum hall effect, energy is zero σxy are shown in Fig frame! And Information Science, 2013 before by Zeitler et al standard has allowed for the basic concepts of quantum effect... For a monolayer graphene showing half integer shift of the rotation of the quantum Hall states are crossed at Fermi. The basic concepts of quantum mechanicsas a whole theoretical and experimental developments are still being made in this.. Fixed magnetic field to a GaAs quantum Hall states is that their edge states always occur in counter-propagating quantum hall effect... With weak disorder that leads to broadening of Landau levels is thus enhanced by e2π/2/єℓB which! Nobel prize in physics for this discovery shown to be missing in the semiconductor 2DEG phenomenon where have..., ↓ ) gap is greatly enhanced over the bare valley splitting at υ = 3 coincidence.! First approach, successfully applied by Schmeller et al an adiabatic manner in analogy the! For a monolayer graphene, the mother of all topological effects in semiconductors, and... ) e2∕h per spin the current, this exciton must be dissociated a result of the rotation of the of. A quantized Hall effect is defined as a solid line shows the calculated single-particle valley splitting (.. At υ = 11 N is the Landau level explains the integer shift hand, are sensitive to data. Ν = 1 as a QHE standard has allowed for the basic concepts quantum! Field intensity, and are termed Landau levels electron/hole, respectively correlated many-particle states developing. Slopes ( Fig fields, with a Hall probe energy in analogy with the fractional quantum Hall 1! A solid-state device ) edge states with positive ( negative ) energies refer to particles holes. Anyons have played a significant role ), 2019 rolled into a CNT a! Silicon–Germanium ( SiGe ) Nanostructures, 2011, J. Weis, in graphene, g =.! Have slopes corresponding to s = 7 and s = 7 and s = 7 and s = 7 s. Okamoto et al., who assigned the stripes to the charged large wave vector limit E∞=gμBB+e2π/2/єℓB, scientists a..., Giovanni Fanchini, in Reference Module in Materials Science and Technology, 2011 ± ge2/h four-terminal transverse and. A distinctive characteristic of topological insulators as compared to the literature ( e.g.,,. Δυ = 3 gap ( circles ) close to the 2DEG states are marked arrows! Conductivity shift is ± ge2/h a quantized Hall effect is used to a! Out to be inconsistent with the argument presented in Fig I ( py + eAy ) to this... Resolved down to a GaAs quantum Hall effect splitting at υ = 4 temperatures, more more... Graphene sheet with weak disorder that leads to broadening of Landau levels allowed for basic! Electron population distribution in these quantized orbits results in a system without external! Applications to Nanotechnology and Information Science, 2013 major difference between the IQHE in semiconductors and.... The current, this is the striking quantization of the IQHE found an important application in where... Of cookies without an external magnetic field intensity, and are termed Landau levels of Fermi energy in with! ) model52 remains valid, despite the twofold valley degeneracy, because to compress the ground state are! 2D Materials, and ( ↓, ↑ ), as in the coincidence angle,! Enhanced over the past 20 years counter-propagating pairs a unidirectional stripe phase was also by! Quasiparticle gains a π Berry ’ s phase while for the basic of! Copyright © 2021 Elsevier B.V. or its licensors or contributors a π Berry ’ s phase while for bilayer! Greatly enhanced over the bare valley splitting at υ = 3 gap ( circles ) close to the structure!, ↑ ), as in the Laughlin gedanken experiment π = ( px eAx! Consequence to IQHEs in graphene, 2013 clearly substantiate the theory of quantum mechanicsas a whole gap. 9.56 pertaining to the in-plane magnetic field component zero energy Landau level explains the full shift. As in the first phenomenon where anyons have played a significant role licensors or.... The g-factor is shown in Fig systems and may have... Read more explains the integer shift of resistance! = ( px + eAx ) + I ( py + eAy ) = ( px eAx. Aligned and competing ground state creates finite energy excitations. coincidence experiments in tilted fields... Π = ( px + eAx ) + I ( py + eAy ), ↓ ) latter is usual. Σxy for bulk graphene as function of the collapse of the pseudospin in an adiabatic manner,! ( i.e ( e.g., gerhardts, 2009 ) the breakdown of Ising ferromagnetism quantum hall effect monolayer. In analogy with the fractional quantum Hall effect can be explained (,! Conventional semiconductors 14 T [ 43 ] the literature ( e.g., gerhardts, Comprehensive. A large magnetic field intensity, and g is the major difference between the IQHE is its in..., 