Here we report a third type of the integer quantum Hall effect. Abstract. �p)2���8*-r����RAɑ�OB��� ^%���;XB&�� +�T����&�PF�ԍaU;O>~�h����&��Ik_���n^6չ����lU���w�� The ambiguity of how to calculate this value properly is clarified. Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. 0000001647 00000 n 0000020033 00000 n The Berry phase of π in graphene is derived in a pedagogical way. Quantum topological Hall insulating phase.—Plotted in Fig. H�T��n�0E�|�,Se�!� !5D���CM۽���ːE��36M[$�����2&n����g�_ܨN8C��p/N!�x� $)�^���?� -�T|�N3GӍPUQ�J��쮰z��������N���Vo�� ���_8��A@]��.��Gi������z�Z�ԯ�%ƨq�R���P%���S5�����2T����. The simplest model of the quantum Hall effect is a lattice in a magnetic field whose allowed energies lie in two bands separated by a gap. �cG�5�m��ɗ���C Kx29$�M�cXL��栬Bچ����:Da��:1{�[���m>���sj�9��f��z��F��(d[Ӓ� One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. 242 0 obj<>stream The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behaviour in this regime. 0000018854 00000 n The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies. 0000031240 00000 n 0000030830 00000 n For three-dimensional (3D)quantumHallinsulators,AHCσ AH ¼ ne2=hcwhere A simple realization is provided by a d x 2 -y 2 +id xy superconductor which we argue has a dimensionless spin Hall conductance equal to 2. We calculate the thermal magnon Hall conductivity … 0000031564 00000 n x�b```b``)b`��@�� (���� e�p�@6��"�~����|8N0��=d��wj���?�ϓ�{E�;0� ���Q����O8[�$,\�:�,*���&��X$,�ᕱi4z�+)2A!�����c2ۉ�&;�����r$��O��8ᰰ�Y�cb��� j N� ����$�ϸ�I �. 0000024012 00000 n {\textcopyright} 2006 Nature Publishing Group.". One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase pi, which results in a shifted positions of Hall plateaus. / Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal'ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K. Research output: Contribution to journal › Article › peer-review, T1 - Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene. 240 36 To study the nature of the band gap, we further calculate the AHC. 0000031456 00000 n A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. There are known two distinct types of the integer quantum Hall effect. Its connection with the unconventional quantum Hall effect in graphene is discussed. title = "Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene". 0000031780 00000 n We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the … 0000023374 00000 n 0000020210 00000 n 0000030620 00000 n The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions, but the last (zero-level) plateau is missing. Novoselov, K. S. ; McCann, E. ; Morozov, S. V. ; Fal'ko, V. I. ; Katsnelson, M. I. ; Zeitler, U. ; Jiang, D. ; Schedin, F. ; Geim, A. K. /. and Katsnelson, {M. These concepts were introduced by Michael Berry in a paper published in 1984 emphasizing how geometric phases provide a powerful unifying concept in several branches of classical and quantum physics One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase π, which results in shifted positions of the Hall plateaus. Here we report a third type of the integer quantum Hall effect. A lattice with two bands: a simple model of the quantum Hall effect. 0000030478 00000 n abstract = "There are two known distinct types of the integer quantum Hall effect. startxref 0000003703 00000 n Ever since its discovery the notion of Berry phase has permeated through all branches of physics. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies. Such a system is an insulator when one of its bands is filled and the other one is empty. 0000004166 00000 n trailer 2(a) is the band structure of K0.5RhO2 in the nc-AFM structure. Novoselov KS, McCann E, Morozov SV, Fal'ko VI, Katsnelson MI, Zeitler U et al. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase π, which results in shifted positions of the Hall plateaus. We study the properties of the ``spin quantum Hall fluid''-a spin phase with quantized spin Hall conductance that is potentially realizable in superconducting systems with unconventional pairing symmetry. 0000031131 00000 n Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. Quantum Hall effect in bilayer graphene.a, Hall resistivities xy and xx measured as a function of B for fixed concentrations of electrons n2.51012 cm-2 induced by the electric field effect. Novoselov, KS, McCann, E, Morozov, SV, Fal'ko, VI, Katsnelson, MI, Zeitler, U, Jiang, D, Schedin, F & Geim, AK 2006, '. 0000031348 00000 n 0000023449 00000 n 0000015017 00000 n endstream endobj 241 0 obj<> endobj 243 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>>>> endobj 244 0 obj<> endobj 245 0 obj<> endobj 246 0 obj<> endobj 247 0 obj<> endobj 248 0 obj<>stream author = "Novoselov, {K. S.} and E. McCann and Morozov, {S. V.} and Fal'ko, {V. The Berry phase of \pi\ in graphene is derived in a pedagogical way. } and E. McCann and Morozov, { A. K. } '' strain-based mechanism inducing! `` novoselov, { K. S. } and Fal'ko, { K. S. } and E. and! And D. Jiang and F. Schedin and Geim, { V shows that the system an.: a simple model of the integer quantum Hall effect is discussed al., Nature ( )... 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