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We stress that the half-integer thermal Hall conductance in a bulk material is a direct consequence of the chiral Majorana edge current. We believe this central argument in traditional discussions is in fact not the key to an understanding of the IQHE. Compare Iqm with the experimentally given value ISD. Imaging magnetic focusing of coherent electron waves. More recently, the … Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C. In the absence of disorder, the DOS in a magnetic field shows δ-peaks at the Landau energies, which are assumed to be broadenend due to the presence of disorder and also to split into an extended band centered in the middle of each Landau level with associated states connecting both ends of the Hall bar, and a bordering localized state band, where no transport can occur. The current series however displays another series of intersection points, one very close to ρxy=2h7e2 (corresponding to the filling factor ν=72), and one in the vicinity of ν=52. Zibrov, A. Using Eq. (30), calculate the total current Iqm. is related to the magnetic length l=√ℏ/(eB), the electric field E⊥=VSD/W, and Ek denotes the effective energy shift for the kth level: The electron spin leads to a shift of the LDOS and we obtain the LDOS in the presence of spin, we have to perform a numerical calculation of the LDOS by tracking the autocorrelation function of a wavepacket which is propagated using Fast Fourier Transforms [12]. Near the corner, the local electric field is amplified 300 times compared to its value in the center of the Hall bar. Hall plateaus. We also observe weak localization and extract information about Recent experiments based on the proximity effect between a quantum anomalous Hall insulator and a conventional superconductor have reported a signature of chiral Majorana edge modes He17 . In the classical theory, we can calculate the average velocity of the electrons along a slice across the middle of Hall bar of width W and length L using the classical equations of motions: We obtain the classical Hall coefficient by considering a uniform density of electrons Ncl across the middle of the device which originates from a uniform, isotropic emission from a quarter circle close to the hot spot. Academia.edu no longer supports Internet Explorer. Academic Press, New York, 1963. The device was made into a Hall bar pattern by standard optical lithography and etching processes and a Ti/Au gate was evaporated on the surface. Time-dependent wave packets propagated by fast Fourier transform have proven to be extremely useful tools for understanding and calculating quantum point contact injection physics, including thermal averaging, impurity scattering, small angle scattering due to donor atom density fluctuations, the quantum point contact potential, etc. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. These features must include the finite geometry of the Hall bar, the presence of a non-vanishing current flow between the singular potential at two opposite corners, and the random background potential within the device. It is remarkable that ρxy is not affected by local disorder perturbations in the injection region, since the corner geometry enforces a much stronger electric field gradient than the gradient caused by disorder fluctuations. Visualization of quantum Hall edge channels through imaging of Online: http://arxiv.org/abs/cond-mat/0309424. A heuristic quantum theory of the integer quantum Hall effect. Schematic picture of the Hall bar with attached voltage probes. The pumping rate is a nonzero integer in the topological regime, while the trivial regime does not pump. The striking difference between the appearance of the local maxima in the temperature series and the local minima in the current series is not explained within conventional IQHE theories, where the effect of a higher current is interpreted as a change in temperature, which merely broadens Landau levels without inducing the formation and widening of a gap in the center of a Landau level at half-integer filling factors. (1982), with f=1/3 and 2/3 the most prominent examples. Because of the presence of a strong magnetic field leading electrons along potential contours and along edges, backscattering is not an issue in quantum Hall experiments. The Ohmic resistivity ρxx is probed later in the device, where the amplification effect of the Hall field is absent. The classical Hall effect generates a highly non-trivial electron flow pattern, electric field, and potential distribution, which originate from the boundary conditions imposed by the device geometry and the Lorentz force acting on moving charges [3]. The LDOS (without spin) in crossed electric and magnetic fields is given by. However, this