# fractional quantum hall effect pdf

The ground state has a broken symmetry and no pinning. The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. The fractional quantum Hall effect is the result of the highly correlated motion of many electrons in 2D ex-posed to a magnetic ﬁeld. This effect, termed the fractional quantum Hall effect (FQHE), represents an example of emergent behavior in which electron interactions give rise to collective excitations with properties fundamentally distinct from the fractal IQHE states. Progress of Theoretical Physics Supplement, Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems, Geometric entanglement in the Laughlin wave function, Detecting Fractional Chern Insulators through Circular Dichroism, Effective Control of Chemical Potentials by Rabi Coupling with RF-Fields in Ultracold Mixtures, Observing anyonic statistics via time-of-flight measurements, Few-body systems capture many-body physics: Tensor network approach, Light-induced electron localization in a quantum Hall system, Efficient Determination of Ground States of Infinite Quantum Lattice Models in Three Dimensions, Numerical Investigation of the Fractional Quantum Hall Effect, Theory of the Fractional Quantum Hall Effect, High-magnetic-field transport in a dilute two-dimensional electron gas, The ground state of the 2d electrons in a strong magnetic field and the anomalous quantized hall effect, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Fractional Statistics and the Quantum Hall Effect, Observation of quantized hall effect and vanishing resistance at fractional Landau level occupation, Fractional quantum hall effect at low temperatures, Comment on Laughlin's wavefunction for the quantised Hall effect, Ground state energy of the fractional quantised Hall system, Observation of a fractional quantum number, Quantum Mechanics of Fractional-Spin Particles, Thermodynamic behavior of braiding statistics for certain fractional quantum Hall quasiparticles, Excitation Energies of the Fractional Quantum Hall Effect, Effect of the Landau Level Mixing on the Ground State of Two-Dimensional Electrons, Excitation Spectrum of the Fractional Quantum Hall Effect: Two Component Fermion System. Letters 48 (1982) 1559). The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. Only the m > 1 states are of interest—the m = 1 state is simply a Slater determinant, ... We shall focus on the m = 3 and m = 5 states. <>/XObject<>/Font<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 2592 1728] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 4 0 obj The ground state energy seems to have a downward cusp or “commensurate energy” at 13 filling. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, $N= 2$. We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. 1���"M���B+83��D;�4��A8���zKn��[��� k�T�7���W@�)���3Y�I��l�m��I��q��?�t����{/���F�N����z��F�=\��1tO6ѥ��J�E�꜆Ś���q�To���WF2��o2�%�Ǎq���g#���+�3��e�9�SY� �,��Ǌ�2��7�D "�Eld�8��갎��Dnc NM��~�M��|�ݑrIG�N�s�:��z,���v,�QA��4y�磪""C�L��I!�,��'����l�F�ƓQW���j i& �u��G��،cAV�������X$���)u�o�؎�%�>mI���oA?G��+R>�8�=j�3[�W��f~̈́���^���˄:g�@���x߷�?� ?t=�Ɉ��*ct���i��ő���>�$�SD�$��鯉�/Kf���$3k3�W���F��!D̔m � �L�B�!�aZ����n <>>> However, for the quasiparticles of the 1/3 state, an explicit evaluation of the braiding phases using Laughlin’s wave function has not produced a well-defined braiding statistics. $${\phi _{n,m}}(\overrightarrow r ) = \frac{{{e^{|Z{|^2}/4{l^2}}}}}{{\sqrt {2\pi } }}{G^{m,n}}(iZ/l)$$ (2) How this works for two-particle quantum mechanics is discussed here. The fractional quantum Hall effect is a very counter- intuitive physical phenomenon. Topological Order. Plan • Fractional quantum Hall effect • Halperin-Lee-Read (HLR) theory • Problem of particle-hole symmetry • Dirac composite fermion theory • Consequences, relationship to ﬁeld-theoretic duality. The quasiparticles for these ground states are also investigated, and existence of those with charge ± e/5 at nu{=}2/5 is shown. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. Quantum Hall Hierarchy and Composite Fermions. However, bulk conduction could also be suppressed in a system driven out of equilibrium such that localized states in the Landau levels are selectively occupied. All rights reserved. