Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State

Maciejko, Joseph; Liu, Chaoxing; Oreg, Yuval; Qi, Xiao Liang; Wu, Congjun; Zhang, Shou Cheng

doi:10.1103/physrevlett.102.256803

Cited by 258 publications

(398 citation statements)

References 23 publications

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“…In addition, the edge states do not exhibit significant variation in transport properties for temperatures between 20 mK and 1 K measured. This is in contrast to theoretical studies, which have predicted power law corrections to the edge conductance as a function of temperature due to single particle inelastic [13][14][15], and correlated two-particle backscattering [16], while such corrections vanish for Kondo scattering from a magnetic impurity in a dc limit [17]. The absence of such power laws in the temperature dependence of the edge conductance observed here indicates that spinflip single particle backscattering [14,18] is the dominant edge scattering process in this system.…”

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confidence: 54%

“…In addition, the energy scale of the inelastic scattering such as from nearby charge puddles [15] is ℏv F =l inelastic ≲ 70 mK, where the inelastic scattering length l inelastic is several μm [20], and, hence, a weak temperature dependence observed here may not be all that surprising. Finally, a low Fermi velocity would indicate that correlations may be important in the edge physics of the TI InAs=GaSb [16], albeit the presence of the electrostatic gates leads to significant screening. …”

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confidence: 99%

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Observation of Edge Transport in the Disordered Regime of Topologically InsulatingInAs/GaSbQuantum Wells

et al. 2014

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We observe edge transport in the topologically insulating InAs=GaSb system in the disordered regime. Using asymmetric current paths we show that conduction occurs exclusively along the device edge, exhibiting a large Hall signal at zero magnetic fields, while for symmetric current paths, the conductance between the two mesoscopicly separated probes is quantized to 2e 2 =h. Both quantized and self-averaged transport show resilience to magnetic fields, and are temperature independent for temperatures between 20 mK and 1 K. DOI: 10.1103/PhysRevLett.112.026602 PACS numbers: 72.25.Dc, 73.23.-b, 73.63.Hs Two-dimensional (2D) topological insulators (TI) are a novel class of materials that are insulating in the bulk but which display uniquely conductive edge channels [1][2][3][4]. These one-dimensional (1D) edge modes are helical, with the spin direction tied to the electron direction of motion, and are protected from backscattering by the time reversal symmetry (TRS) [5,6]. Applying magnetic fields breaks the TRS, removing the topological protection of the 1D helical liquid (HL) from single particle backscattering, resulting in a gap opening in the edge spectrum. Such HL channels were first observed in transport measurements in HgTe=CdTe quantum wells, and much of the HL phenomenology has been confirmed and elucidated in those first experiments [7,8]. Recently, Du et al. reported quantized transport in the inverted regime of Si-doped InAs=GaSb quantum wells in mesoscopic samples [9], where the existence of helical edge states was proposed in Ref.[10] and the first experimental evidence provided in Ref.[11] through scaling arguments due to the presence of residual bulk carriers. Unlike that observed in HgTe=CdTe [7], quantized transport in InAs=GaSb persists to magnetic fields of several Tesla [9,11], challenging the common understanding of 2D TIs in terms of TRS protected edge states and associated Z 2 topological invariant.Much remains to be learned about the nature and robustness of HL, in particular, to TRS breaking and disorder. In addition, edge transport in InAs=GaSb has so far only been indirectly assessed in ballistic samples [9,11]. In this Letter we study TI InAs=GaSb quantum wells in the disordered regime [12], where the total device size is much larger than the ballistic length of the HL, and show that transport in the topological regime manifestly occurs along the sample perimeter and is quantized to values consistent with the existence of a HL. Similar to ballistic regime studies [9,11], the conduction is also seen to be only weakly dependent on externally applied magnetic fields of up to 1 T. We argue that this behavior is due to the reduced effective g factor of the edge states originating from their small Fermi velocity v F . In addition, the edge states do not exhibit significant variation in transport properties for temperatures between 20 mK and 1 K measured. This is in contrast to theoretical studies, which have predicted power law corrections to the edge conductance as a function of temperatur...