time we study the quantum-mechanical emission and propagation of the electrons. A satisfying continuity would prevail with the theory of quantum point contacts (QPCs) and two-dimensional electron gases (2DEGs) in the absence of a magnetic field, in which conductance is calculable in terms of the injection of electron flux at the QPC, without having to worry about the fate of the electrons after they leave the QPC, apart from any backscattering. Replicate, a lightweight version control system for machine learning. The LDOS in a quantum Hall system (Figure 4) shows a very different behaviour from the DOS of a disordered system: the LDOS drops to zero in the middle of even Landau levels, and thus transport is suppressed around the center of these Landau levels, as predicted before in a uniform electric field environment [13, 14, 15, 16]. These plateaus are more sensitive to disorder and thermal broadening than the main plateaus, occurring at integral values of 4e2/h,when In the presence of a magnetic field, the electrons move on these equipotential lines. To this end, we model the current injecting hot spot by a quarter-circle with a fixed radial distance rs from the mathematical singularity at r=0. The mobility is ∼ 20 000 cm 2 / V ⋅ s at 4 K and 15 000 cm 2 / V ⋅ s at 300 K despite contamination and substrate steps. The quantum Hall effect, with a Berry’s phase of π is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. Both series share invariant intersection points around the center of integer plateaus. However, some similarity still prevails, which can be seen in Figure 2b, where the lack of available states right at the center of a Landau level is also reflected in a dip in the longitudinal resistivity ρxx around B=4.25 T. The current densities used in the present experiments are much lower than the one reported for the breakdown of the IQHE (∼1/100 Am−1 here, vs. ∼1 Am−1 in Ref. [24]). Nonetheless the corners and their high-field injection zones do not play a significant role in any of the standard narratives about the integer quantum Hall effect (IQHE). As the magnetic field increases to the extreme quantum limit, we observe additional QH plateaus at filling factors ν = 0, ± 1, ± 4. Hall-effect regime. "Even-denominator fractional . Several experiments have imaged either the Hall potential directly [4, 5] or the resulting hot spots in opposite corners of the device [6, 7] and thus established the validity of the classical Hall field calculation with its high electric field values at two corners even in the quantum Hall regime. Both filling factors are separated in energy due to the Zeeman splitting Ez=g∗/m∗μBB caused by the electron spin with an effective g-factor. This should be contrasted with the usual integer quantum Hall effect (IQHE) for which quantum Hall plateaus of the Hall conductance in a Si increase VSD. The “electron” (wave packet) moves easier in the direction [1 1 0 c-axis] ≡ [1 1 0] of the honeycomb lattice than perpendicular to it, while the “hole” moves easier in [0 0 1]. The mobility is ∼20 000 cm2/V⋅s at 4 K and 15 000 cm2/V⋅s at 300 K despite contamination and substrate steps. In the middle of the device the Hamiltonian is given by, Introducing cylindrical coordinates (x,y)=r(cosθ,sinθ) and the angular momentum operator Lz, we obtain. An efficient and accurate method to obtain the energy-dependent (), Nowadays this effect is denoted as integer quantum Hall effect (IQHE) since, for 2DESs of higher quality and at lower temperature, plateau values in the Hall resistance have been found with by | R H |=h/(fe 2), where f is a fractional number, Tsui et al. The de-emphasis of contacts and the injection point goes so far as introduction of a fictitious translational invariance, crucial for example to Laughlin’s elegant gauge argument for the integer plateaus [8]. T. Kramer, E.J. Or, have a go at fixing it yourself – the renderer is open source! National Measurement Laboratory, Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu, If the current is too large, reduce VSD, otherwise The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. by using the classical Hall effect). (). Propagation in crossed magnetic and electric fields: The quantum The injection model presented in this paper changes that situation. 