Nonlocal Transport in the Quantum Spin Hall State

Roth, Albrecht; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; Maciejko, Joseph; Qi, Xiao-Liang; Zhang, Shoucheng

doi:10.1126/science.1174736

Cited by 900 publications

(1,078 citation statements)

References 16 publications

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“…Although midgap helical edge sates in 2D quantum spin Hall systems can support long-range nonlocal conduction [24][25][26] , such spin helical edge states did not exist in our study because BLG is topologically trivial. Midgap valley helical modes may still exist at topological domain walls or edges of BLG in certain circumstances [27][28][29] , and may potentially lead to nonlocal conduction.…”

mentioning

confidence: 75%

Gate-tunable topological valley transport in bilayer graphene

et al. 2015

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Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands 1 , is a distinct feature of two-dimensional Dirac materials [1][2][3][4][5] . Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests [2][3][4][5] . Bilayer graphene (BLG) is a unique system whose intrinsic inversion symmetry can be controllably broken by a perpendicular electric field, offering a rare possibility for continuously tunable valley-topological transport. Here, we used a perpendicular gate electric field to break the inversion symmetry in BLG, and a giant nonlocal response was observed as a result of the topological transport of the valley pseudospin. We further showed that the valley transport is fully tunable by external gates, and that the nonlocal signal persists up to room temperature and over long distances. These observations challenge contemporary understanding of topological transport in a gapped system, and the robust topological transport may lead to future valleytronic applications.In crystalline solids, a topological current can be induced by the Berry phase of the electronic wave function 6 . Examples include the quantum Hall current in a magnetic field, and the spin Hall current arising from spin-orbit coupling. Such topological transport is robust against impurities and defects in materials -a feature that is much sought after in potential electronic applications. In such applications, the ability to switch and to continuously tune the topological transport is crucial. The topological current is in principle dictated by the crystal symmetry, which is difficult to change in Page 3 of 16 bulk materials. Bilayer graphene, however, offer new opportunities in which inversion symmetry can be controllably broken by an external electric field in the perpendicular direction.The topological current controlled by the inversion symmetry breaking is associated with carriers' valley pseudospin, which characterises the two-fold degenerate band-edges located at the corners of the hexagonal Brillouin zone. The topological Hall current, odd under time-reversal but even under inversion, is strictly zero in pristine mono-and bi-layer graphene which respect both symmetries. When the inversion symmetry is broken, however, time-reversal symmetry requires the Hall currents to have opposite signs and equal magnitudes in the two valleys (i.e., a valley The nonlocal transport persists up to room temperature and over long distances (up to 10 m). Our results represent major progress in the quest for a robust, tunable valley pseudospin system among various alternatives [3][4][5]11,12 , and indicate the possibility of using the nonlocal topological transport in practical applications under ambient conditio...

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confidence: 75%

Gate-tunable topological valley transport in bilayer graphene

et al. 2015

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“…The bulk boundary correspondence relates these modes to a Z 2 topological invariant characterizing time-reversal invariant Bloch Hamiltonians. Signatures of these protected boundary modes have been observed in transport experiments on 2D HgCdTe quantum wells [14][15][16] and in photoemission and scanning tunnel microscope experiments on three-dimensional ͑3D͒ crystals of Bi 1−x Sb x , [17][18][19] Bi 2 Se 3 , 20 Bi 2 Te 3 , 22,23,25 and Sb 2 Te 3 . 26 Topological insulator behavior has also been predicted in other classes of materials with strong spin-orbit interactions.…”

Section: Introductionmentioning

confidence: 93%

“…Recent interest in topological states 2-4 has been stimulated by the realization that the combination of time-reversal symmetry and the spin-orbit interaction can lead to topological insulating electronic phases [5][6][7][8][9][10] and by the prediction [11][12][13] and observation [14][15][16][17][18][19][20][21][22][23][24][25][26] of these phases in real materials. A topological insulator is a two-or three-dimensional material with a bulk energy gap that has gapless modes on the edge or surface that are protected by time-reversal symmetry.…”

Section: Introductionmentioning

confidence: 99%

Topological defects and gapless modes in insulators and superconductors

2010

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We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians.We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H͑k , r͒ that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. Disciplines Physical Sciences and Mathematics | Physics

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“…The reason for this discrepancy is unclear. It is possibly caused by variations due to universal conductance fluctuations in the nanowire, or the effects of macroscopic irreversibility brought about by quasiparticles that enter and are emitted from the metallic voltage probes 19,26 . The data also show finite conductance (E0.5e 2 /h in Fig.…”

Section: Aharonov-bohm Oscillations As a Function Of Fermi Energymentioning

confidence: 99%

Aharonov–Bohm oscillations in a quasi-ballistic three-dimensional topological insulator nanowire

et al. 2015

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Aharonov-Bohm oscillations effectively demonstrate coherent, ballistic transport in mesoscopic rings and tubes. In three-dimensional topological insulator nanowires, they can be used to not only characterize surface states but also to test predictions of unique topological behaviour. Here we report measurements of Aharonov-Bohm oscillations in (Bi 1.33 Sb 0.67 )Se 3 that demonstrate salient features of topological nanowires. By fabricating quasi-ballistic three-dimensional topological insulator nanowire devices that are gate-tunable through the Dirac point, we are able to observe alternations of conductance maxima and minima with gate voltage. Near the Dirac point, we observe conductance minima for zero magnetic flux through the nanowire and corresponding maxima (having magnitudes of almost a conductance quantum) at magnetic flux equal to half a flux quantum; this is consistent with the presence of a low-energy topological mode. The observation of this mode is a necessary step towards utilizing topological properties at the nanoscale in post-CMOS applications.

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Nonlocal Transport in the Quantum Spin Hall State

Cited by 900 publications

References 16 publications

Gate-tunable topological valley transport in bilayer graphene

Gate-tunable topological valley transport in bilayer graphene

Topological defects and gapless modes in insulators and superconductors

Aharonov–Bohm oscillations in a quasi-ballistic three-dimensional topological insulator nanowire

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