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Observation of Edge Transport in the Disordered Regime of Topologically InsulatingInAs/GaSbQuantum Wells

et al. 2014

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“…(17). Here, the explicit dependence on the position Z n of the nuclear spin has been suppressed in the notation for simplicity, i.e., A υυ P ,j n…”

Section: The Hf Interactions For P-like Statesmentioning

confidence: 99%

“…10 However, also deviations from perfect conductance have been observed in longer HgTe devices, 6,7,11,12 which could stem from, e.g., inelastic scattering mechanisms. [13][14][15][16][17][18] The effect of external magnetic fields have also been considered. 6,8,[19][20][21][22][23][24] The TI state in HgTe QWs was predicted by Bernevig, Hughes, and Zhang (BHZ) 25 by using a simplified k · p model containing states with S-and P -like symmetries, respectively.…”

Section: Introductionmentioning

confidence: 99%

Hyperfine interactions in two-dimensional HgTe topological insulators

Lunde

Platero

2013

Phys. Rev. B

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We study the hyperfine interaction between the nuclear spins and the electrons in a HgTe quantum well, which is the prime experimentally realized example of a two-dimensional topological insulator. The hyperfine interaction is a naturally present, internal source of broken time-reversal symmetry from the point of view of the electrons. The HgTe quantum well is described by the so-called Bernevig-Hughes-Zhang (BHZ) model. The basis states of the BHZ model are combinations of both S-and P -like symmetry states, which means that three kinds of hyperfine interactions play a role: (i) the Fermi contact interaction, (ii) the dipole-dipole-like coupling, and (iii) the electron-orbital to nuclear-spin coupling. We provide benchmark results for the forms and magnitudes of these hyperfine interactions within the BHZ model, which give a good starting point for evaluating hyperfine interactions in any HgTe nanostructure. We apply our results to the helical edge states of a HgTe two-dimensional topological insulator and show how their total hyperfine interaction becomes anisotropic and dependent on the orientation of the sample edge within the plane. Moreover, for the helical edge states, the hyperfine interaction due to the P -like states can dominate over the S-like contribution in certain circumstances.

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“…3c, the coexisting non-chiral states can potentially enable kink states from different valleys to mix via multiple-particle processes, thus introducing backscattering. Indeed, several such mechanisms have been put forward to explain the imprecise conductance quantization of the quantum spin hall edge states 27 including the possibility of a Kondo effect [28][29][30][31] . Similar mechanisms may be of relevance here and will be the subject of future studies.…”

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Gate-controlled topological conducting channels in bilayer graphene

et al. 2016

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The existence of inequivalent valleys K and K′ in the momentum space of two-dimensional hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types of electronics, in analogy to the role played by electron spin 1-3 . In materials with broken inversion symmetry, such as an electrically gated bilayer graphene 4,5 , the momentum-space Berry curvature  carries opposite sign in the K and K′ valleys. A sign reversal of  along an internal boundary of the sheet gives rise to counterpropagating one-dimensional conducting modes encoded with opposite valley indices. These metallic states are topologically protected against backscattering in the absence of valley-mixing scattering, and thus can carry current ballistically 1,6-11 . In bilayer graphene, the reversal of  can occur at the domain wall of AB and BA stacked domains 12-14 , or at the line junction of two oppositely gated regions 6 . The latter approach can provide a scalable platform to implement valleytronic operations such as valves and waveguides 9,15 , but is technically challenging to realize. Here we fabricate a dual-split-gate structure in bilayer graphene and demonstrate transport evidence of the predicted metallic states. They possess a mean free path of up to a few hundred nanometers in the absence of a magnet field. The application of perpendicular magnetic field suppresses backscattering significantly and enables a 400-nanometer-long junction to exhibit conductance close to the ballistic limit of 4 e 2 /h at 8 Tesla. Our experiment paves the path to the realization of gate-controlled ballistic valley transport and the development of valleytronic applications in atomically thin materials.Exploiting the valley degree of freedom in hexagonal lattices may offer an alternative pathway to achieving low-power-consumption electronics. Experiments have shown that a net valley polarization in the material can be induced by the use of circularly polarized light 2,16,17 or a net bulk current [18][19][20] . However the use of light is not always desirable in electronics and device proposals using bulk valley polarization often put stringent requirements on the size and edge orientation of the active area 3 . Alternatively, electrically created, valley-polarized topological conducting channels in high-mobility bilayer graphene may offer a robust, scalable platform to realize valleytronic operations 1,6,[8][9][10][11][12][13][14][15] . Figure 1a illustrates the dual-split-gating scheme proposed by Martin et al 6 , where an AB-stacked bilayer graphene (BLG) sheet is controlled by two pairs of top and bottom gates separated by a line junction. The device operates in the regime where both the left and the right regions of the BLG sheet are insulating due to a bulk band gap induced by the independently applied displacement fields DL and DR. In the "odd" field configuration, where DLDR < 0, theory predicts the existence of eight conducting modes (referred to as the "kink" states) propagating along the line ...

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Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State

Cited by 258 publications

References 23 publications

Observation of Edge Transport in the Disordered Regime of Topologically InsulatingInAs/GaSbQuantum Wells

Observation of Edge Transport in the Disordered Regime of Topologically InsulatingInAs/GaSbQuantum Wells

Hyperfine interactions in two-dimensional HgTe topological insulators

Gate-controlled topological conducting channels in bilayer graphene

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