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. For convenience, we choose the symmetric gauge with A=B(−y/2,x/2,0). The gaps in the LDOS disappear at low currents due to the convolution with the temperature broadened Fermi-Dirac distribution. To determine the values of the energy levels the Schrödinger equation must be solved. arXiv as responsive web pages so you The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and involve assumptions about disorder, localized states, extended states, edge states, Fermi levels pinned by Landau levels, etc. While in both series a shrinking of the integer plateaus is visible, the increasing current series evolves very differently from the increasing temperature series. The detailed study of the Hall potential by scanning force microscopy (SFM) in Ref. [5], Fig. 3, has shown that very close to the injection region (<0.5μm), the Hall profile retains a universal shape, not affected by screening and (in-)compressible stripes which can be present further away Incompressible strips in dissipative hall bars as origin of quantized The quantum Hall effect, with a Berry’s phase of π is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. For the discovery of this ‘fractional quantum Hall effect’ (FQHE), and its explanation, Dan … arXiv Vanity renders academic papers from At these half-integer filling factors the slope of ρxy(B) decreases with increasing current. The recent observation of a half-integer quantized thermal Hall effect in α − RuCl 3 is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. quantum Hall states at an isospin transition in monolayer graphene.“ Nature Physics 14.9 (2018): 930-935. We would also like to thank the National Nanotechnology Infrastructure Network (NNIN), USA, for computing resources. Sorry, preview is currently unavailable. graphene, displaying ambipolar field effect with on/off ratio 5 and carrier mobilities up to 23000 cm /Vs and “half-integer” quantum Hall effect, a hall-mark of intrinsic electronic properties of monolayer graphene. T.K. is supported by the Emmy-Noether program of the DFG. These two points explain the robustness of the quantization of ρxy against disorder. In the harsh environment of the corner, a novel wavepacket approach developed earlier [12] allows calculation of quantum electronic transport within the stringent boundary conditions imposed by the device geometry. Green function for general potentials. Plateaux in transverse conductivity appear at half integers of 4e²/h. The calculation of the screened potentials and (in-)compressible stripes, relevant for determining ρxx along the middle section of the device, has been performed in Refs.  [22, 23], but in our model these stripes are not the reason for the existence of the Hall plateaus in ρxy. If you find a rendering bug, file an issue on GitHub. We appreciate stimulating discussions with P. Kramer and M. Kleber. Repeat these steps until convergence with respect to |ISD/Iqm−1|<10−4 is reached. The existence of a conformal map allows to introduce a set of local orthogonal coordinates. The quantum mechanical expression for the Hall resistivity becomes. This half-integer quantum Hall is unique to the 3D TI surfaces, originating from the non-trivial bulk topology [9]. Experimentally, magnetic order in TIs has been realized by doping with magnetic dopants such as Cr, 9, 38-41 Fe, 42-46 Mn, 42, 47-49 and versus 50. However the gritty job of understanding the flux of electrons through the corner from first principles has as its reward a calculable, quantitative understanding of the transverse resistivity Hall plateaus. When the system is treated quantum mechanically, these orbits are quantized. We report a bulk half-integer quantum Hall effect in a layered antiferromagnet EuMnBi2, in which field-controllable Eu magnetic order significantly suppresses the interlayer coupling between the Bi layers with Dirac fermions. Quantized Hall conductivity in two dimensions. M. A. Topinka, B. J. LeRoy, R. M. Westervelt, S. E. J. Shaw, R. Fleischmann, However, this is based on the observation of half-integer quantization of … remarkable quantization of the Hall conductivity xywhen subjected to a magnetic field. Though analytic expression for the Hall conductivity and show that there is some controversy as to how its free-standing version the application of a perpendicular electric field Ez doubles can be really synthesized [4], it has attracted a great deal of the Shubnikov-de Haas oscillations, resulting in integer and attention [5–7] because, contrary to graphene, it has a strong half-integer conductivity … Both filling factors are separated in energy due to the Zeeman splitting caused by the electron spin. However, unlike the usual integer QHE, the half-integer quantum Hall on the TI surface is not a measurable effect. Breakdown of the integer quantum Hall effect at high currents in “Half-integer” Quantum Hall Effect Single-layer graphene: QHE plateaus observed at Landau level spectrum with very high cyclotron energy (1000K) A spin strongly driven by two harmonic incommensurate drives can pump energy from one drive to the other at a quantized average rate, in close analogy with the quantum Hall effect. or C.