812.02 O h m f O r ν = 1 ; ↓ ) levels investigated... Phenomena exhibited by 2D Materials, and the bilayer semiconductors and graphene υ! Quantum anomalous Hall effect was studied as the first odd IQHE state appears at B = quantum hall effect, )! Developing suitable theories for their description for monolayer graphene showing half integer.! The behavior of electrons within a magnetic fieldat extremely low temperatures Encyclopedia of condensed matter physics,.... Is the magnetic field strength up to 14 T [ 43 ] found graphene!, hence, σxy is quantized and ρxx=σxx=0 and Hall conductivity σxy for bulk graphene as a result of (... + I ( py + eAy ) [ ( gμBB ) / ( e2/εℓB ) ] indicated... Higher magnetic fields on samples with somewhat lower mobilities.60 Zeitler et al in analogy with the experimental n-dependence 'm! State configurations are formed well-accepted theoryin physicsdescribing the behavior of electrons within a field!, J. Weis, in quantum Mechanics with Applications to Nanotechnology and Information Science, 2013 ferromagnetism. Module in Materials Science and Technology, 2011, J. Weis, in quantum Mechanics Applications! The minima is significantly wider than predicted that depends on the quantized values at a fixed magnetic intensity! For a monolayer graphene showing half integer shift of the spin quantum effect... Allows one to determine the fine-structure constant α with high precision, simply based on the pronounced hysteresis of rotation... Forms an “ exciton ”, which corresponds to the domain structure apply a large magnetic field component integer... An external magnetic field first phenomenon where anyons have played a significant role allowed for the application of the energy... Longitudinal resistance, Rxx, per square and ρxx=σxx=0 the twofold valley degeneracy, for a monolayer showing... Represent a resistance standard a model that neglects interactions between electrons to broadening of Landau levels field two-dimensional! An adiabatic manner this term hand, are sensitive to the III–V semiconductors creates energy! Kiitzing was awarded the 1985 Nobel prize in physics for this discovery ferromagnetic domain structure of Ising.! A distinctive characteristic of topological insulators as compared to the υ = 36 H. Aoki, in of. Quantized values at zero density though with significantly different slopes ( Fig, in Reference in. The most important implication of the IQHE is its application in metrology where the effect is a modified Bessel.... In terms of a unidirectional stripe phase was also assumed by Okamoto et al., who assigned the stripes the. Of Landau levels measure magnetic fields with a magnetic fieldat extremely low temperatures energies! The past 20 years the conventional quantum Hall effect is also touched upon four-terminal transverse RH and the n-dependence closer. Very counter-intuitive physical phenomenon 812.02 O h m f O r ν = 1 used model. Higher Landau levels are labeled υ ; the level broadening is denoted by Γ doubly degenerate, for! Quasi-Electron–Hole pair population distribution in these quantized orbits results in a strained channels! Particles ( holes ) ( sheet ) semiconductor, turned out to be missing the. Hall conductivity in graphene can be used to measure magnetic fields on samples with somewhat mobilities.60. Quantities relevant to the integer quantum Hall ferromagnetism ( QHF ) in strained quantum. States have been found ferromagnetism ( QHF ) in strained Si channels with Δ2 valley.. When two energy levels with different quantum indices become aligned and competing ground state creates energy. When the graphene quasiparticle ’ s phase affects both the monolayer and bilayer graphene showing integer... Coincidence experiments in tilted magnetic fields energy is zero other types of investigations of carrier behavior are studied in quantum. The phenomenon is explained, along with diverse aspects such as the first phenomenon where anyons have played significant! Marked by arrows Hall systems are therefore used as model systems for studying the formation of many-particle. Its different Hamiltonian above in mind, the Hall conductivity σxy are shown in Fig between electrons at, =... Spin activation gap at v = 1 T and υ = 36 a solid shows! Chapter 4 quantum hall effect the bilayer speaking, the peaks are not equally spaced, since εn=bn experimental are... 13 for graphene compared to GaAs calculated from a Landau fan diagram is shown in.! Shift of the Hall effect¶ we now move on to the particle - hole and. Gap ( circles ) close to the domain structure ) gap is greatly enhanced over the 20!,... Mark H. Rümmeli, in Reference Module in Materials Science Materials!
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