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light. electron system with 6×1010 cm-2 carriers in Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. Exact diagonalization of the Hamiltonian and methods based on a trial wave function proved to be quite effective for this purpose. At ﬁlling 1=m the FQHE state supports quasiparticles with charge e=m [1]. This observation, unexpected from current theoretical models for the quantized Hall effect, suggests the formation of a new electronic state at fractional level occupation. Next, we consider changing the statistics of the electrons. The activation energy Δ of ϱxx is maximum at the center of the Hall plateau, when , and decreases on either side of it, as ν moves away from . Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. ��-�����D?N��q����Tc An insulating bulk state is a prerequisite for the protection of topological edge states. changed by attaching a fictitious magnetic flux to the particle. ����Oξ�M ;՘&���ĀC���-!�J�;�����E�:β(W4y���$"�����d|%G뱔��t;fT�˱����f|�F����ۿ=}r����BlD�e�'9�v���q:�mgpZ��S4�2��%��� ����ґ�6VmL�_|7!Jl{�$�,�M��j��X-� ;64l�Ƣ �܌�rC^;��v=��bXLLlld� By these methods, it can be shown that the wave function proposed by Laughlin captures the essence of the FQHE. We report results of low temperature (65 mK to 770 mK) magneto-transport measurements of the quantum Hall plateau in an n-type GaAsAlxGa1−x As heterostructure. It is found that the ground state is not a Wigner crystal but a liquid-like state. This effect is explained successfully by a discovery of a new liquid type ground state. Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic modes are given in compact forms with the input interaction and the corresponding ground state structure factors. 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. Moreover, we discuss how these quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the quantum Hall system. Join ResearchGate to find the people and research you need to help your work. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) confirmed. In the presence of a density imbalance between the pairing species, new types of superfluid phases, different from the standard BCS/BEC ones, can appear [4][5][6][7][8][9][10][11][12]. a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). These excitations are found to obey fractional statistics, a result closely related to their fractional charge. This is not the way things are supposed to … The fractional quantum Hall effect (FQHE), i.e. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. The Hall conductivity takes plateau values, σxy =(p/q) e2/h, around ν=p/q, where p and q are integers, ν=nh/eB is the filling factor of Landau levels, n is the electron density and B is the strength of the magnetic field. has eigenfunctions1 We shall see that the fractional quantum Hall state can be considered as a Bose-condensed state of bosonized electrons. v|Ф4�����6+��kh�M����-���u���~�J�������#�\��M���$�H(��5�46j4�,x��6UX#x�g����գ�>E �w,�=�F4�VX� a�V����d)��C��EI�I��p݁n ���Ѣp�P�ob�+O�����3v�y���A� Lv�����g� �(����@�L���b�akB��t��)j+3YF��[H�O����lЦ� ���΁e^���od��7���8+�D0��1�:v�W����|C�tH�ywf^����c���6x��z���a7YVn2����2�c��;u�o���oW���&��]�CW��2�td!�0b�u�=a�,�Lg���d�����~)U~p��zŴ��^�Q0�x�H��5& �w�!����X�Ww��#)��{���k�1�� �J8:d&���~�G3 When the cyclotron energy is not too small compared to a typical Coulomb energy, no qualitative change of the ground state is found: A natural generalization of the liquid state at the infinite magnetic field describes the ground state. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. tailed discussion of edge modes in the fractional quantum Hall systems. The knowledge of the quasiparticle charge makes extrapolation of the numerical results to infinite momentum possible, and activation energies are obtained. Quasi-Holes and Quasi-Particles. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. and eigenvalues Both the diagonal resistivity ϱxx and the deviation of the Hall resistivity ϱxy, from the quantized value show thermally activated behavior. Here m is a positive odd integer and N is a normalization factor. The Hall conductivity is thus widely used as a standardized unit for resistivity. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The ground state energy of two-dimensional electrons under a strong magnetic field is calculated in the authors' many-body theory for the fractional quantised Hall effect, and the result is lower than the result of Laughlin's wavefunction. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. However, in the former we need a gap that appears as a consequence of the mutual Coulomb interaction between electrons. Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). linearity above 18 T and exhibited no additional features for filling The numerical results of the spin models on honeycomb and simple cubic lattices show that the ground-state properties including quantum phase transitions and the critical behaviors are accurately captured by only O(10) physical and bath sites. Here the ground state around one third filling of the lowest Landau level is investigated at a finite magnetic, Two component, or pseudospin 1/2, fermion system in the lowest Landau level is investigated. fractional quantum Hall effect to three- or four-dimensional systems [9–11]. a GaAs-GaAlAs heterojunction. The fractional quantum Hall e ect (FQHE) was discovered in 1982 by Tsui, Stormer and Gossard[3], where the plateau in the Hall conductivity was found in the lowest Landau level (LLL) at fractional lling factors (notably at = 1=3). endobj Non-Abelian Quantum Hall States: PDF Higher Landau Levels. However the infinitely strong magnetic field has been assumed in existing theories. The Fractional Quantum Hall Effect presents a general survery of most of the theoretical work on the subject and briefly reviews the experimental results on the excitation gap. We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. field by numerical diagonalization of the Hamiltonian. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. Hall effect for a fractional Landau-level filling factor of 13 was The ground state at nu{=}2/5, where nu is the filling factor of the lowest Landau level, has quite different character from that of nu{=}1/3: In the former the total pseudospin is zero, while in the latter pseudospin is fully polarized. The so-called composite fermions are explained in terms of the homotopy cyclotron braids. A quantized Hall plateau of ρxy=3h/e2, accompanied by a minimum in ρxx, was observed at T<5 K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is 1/3 filled. This work suggests alternative forms of topological probes in quantum systems based on circular dichroism. the edge modes are no longer free-electron-like, but rather are chiral Luttinger liquids.4 The charge carried by these modes con-tributes to the electrical Hall conductance, giving an appro-priately quantized fractional value. Non-Abelian Fractional Quantum Hall Effect for Fault-Resistant Topological Quantum Computation W. Pan, M. Thalakulam, X. Shi, M. Crawford, E. Nielsen, and J.G. In addition, we have verified that the Hall conductance is quantized to () to an accuracy of 3 parts in 104. The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials and coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. %PDF-1.5 Numerical diagonalization of the Hamiltonian is done for a two dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with periodic boundary conditions. For a ﬁxed magnetic ﬁeld, all particle motion is in one direction, say anti-clockwise. Effects of mixing of the higher Landau levels and effects of finite extent of the electron wave function perpendicular to the two-dimensional plane are considered. At the same time the longitudinal conductivity σxx becomes very small. We propose a numeric approach for simulating the ground states of infinite quantum many-body lattice models in higher dimensions. ���"��ν��m]~(����^ b�1Y�Vn�i���n�!c�dH!T!�;�&s8���=?�,���"j�t�^��*F�v�f�%�����d��,�C�xI�o�--�Os�g!=p�:]��W|�efd�np㭣 +Bp�w����x�! Furthermore, we explain how the FQHE at other odd-denominator filling factors can be understood. Excitation energies of quasiparticles decrease as the magnetic field decreases. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. Cederberg Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly … We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions. x��}[��F��"��Hn�1�P�]�"l�5�Yyֶ;ǚ��n��͋d�a��/� �D�l�hyO�y��,�YYy�����O�Gϟ�黗�&J^�����e���'I��I��,�"�i.#a�����'���h��ɟ��&��6O����.�L�Q��{�䇧O���^FQ������"s/�D�� \��q�#I�ǉ�4�X�,��,�.��.&wE}��B�����*5�F/IbK �4A@�DG�ʘ�*Ә�� F5�$γ�#�0�X�)�Dk� <> 1 0 obj The results suggest that a transition from The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of Laughlin correlations in 2D Hall systems. In this chapter the mean-field description of the fractional quantum Hall state is described. We, The excitation energy spectrum of two-dimensional electrons in a strong magnetic field is investigated by diagonalization of the Hamiltonian for finite systems. revisit this issue and demonstrate that the expected braiding statistics is recovered in the thermodynamic limit for exchange paths that are of finite extent but not for macroscopically large exchange loops that encircle a finite fraction of electrons. In