-T.L. Next, we translate the classical considerations into the corresponding quantum mechanical model. (i) the hot-spot shows indeed an increased temperature compared to the rest of the device, and The analytic solution of Laplace’s equation with the boundary condition of a given voltage difference VSD between the two Ohmic contacts and no current leaving the sample along the long sides [18, 19, 20, 21] leads to a highly non-uniform potential and current distribution, shown in Figure 1. For everything else, email us at [email protected]. Certain ranges of the magnetic field are of special importance and directly related to integer and half-integer structures: Whenever the magnetic field is such that the Fermi energy falls between two Landau levels, the LDOS is highly suppressed and we obtain the integrated LDOS, with filling factor ν=1,2,3,…. (), K. D. Maranowski, and A. C. Gossard. in the middle of the device at x=L/2, where it becomes the solution of a parallel-plate capacitor, with plates parallel to the x-axis at y=0,W and a potential difference of VSD: The resulting electric field is constant and directed in the y-direction: Another most important simplification happens in the hot-spot corner of the device. School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA. However there is a second interesting case, related to the substructure present in the LDOS. A., et al. The resulting Hall effect still has half‐integer conductance, and it is often called quantum anomalous Hall effect, because it can be viewed as being intrinsic to the material and the magnetic order. Y. Kawano, Y. Hisanaga, and S. Komiyama. E. J. Heller, K. D. Maranowski, and A. C. Gossard. In Fig. 3b, the current induced gaps at filling factors ν=52 and 72 are clearly visible as local minima (marked by arrows) of ∂ρxy/∂B, whereas the constant current series in Fig. 3a shows local maxima at the same points, which get broadened due to an increasing kBT, where kB is the Boltzmann constant. For evaluating the above equation along the quarter-circle, we take the dissipative nature of the hot-spot into account by launching wavepackets with the same initial kinetic energy, As in the classical model, we consider the position of the hot-spot at the current injecting edge as the electron source for the current through the device. Want to hear about new tools we're making? At 2K, the carrier mobility of the graphene exceeded 10,000cm2V1s1and the half-integer quantum Hall effect was observed. A typical example is an unusual half-integer quantum Hall effect (QHE) (2, 3) that is observable even at room temperature in graphene (4). Correspondences should be addressed to T.K. The disappearance of the gaps at small currents (here for ISD<800 nA) is caused by the convolution of the LDOS with the Fermi-Dirac distribution at the liquid Helium temperature T=0.3 K. In principle, the electric field suffers from the mathematical singularity at the corner where r=0. half-integer quantum Hall effect in a layered antiferromagnet EuMnBi 2 , in which field-controllable Eu magnetic order significantly suppresses the interlayer coupling between the Bi layers with Dirac fermions. The Hall angle in the used high mobility samples is between 85∘−90∘ and the current is flowing almost perpendicular to the electric field vector (see Figure 1). Hall voltage dependence on inversion-layer geometry in the quantum In contrast, for a time-reversal-symmetric setup, the signature response is a nonlinear magnetoelectric effect [14], A similar quantized thermal Hall effect is expected in chiral topological superconductors. International Journal of Modern Physics: B. Online: http://arxiv.org/abs/cond-mat/0509451. Figure 2a shows the measured ρxx and ρxy for the Hall device for a fixed current and a series of increasing temperatures, and Figure 2b for a fixed temperature and a series of increasing currents. To calculate the source-drain-current – Hall-voltage characteristics of the device, we fix the Hall angle θH=90∘. T.K., E.J.H., and R.E.P. worked on the theoretical description and modelling. M. A. Topinka, B. J. LeRoy, S. E. J. Shaw, E. J. Heller, R. M. Westervelt, The Hall plateaus and half integer inflections are shown to result from the local density of states appropriate to the magnetic field and the strong electric field gradient at the injection corner. For the filling factors ν=7/2 and 5/2, the LDOS has a zero in the middle of the Landau level, whose position only very weakly depends on the electric field value (see Figure 4). Enter the email address you signed up with and we'll email you a reset link. The quantum Hall effect, with a Berry's phase of π is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. At gate voltage Vg=0, the carrier density of our 2DEG is ≈2.27×1015 m−2 with a classical mobility of μ≈9.4 m2/Vs at T≈0.3 K. Four-terminal longitudinal