Emergent Conformal Symmetry and Geometric Transport Properties of Quantum Hall States on Singular Surfaces

Can, Tankut; Chiu, Yi Hsing; Laskin, Michael; Wiegmann, P.

doi:10.1103/physrevlett.117.266803

Cited by 50 publications

(59 citation statements)

References 45 publications

(121 reference statements)

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“…TINCs and junctions thereof could act as building blocks for more complex 3D mesoscopic setups for Dirac electrons -much as quantum point contacts and AB rings are used for planar setups -in particular for hybrid TIsuperconducting systems typically used in the search for Majorana fermions [9,38,39]. TINCs can also be seen as building units of arbitrarily shaped TINWs [29], where more exotic aspects of QH physics on curved surfaces can be studied [40,41]. Indeed, in Ref.…”

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confidence: 99%

Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

et al. 2020

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Magnetotransport through cylindrical topological insulator (TI) nanowires is governed by the interplay between quantum confinement and geometric (Aharonov-Bohm and Berry) phases. Here, we argue that the much broader class of TI nanowires with varying radius -for which a homogeneous coaxial magnetic field induces a varying Aharonov-Bohm flux that gives rise to a non-trivial masslike potential along the wire -is accessible by studying its simplest member, a TI nanocone. Such nanocones allow to observe intriguing mesoscopic transport phenomena: While the conductance in a perpendicular magnetic field is quantized due to higher-order topological hinge states, it shows resonant transmission through Dirac Landau levels in a coaxial magnetic field. Furthermore, it may act as a quantum magnetic bottle, confining surface Dirac electrons and leading to Coulomb blockade. We show numerically that the above-mentioned effects occur for experimentally accessible values of system size and magnetic field, suggesting that TI nanocone junctions may serve as building blocks for Dirac electron optics setups.Electronic transport across phase-coherent structures has been a central topic of solid state research ever since the birth of mesoscopic physics some 40 years ago. While the complexity of mesoscopic setups has steadily increased, from the simple gate-defined quantum point contacts of the '80s [1] to elaborate present-day electron optics circuits in semiconductors [2] and graphene [3,4], their structure remains in the vast majority of cases planar -i.e. transport takes place in flat two-dimensional (2D) space. Exceptions to the 2D scenario are samples based on carbon nanotubes and 3D topological insulator (3DTI) nanowires [5][6][7][8]. 3DTIs are bulk band insulators hosting protected 2D surface metallic statesà la Dirac [9]. In mesoscopic nanostructures built out of 3DTIs low-temperature phase-coherent transport takes place on a 2D Dirac metal wrapped around an insulating 3D bulk. As such, it is strongly dependent on a peculiar conjunction of structural (real space) and spectral (reciprocal space) geometrical properties. This has remarkable consequences even for the possibly simplest setup, a topological insulator nanowire (TINW) with constant circular cross section in a coaxial magnetic field, shown in Fig. 2(a). The magnetoconductance of such an object is characterized by a non-trivial interplay between two fundamentals of mesoscopic physics: quantum confinement and geometric [Aharonov-Bohm (AB) and Berry] phases [6][7][8][10][11][12].

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confidence: 99%

Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

et al. 2020

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“…Geometry can also induce a reminiscent of the Hall effect [5]. Related important investigations can also be found in the literature, for instance: the quantum Hall effect near conical singularities [6] and investigations taking into account the Pauli equation for a charged spin particle on a curved surface with externally applied fields [7,8]. Recent developments can also be found in [9,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Position-dependent mass effects in the electronic transport of two-dimensional quantum systems: Applications to nanotubes

Serafim

Santos

Lima

et al. 2019

Physica E: Low-dimensional Systems and Nanostructures

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In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We find the Schrödinger equation for a general surface following the da Costa approach, obtaining the geometrical potential for systems with PDM. We obtain expressions for the transmittance and reflectance for a general surface of revolution and, as a first application of the general results obtained here, we investigate the transport properties of deformed nanotubes whose variation of the effective mass with the radius has been disconsidered in previous studies. We find that the inclusion of the position-dependent mass, can induce a significant correction in the transport properties of the system. This reveals that the transport properties of two-dimensional quantum systems are sensitive to the PDM and that, when modeling electronic transport in surfaces, this effects should be considered.

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“…The version for a curved non-interacting 2DEG in the presence of an electric and magnetic field was investigated in [7], where it was showed that no coupling between the fields and the quantum geometric potential arises. An application in this case can be viewed in [9], where important features concerned to the quantum Hall states on surfaces with conical singularities has been presented. The version for Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field has been addressed in [10].…”

Section: Introductionmentioning

confidence: 99%

A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

et al. 2018

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In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric potential arises and, since it manifests due to this confinement procedure, it depends on the transverse to the surface mass component. This inspired us to consider, in this paper, the effects due to an anisotropic effective mass on a non-interacting two dimensional electron gas confined on a curved surface, a fact not explored before in this context. By tailoring the mass, many investigations carried out in the literature can be improved which in turns can be useful to better designing electronic systems without modifying the geometry of a given system. Some examples are examined here, as a particle on helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.

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Emergent Conformal Symmetry and Geometric Transport Properties of Quantum Hall States on Singular Surfaces

Cited by 50 publications

References 45 publications

Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

Position-dependent mass effects in the electronic transport of two-dimensional quantum systems: Applications to nanotubes

A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

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