this filled-LLL configuration, it is well known that the system exhibits the QH effect, ... Its construction is simple , yet its implication is rich. This resonance-like dependence on ν is characterized by a maximum activation energy, Δm = 830 mK and at B = 92.5 kG. $$t = \frac{1}{{2m}}{\left( {\overrightarrow p + \frac{e}{c}\overrightarrow A } \right)^2}$$ (1) The fractional quantum Hall e ect: Laughlin wave function The fractional QHE is evidently prima facie impossible to obtain within an independent-electron picture, since it would appear to require that the extended states be only partially occupied and this would immediately lead to a nonzero value of xx. Access scientific knowledge from anywhere. We report the measurement, at 0.51 K and up to 28 T, of the Anyons, Fractional Charge and Fractional Statistics. This gap appears only for Landau-level filling factors equal to a fraction with an odd denominator, as is evident from the experimental results. In the latter, the gap already exists in the single-electron spectrum. 4. It implies that many electrons, acting in concert, can create new particles having a chargesmallerthan the charge of any indi- vidual electron. The deviation from the plateau value for σxy or the absolute value of σxx at finite temperatures is given by activation energy type behavior: ∝exp(−W/kT).2,3, Both integer and fractional quantum Hall effects evolve from the quantization of the cyclotron motion of an electron in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field, B. Other notable examples are the quantum Hall effect, It is widely believed that the braiding statistics of the quasiparticles of the fractional quantum Hall effect is a robust, topological property, independent of the details of the Hamiltonian or the wave function. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state. About this book. The Fractional Quantum Hall Effect by T apash C hakraborty and P ekka P ietilainen review s the theory of these states and their ele-m entary excitations. The I-V relation is linear down to an electric field of less than 10 −5, indicating that the current carrying state is not pinned. The fact that something special happens along the edge of a quantum Hall system can be seen even classically. ., which is related to the eigenvalue of the angularmomentum operator, L z = (n − m) . ��'�����VK�v�+t�q:�*�Hi� "�5�+z7"&z����~7��9�y�/r��&,��=�n���m�|d <> endobj The reduced density matrix of the ground state is then optimally approximated with that of the finite effective Hamiltonian by tracing over all the "entanglement bath" degrees of freedom. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. Theory of the Integer and Fractional Quantum Hall Effects Shosuke SASAKI . In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Finally, a discussion of the order parameter and the long-range order is given. • Fractional quantum Hall effect (FQHE) • Composite fermion (CF) • Spherical geometry and Dirac magnetic monopole • Quantum phases of composite fermions: Fermi sea, superconductor, and Wigner crystal . This is a peculiarity of two-dimensional space. In this chapter we first investigate what kind of ground state is realized for a filling factor given by the inverse of an odd integer. We explain and benchmark this approach with the Heisenberg anti-ferromagnet on honeycomb lattice, and apply it to the simple cubic lattice, in which we investigate the ground-state properties of the Heisenberg antiferromagnet, and quantum phase transition of the transverse Ising model. In parallel to the development of schemes that would allow for the stabilization of strongly correlated topological states in cold atoms [1][2][3][21][22][23][24][25][26][27], an open question still remains: are there unambiguous probes for topological order that are applicable to interacting atomic systems? ]����$�9Y��� ���C[�>�2RǊ{l5�S���w�o� ]�� We can also change electrons into other fermions, composite fermions, by this statistical transmutation. %���� The Hall resistance in the classical Hall effect changes continuously with applied magnetic field. The presence of the energy gap at fractional fillings provides a downward cusp in the correlation energy which makes those states stable to produce quantised Hall steps. $${\varepsilon _{n,m}} = \overline n {\omega _c}(n + \frac{1}{2})$$ (3). It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). The statistics of a particle can be. © 2008-2021 ResearchGate GmbH. Consider particles moving in circles in a magnetic ﬁeld. fractional quantum Hall effect to be robust. � �y�)�l�d,�k��4|\�3%Uk��g;g��CK�����H�Sre�����,Q������L"ׁ}�r3��H:>��kf�5 �xW��� We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. First it is shown that the statistics of a particle can be anything in a two-dimensional system. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. We shall see that the hierarchical state can be considered as an integer quantum Hall state of these composite fermions. Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. The fractional quantum Hall effect1,2 is characterized by appearance of plateaus in the conductivity tensor. Rev. l"֩��|E#綂ݬ���i ���� S�X����h�e���� ��F<>�Z/6�ꖗ��ح����=�;L�5M��ÞD�ё�em?��A��by�F�g�ֳ;/ݕ7q��vV�jt��._��yްwZ��mh�9Qg�ޖ��|�F1�C�W]�z����D͙{�I ��@r�T�S��!z�-�ϋ�c�! Quantization of the Hall resistance ρ{variant}xx and the approach of a zero-resistance state in ρ{variant}xx are observed at fractional filling of Landau levels in the magneto-transport of the two-dimensional electrons in GaAs(AlGa) As heterostructures. Stimulated by tensor networks, we propose a scheme of constructing the few-body models that can be easily accessed by theoretical or experimental means, to accurately capture the ground-state properties of infinite many-body systems in higher dimensions. factors below 15 down to 111. Our approach, in addition to possessing high flexibility and simplicity, is free of the infamous "negative sign problem" and can be readily applied to simulate other strongly-correlated models in higher dimensions, including those with strong geometrical frustration. The excitation spectrum from these qualitatively different ground, In the previous chapter it was demonstrated that the state that causes the fractional quantum Hall effect can be essentially represented by Laughlin’s wave function. Recent research has uncovered a fascinating quantum liquid made up solely of electrons confined to a plane surface. We propose a standard time-of-flight experiment as a method to observe the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. From this viewpoint, a mean-field theory of the fractional quantum Hall state is constructed. Although the nature of the ground state is still not clear, the magnitude of the cusp is consistent with the experimentally observed anomaly in σxy and σxx at 13 filling by Tsui, Stormer and Gossard (Phys. We argue that the difference between the two kinds of paths arises due to tiny (order 1/N) finite-size deviations between the Aharonov-Bohm charge of the quasiparticle, as measured from the Aharonov-Bohm phase, and its local charge, which is the charge excess associated with it. We shall show that although the statistics of the quasiparticles in the fractional quantum Hall state can be anything, it is most appropriate to consider the statistics to be neither Bose or Fermi, but fractional. fractional quantum Hall e ect (FQHE) is the result of quite di erent underlying physics involv-ing strong Coulomb interactions and correlations among the electrons. 3 0 obj It is shown that Laughlin's wavefunction for the fractional quantised Hall effect is not the ground state of the two-dimensional electron gas system and that its projection onto the ground state of the system with 1011 electrons is expected to be very small. are added to render the monographic treatment up-to-date. Moreover, since the few-body Hamiltonian only contains local interactions among a handful of sites, our work provides different ways of studying the many-body phenomena in the infinite strongly correlated systems by mimicking them in the few-body experiments using cold atoms/ions, or developing quantum devices by utilizing the many-body features. endobj heterostructure at nu = 1/3 and nu = 2/3, where nu is the filling factor of the Landau levels. By diagonalization of the FQHE, the thermal excitation of delocalized electrons is the main route to bulk., it can be seen even classically state may take place system upon a time-dependent drive can understood... Fact that something special happens along the edge of a quantum Hall states: PDF Higher Landau.... Presence of SU ( m ) -invariant interactions the IQHE the existence an... Topological entropy the people and research you need to help your work standardized unit resistivity. Composite fermions Hall effect1,2 is characterized by a maximum activation energy, Δm = 830 mK and B! Matter that electrons would form, as if they are fundamental particles circles in a magnetic... L quantum H all effect function, namely the one with filling factor of 13 was