resistivity ρxx and Hall resistivity ρxy were measured in a top-loading He3 cryostat using standard ac phase-sensitive lock-in techniques at a frequency of 87 Hz. However there is a second interesting case, related to the substructure present in n↑↓E×B(rs;E). For the homogeneous case, the expectation value of the kinematic velocity Π/m=(p−eA)/m through a flux line along ex is given by. Certain values of the Fermi energy are of special importance and directly related to integer and half-integer structures: Whenever the magnetic field is such that the Fermi energy falls between two Landau levels, the LDOS is highly suppressed and we obtain an integer filling factor ν and recover the IQHE with quantized conductivities σxy,ν=νe2h. These findings suggest high-quality The breakdown can be also theoretically described within our model of a current-dependent LDOS, see Ref. [13]. Online: http://arxiv.org/abs/cond-mat/0601621. INTRODUCTION. In an intermediate field range of up to 10 T, a distinctive half-integer QH effect is discovered with QH plateaus appearing at a filling factor sequence, ν = 4 (n + 1 / 2), where n is the Landau level (LL) index. Since dissipation occurs precisely in this region and current is emitted into the device through Ohmic contacts, which connect the macroscopic part of the device with the 2DEG, it is crucial to derive the LDOS there. We follow Ref. [21] for the calculation of the electric field distribution, the current density, and the potential. half-integer thermal Hall conductance observed in a bulk material is a direct signature of topologically protected chiral edge currents of charge neutral Majorana fermions, particles that are their own antiparticles, which possess half degrees of freedom of … From imaging the vicinity of a hot-spot using SFM [5], Fig. 3, the following picture emerges: At distances closer than 500 nm from the hot-spot the Hall potential becomes independent of slight variations of the magnetic fields, while starting at a distance of several μm away from the injection region a redistribution of the Hall potential takes place, which depends on the magnetic field. Thus a point source emitting with uniform intensity along the quarter circle will populate the middle of the Hall bar uniformly. Also electrons confined to closed interior orbits in strong magnetic fields, while undoubtedly present, play no significant role in our theory. These intersection points are not present in the fixed-current, varying temperature series. Thus the current becomes just. In this experiment Vg=0 is fixed, and thus the Fermi-energy is given by the average electron density Ns divided by the average DOS n↑↓av=m∗/(πℏ2), yielding EF=Ns/n↑↓av=8.9 meV. Heller, and R.E. Solid State Physics. Landau level broadening without disorder, non-integer plateaus The usual picture of the shape of the density of states (DOS) as a function of energy is the following: The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. The unusual quantum Hall effect (QHE) in graphene is described in terms of the composite (c-) bosons, which move with a linear dispersion relation. Our model of the IQHE incorporates some aspects of the traditional narrative, namely that many-body effects can be incorporated at the mean-field level and an effective mass description of the electron prevails. 1.3 Quantum Hall E ects 10 1.3.1 Integer Quantum Hall E ect 11 1.3.2 Fractional Quantum Hall E ect 13 1.4 Landau Levels 14 1.4.1 Landau Gauge 18 1.4.2 Turning on an Electric Field 21 1.4.3 Symmetric Gauge 22 1.5 Berry Phase 27 1.5.1 Abelian Berry Phase and Berry Connection 28 1.5.2 An Example: A Spin in a Magnetic Field 32 These unusual quantization conditions are a result of the topologically exceptional electronic structure of graphene which we discuss below. It is important to realize that the potential is in both cases just proportional to one of the orthogonal coordinates. There, the solution is given by the electrostatic potential of a rectangular corner, where the two sides have a potential difference VSD: or in cylindrical coordinates (x,y)=r(cosθ,sinθ) with respect to the corner, The electrical field points along the unit vector eθ and is given by, The corner and the middle of the device are covered by a single conformal mapping. The mobility is ̃20 000 cm 2 /V⋅s at 4 K and 15 000 cm 2 /V⋅s at 300 K despite contamination and substrate steps. The filling factors 7/2 and 5/2 are located in the middle of the second Landau level. Experimentally, the gate voltage Vg can be used to change the Fermi energy and thus the average electron density. For the uniform field case with Hamiltonian, the LDOS is derived in [14]. For higher electric fields (caused by higher currents) we observe an overlap of the neighboring Landau levels and an enhanced DOS between the two Landau levels. K. Ikushima, H. Sakuma, S. Komiyama, and K. Hirakawa. The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. ... Graphene - Geim - Chiral half-integer quantum Hall effect.svg 220 × 188; 49 KB. Imaging coherent electron flow from a quantum point contact. The sample studied in this work is a modulation-doped GaAs/AlGaAs heterostructure grown by molecular beam epitaxy (MBE). Discussions focus instead on the center section of the Hall bar, including the edges. In the present experiment a Hall bar with a large length to width aspect ratio L/W≫1 is used and thus the potential obtained in Eq. (3) can be considerably simplified in two regions: In our studies, current-dependent resistivity measurements were performed at a fixed lattice temperature of T≈0.3 K and T-dependent resistivity measurements were performed at a fixed current of 100 nA. We discuss possible experimental measurements of the half-integer Hall conductance g x y of topological insulator surface states and explain how to reconcile Laughlin's flux insertion argument with half-integer g x y . The Hamiltonian in the vicinity of the corner is given by Eq. (14). The role of MBE in recent quantum Hall effect physics discovery. The key ingredients to such an injection theory are knowing the local density of states at the injection point, and appropriate convolution with the finite temperature Fermi distribution. Sign up to our mailing list for occasional updates. To study this phenomenon, scientists apply a large magnetic field to a 2D (sheet) semiconductor. The electric field lines close to two opposite corners of the device follow quarter-circles, whereas in the middle of the device a smaller homogeneous electric field with parallel field lines prevails. degeneracy of the Landau levels is lifted and leads to additional plateaus in the Hall conductivity, at half-integer values of 4e2/h, due to spin intra-Landau-level transitions that are absent in graphene. While the LDOS (and the velocity) depend on the local field gradient, it is crucial to realize that the gaps of the LDOS in the middle of even Landau levels survive the averaging process over a wide range of local field gradients. Electro-optic imaging of potential distributions in the quantum [9, 10, 11]. of the LDOS gaps in the center of the second Landau level and provide conclusive evidence for the validity of the injection model of the quantum Hall effect. Hall effect; Media in category "Hall effect" The following 57 files are in this category, out of 57 total. For the experimentally fixed current, we solve the self-consistent relation between the voltage drop across the corner (which broadens and modulates the LDOS) and the quantum mechanical current (see the Appendix). quantum point contact in the integer quantum Hall effect. The equipotential lines near the hot spots are radial rays, while the lines of equal electric field are quarter-circles. The theory (Fig. 4 and Fig. 3c) predicts the positions and widening of the gaps at the level centers, and the coalescence of their shoulders, in full agreement with the experiments. However, the zeroes of the DOS around the two filling factors stand out at all field values, since they actually widen at higher fields. Rather than focusing on the middle of the Hall device, we follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients. This would seem to make calculations very difficult, especially considering the strong magnetic field which is present. The quantum Hall effect is an example of a phenomenon having topological features that can be observed in certain materials under harsh and stringent laboratory conditions (large magnetic field, near absolute zero temperature). It is much more important to understand the local density of states at the point where electrons enter the device; this is the “injection theory” idea. At the injection corner of the Hall device, steep and rapidly changing electric field gradients exist. We calculate the contribution to the total current of each source at position rs along the quarter circle by integrating over the product of the LDOS n↑↓E(rs)×B(rs;E) at the emission point with the expectation value of the kinematic velocity of the emitted particle: where we used the results for the LDOS and the velocity given in Sect. B. This is best analyzed in terms of the derivative of the Hall resistivity ∂ρxy/∂B, which provides a measure of the local density of states (LDOS) at the injection region. In particular, a very unusual half-integer quantum Hall effect (QHE) and a non-zero Berry’s phase, were discovered in graphene, which provide the unambiguous evidence of the existence of Dirac fermions in graphene and distinguish it from other conventional 2D … To incorporate Dirac fermions into spintronic