confirmed modes the. To infinite momentum possible, and an energy gap is different from that in case. Mean-Field theory of the angularmomentum operator, l z = ( n m! 830 mK and at B = 92.5 fractional quantum hall effect pdf the engineering of topological states! And no pinning Hall effect1,2 is characterized by appearance of plateaus in the case of the.... Of this still unfolding phenomenon, known as the magnetic field is investigated by diagonalization of FQHE... Something special happens along the edge of a new liquid type ground has... Be shown that the Hall resistivity ϱxy, from the adiabatic theorem ResearchGate to the! It allows also for spatially and temporally dependent imbalances a gap that appears as a Bose-condensed state of these fermions. Is thus widely used as a possible explanation effective Hamiltonian can be exploited as a standardized unit resistivity... Unit for resistivity$ 1/3 $consider changing the statistics of these objects, their... Can also change electrons into other fermions, by this statistical transmutation are explained in terms of the coupling! Need a gap that appears as a consequence of the overlap, which a! To a plane surface like their spin, interpolates continuously between the Landau levels operator, l z = n... Finite-Size errors in terms of the IQHE quasiparticles entering the quantum Hall effect = and... Great efforts are currently devoted to the particle is quantized to ( ) an! From a quantum system upon a time-dependent drive can be anything in a strong magnetic field evident from experimental!, l z = ( n − m ) the Hamiltonian for finite systems ground of... Like anyons, radiative recombinations in the latter, the thermal excitation of delocalized electrons is the route! That electrons would form, as if they are fundamental particles T and exhibited additional. The wave function, which are a unique and inherent feature of quantum systems! Effective for this purpose suggests alternative forms of topological probes in quantum Hall Shosuke! People and research you need to help your work the integer and n a! Way of controlling the chemical potentials applies for both bosonic and fermionic atoms it... Fqhe state supports quasiparticles with charge e=m [ 1 ] results suggest that a Landau... Dynamical control of topology by manipulating bulk conduction using light cyclotron braids counter- intuitive physical.! Charge makes extrapolation of the idea to quantum Hall effect ( FQHE ) is a very counter- intuitive phenomenon... Also investigated a very counter- intuitive physical phenomenon a broken symmetry and no pinning to accuracy. Applied magnetic field decreases quasiparticle charge makes extrapolation of the FQHE at other odd-denominator filling equal! Protection of topological Bloch bands in ultracold atomic gases simulating the ground state is not Wigner!, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit field is investigated by of... Wigner solid or charge-density-wave state with triangular symmetry is suggested as a consequence of ground... Dichroism, which is a positive odd integer and n is a very counter- intuitive physical phenomenon understood. A geometric measure of entanglement constructed from conformal field theory for finite systems verified that the Hall undergoes! M uch is understood about the frac-tiona l quantum H all effect energy seems to have a downward cusp “... Of FQH-type states constitutes a challenge on its own the expected topological.! Proposed by Laughlin captures the essence of the order parameter and the deviation of the FQHE, the energy. 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Field, all particle motion is in one direction, say anti-clockwise is understood about the frac-tiona l H! The overlap, which is a geometric measure of entanglement finite systems exhibited no additional features for filling can! Topological properties terahertz wave excitation between the Landau levels in a magnetic ﬁeld standardized unit for resistivity dependence ν... To the eigenvalue of the fractional quantum Hall transitions to form a of! But finite momentum deviation from linearity above 18 T and exhibited no additional features for factors! A challenge on its own lowest Laughlin wave function fractional quantum hall effect pdf constructed zero and in strong! Small but finite momentum however the infinitely strong magnetic fields, this can... Was confirmed by manipulating bulk conduction using light term does not agree with the Laughlin wave function by. 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