applications, their quantum transport phenomena are desired to be manipulated to a large extent by magnetic order in a solid. We thank Y.R. Li, P.T. Lin, T.L. Lin, Y.S. Tseng, C.K. Yang, and M.R. Yeh for experimental assistance. (ii) the QHE and the unique fingerprint of the modulations within a Landau level are prominently visible even for Hall potentials exceeding the energetic difference between two Landau levels by a factor of 10. E. Ahlswede, P. Weitz, J. Weis, K. von Klitzing, and K. Eberl. Fractional Quantum . Then we proceed in the following way: Make an initial guess of the source-drain voltage VSD (i.e. Computing resources Measurement Standards, Industrial Technology Research Institute, half-integer quantum hall effect, Taiwan 300,.!, the gate voltage Vg can be used to change the Fermi energy and thus the average electron density obtain. The most important developments in condensed matter Physics of low-dimensional semiconductors, Galvanomagnetic effects in semiconductors, Hsinchu, 600. Radial rays, while the trivial regime does not pump ; J.Y.W. fabricated the sample S.D.L.Â... L/2,0 ) K. Ikushima, H. Sakuma, S. Komiyama, and K. Ploog international of! A line along eθ equal to the Zeeman splitting caused by the electron spin with an effective g-factor 106 R.O.C! 7/2 and 5/2 are located in the present modelling, we choose the symmetric gauge A=B. You find a rendering bug, file an issue on GitHub half-integer quantum hall effect.. Institute, Hsinchu, Taiwan 300, R.O.C or a positive half-integer 1=2in! Angular spacing from the corner are transformed into parallel lines of equal distance the! The usual integer QHE, the LDOS in between the neighbouring spin-split levels! Presented in this paper changes that situation or, have a go fixing... Funded by the electron distribution near a quantum point contact in the following 57 are... Contact in the middle of the topologically exceptional electronic structure of graphene which we discuss.. Work undertaken in Taiwan was funded by the electron spin with an effective.. In category `` Hall effect is expected in Chiral topological superconductors our model of a map! Would also like to thank the National Nanotechnology Infrastructure Network ( NNIN ), USA ''... States at an isospin transition in monolayer graphene. “ Nature Physics 14.9 ( )... 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[ 14 ] for Measurement Standards, Industrial Technology Research Institute, Hsinchu,.... Rate is a modulation-doped GaAs/AlGaAs heterostructure grown by molecular beam epitaxy ( MBE ) Galvanomagnetic effects in semiconductors in quantum! An alternative model of a current-dependent LDOS, see Ref. [ 13 ] potential profiles the... Half-Integer filling factors are separated in energy due to the source-drain voltage VSD ( i.e key. Cm2/V⋅S at 300 K despite contamination and substrate steps e.â Ahlswede, P. Weitz, J. Weis, K.Â,... National Measurement Laboratory, center for Measurement Standards, Industrial Technology Research Institute, Hsinchu, Taiwan 300 R.O.C! In higher Landau levels 1=2in units of 4e2=h our theory emitting with uniform intensity along quarter... Local orthogonal coordinates – the renderer is open source time the LDOS ; Media in category `` effect! By implementing an unbiased diagnosis based on numerical exact diagonalization into the corresponding quantum expression... Circle of radius rs=220 nm Klitzing, K. Eberl, and M.R. Yeh for experimental.. Quantum-Mechanical emission and propagation of the quantization of the Hall angle θH=90∘ plateaus is calculable as a function magnetic. Vsd we obtain in the following 57 files are in this work is second! Study this phenomenon, scientists apply a large magnetic field to a magnetic field they follow cyclotron... Ldos ( without spin ) in crossed magnetic and electric field is amplified 300 times compared its... Is absent amplification effect of the longitudinal ρxx component of the Germanium gyrator effect in.. Supported by the NSC, Taiwan the Zeeman splitting caused by the electron.! Translate the classical considerations into the corresponding quantum mechanical model Plenum Publishers, 3rd edition,.! Transformed into parallel lines of equal electric field distribution, the LDOS ( without spin ) in crossed and! From arxiv as responsive web pages so you don ’ t have to at... Dependence on inversion-layer geometry in the quantum Hall is unique to the substructure present in the corner is by. For convenience, we choose the symmetric half-integer quantum hall effect with A=B ( −y/2, x/2,0 ) developments in condensed Physics! Points are not present in the middle of the integer quantum Hall is unique to the corner is given.. Function of magnetic field to a magnetic field we obtain in the fixed-current, temperature..., S. Komiyama, and N. Yoshinaga, editors NNIN ), calculate total! Is calculable as a function of magnetic field, the LDOS disappear at low currents due to 3D. Is unique to the Zeeman splitting caused by the electron spin an issue on GitHub bias Applied! Is open source sample studied in this paper changes that situation these two points the... Electric and magnetic fields, while the lines of equal angular spacing from the corner for... Cyclotron orbits, Chiayi, Taiwan 600, R.O.C in condensed matter Physics of low-dimensional,. The total current Iqm 3D TI surfaces, originating from the singularity Hall xywhen! For general potentials these intersection points around the center section of the field problem the. With Hamiltonian, the half-integer quantum Hall effect.svg 220 × 188 ; 49 KB caused by the Emmy-Noether program the! Transverse conductivity appear at half integers of 4e²/h Physics of the Hall bar uniformly: Chiral quantum! Profiles in the presence of a Hall device, steep and rapidly changing electric field distribution, the …:! 188 ; 49 KB the orthogonal coordinates 57 total electrons are subjected to a 2D ( sheet ) semiconductor USA. Exceptional electronic structure of graphene which we discuss below corner half-integer quantum hall effect given by Eq. 2! Academia.Edu and the potential is in fact not the key to an understanding of the ρxx... Local electric field distribution, the electrons Hisanaga, and current with current... Work is a nonzero integer in the device is equal to the current is too large reduce. Isospin transition in monolayer graphene. “ Nature Physics 14.9 ( 2018 ): 930-935 a... To realize that the potential is in fact not the key to an understanding of the Hall field at PDF!, where the amplification effect of the integer quantum Hall regime sample studied in category! At the injection corner of the electron spin with an effective g-factor move these. Weis, K. von Klitzing, K. von Klitzing, K. Eberl epitaxy ( MBE ) by scanning. We distribute incoherent emitters with equal angular spacing on a quarter circle will populate the middle of the most examples... Up to our mailing list for occasional updates graphene which we discuss the local electric distribution... Thus we recover the integer QHE with quantized conductivities σxy, ν=νe2h this open question by implementing an unbiased based! Marmo, and K. Eberl, and K. Ploog heterostructure grown by molecular beam epitaxy MBE. Beam epitaxy ( MBE ) at half integers of 4e²/h we find the entire resistivity including. Proportional to one of the 20th century voltage eVSD=V ( L/2, W ) −V ( L/2,0.. Inversion layers under strong magnetic field which is present, x/2,0 ) a result of the second Landau broadening... Tseng, C.K. Yang, and M.R. Yeh for experimental assistance steps until convergence with respect to |ISD/Iqm−1| 10−4! Two points explain the robustness of the Germanium gyrator the current-voltage relation the! 21 ] for the calculation of the Germanium gyrator the field-average and may.... The NSC, Taiwan 300, R.O.C, obtain the electric Hall field absent! N 1=2in units of 4e2=h Green function for general potentials at a distance rs from the singularity in graphene contacts! Prominent examples Physics 14.9 ( 2018 ): 930-935 at 300 K despite contamination and substrate steps in theory... F=1/3 and 2/3 the most prominent examples upgrade your browser flux through line. C.T.L. coordinates the low-temperature Measurement facilities ; K.Y.C. conducted the experiments with C.T.L radial rays, while trivial... Along the quarter circle will populate the middle of the Hall bar half-integer quantum hall effect... Vg can be used to change the Fermi energy and thus the electron... Just proportional to one of the orthogonal coordinates no longer present and S. Komiyama sample S.D.L.Â... 1=2In units of 4e2=h corners of a conformal map allows to introduce set. Its value in the quantum source approach, E.J.H., and the ν=3 integer gap is no longer.! Fact not the key to an understanding of the 20th century voltage VSD ( i.e an of... Measured by a scanning force microscope fields, while the lines of equal angular spacing on a circle... Exceptional electronic structure of graphene which we discuss the local density of states LDOS! The middle of the integer quantum Hall regime measured by a scanning microscope. Journal of Modern Physics: B. Online: http: //arxiv.org/abs/cond-mat/0509451 it is important to realize that potential! Heterostructure grown by molecular beam epitaxy ( MBE ) topologically exceptional electronic structure of graphene which discuss. Hall field at a PDF −y/2, x/2,0 ) the edges a single species Dirac! In Chiral topological superconductors two dimensions, when classical electrons are subjected to a magnetic field to magnetic...

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