Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

Hsu, Chia-Hsiang; Stano, Peter; Klinovaja, Jelena; Loss, Daniel

doi:10.1103/physrevb.97.125432

Cited by 64 publications

(73 citation statements)

References 101 publications

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“…Experimentally, however, the perfect quantization of the conductance was not observed, despite measurements in different topological insulators such as HgTe/CdTe and InAs/GaSb quantum wells, bismuth layers and WTe 2 monolayers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Suggestions for the potential sources for the deviation from perfect conductance include effects such as electron-electron interactions, disorder, electrical noise, inelastic scattering, and others [25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

2020

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We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance G0 of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature TK for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global U (1) symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the linear conductance of the backscattering current follows a power-law behavior G ∼ (T /TK ) 2 , and the strong exponent implies that the anisotopry might be a dominant cause for reducing the perfect edge conductance. arXiv:1912.02838v1 [cond-mat.str-el] 5 Dec 2019 Q S H I Impurity site t J I B e/(G 0 Γ) (b) J yy /Γ =1 J yy /Γ =0.7 J yy /Γ =0.5 J yy /Γ =0.3 J yy /Γ =0.1 0.0 0.2 0.4 0.6 0.8 1.0 J yy /Γ T eq K eG/(G 0 Γ) ·10 3(a) J yy /Γ =0.9 J yy /Γ =0.7 J yy /Γ =0.5 J yy /Γ =0.3 J yy /Γ =0.1

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Section: Introductionmentioning

confidence: 99%

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

2020

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“…Several other mechanisms might explain the 0.5 anomaly in QPCs or nanowires. These mechanisms include helical edge reconstruction [38], the formation of a Wigner crystal [39], or hyperfine interactions [40]. However, given the importance of the camel back in the valence band for our observation of the 0.5 anomaly, we believe that the mechanism presented here is the most plausible one.…”

Section: Experimental Consequences Of a Spin Gapmentioning

confidence: 76%

“…Another proposal considers the hyper-fine interaction of electrons with the nuclear spins which can spontaneously break TR symmetry and lead to an k F independent partial gap [40,51]. Because of the low non-zero nuclear spin in HgTe, we expect the gap to be one order of magnitude smaller than in systems based on GaAs.…”

Section: S-12mentioning

confidence: 98%

Interacting topological edge channels

et al. 2019

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Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical character of those states is by now well established experimentally, it is a fundamental open question how those edge states interact with each other when brought in spatial proximity. We employ a topological quantum point contact to guide edge channels from opposite sides into a quasi-onedimensional constriction, based on inverted HgTe quantum wells. Apart from the expected quantization in integer steps of 2e 2 /h, we find a surprising additional plateau at e 2 /h. We explain our observation by combining band structure calculations and repulsive electron-electron interaction effects captured within the Tomonaga-Luttinger liquid model. The present results may have direct implications for the study of one-dimensional helical electron quantum optics, Majorana-and potentially para-fermions. The quantum spin Hall effect has been predicted in several systems [1][2][3][4] and was first realized in HgCdTe/HgTe quantum wells [5]. Later, this phase was observed in other material systems such as InAs/GaSb double quantum wells [6] and in monolayers of WTe 2 and bismuthene [7,8]. The defining properties of this state, related to its helical nature, are well established by numerous experiments such as the observation of conductance quantization of two spin polarized edge channels G 0 = 2e 2 /h with e the electron charge and h the Planck's constant [5]. Additionally, non-local edge transport and spin-polarization of the edge channels were demonstrated by suitable transport experiments [9,10]. We instead target a still open question, namely how helical edge states interact with each other.A quantum point contact (QPC) can be used to guide * All three authors contributed equally to this work, email: Jonas.Strunz@physik.uni-wuerzburg.de edge channels from opposite boundaries of the sample into a constriction. Such a device allows for studies of charge and spin transfer mechanisms by, e.g., adjusting the overlap of the edge states [11][12][13][14][15][16][17][18][19][20]. Besides the general interest in the study of transport processes in such a device, the appropriate model to describe the essential physics and to capture interaction effects of helical edge states is still unclear. The one-dimensionality of the helical edge modes suggests a description in terms of the Tomonaga-Luttinger liquid when electron-electron interactions are taken into account. In this respect, the QPC setup provides an illuminating platform as it may give rise to particular backscattering processes.We present the realization of a QPC based on HgTe quantum wells as evidenced by the observation of the expected conductance steps in integer values of G 0 . The newly developed lithographic process allows the fabrication of sophisticated nanostructures based on topological materials without lowering the material quality. It t...

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“…On the other hand, for a 1D spin-momentum-locked edge state in QSH phase, elastic backscattering is prohibited due to the energy cost of spin to flip, and only a process breaking the time reversal symmetry or an inelastic scattering allowing the spin-flip may destroy the quantization of edge conductance. Several backscattering mechanisms that have been proposed include magnetic impurities [28][29][30][31][32][33], magnetic-field-induced localization [34], nuclear-spin-induced backscattering via hyperfine interaction [35][36][37][38], inelastic interactions induced by nonuniform Rashba spin orbit coupling [39][40][41], phonons [42], multiparticle scattering [43][44][45] and charge puddles [46]. Future experiments look for a non-invasive timereversal-invariant perturbation to eliminate the trivial arXiv:1910.10517v1 [cond-mat.mes-hall] 23 Oct 2019 edge states whereas the topological phase remains intrinsically immune.…”

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confidence: 99%

Localization of trivial edge states in InAs/GaSb composite quantum wells

2019

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InAs/GaSb heterostructure is one of the systems where quantum spin Hall effect is predicted to arise. However, as confirmed by recent experimental studies, the most significant highlight of the effect i.e., the conductance quantization due to non-trivial edge states is obscured by spurious conductivity arising from trivial edge states. In this work, we present experimental observation of strong localization of trivial edge modes in an InAs/GaSb heterostructure which was weakly disordered by silicon delta-like dopants within the InAs layer. The edge conduction which is characterized by a temperature-independent behavior at low temperatures and a power law at high temperatures is observed to be exponentially scaled with the length of the edge. Comprehensive analysis on measurements with a range of devices is in agreement with the localization theories in quasi one-dimensional electronic systems.Topological Insulator (TI) is a new phase of matter that has attracted a great interest not only for fundamental scientific research but also for its potential applications. Specifically, the quantum spin Hall (QSH) insulator is a two-dimensional topologically non-trivial insulator that is theoretically predicted to manifest an insulating bulk but accompanied by dissipationless helical states at the edges [1,2]. These new class of materials provide an ideal platform for novel spintronic applications, quantum information, and quantum engine [3][4][5]. The QSH effect was first predicted and soon observed in band inverted HgTe/(Hg,Cd)Te quantum wells (QWs) [2,6,7], where a transition from normal to topological phase can only be tuned by the thickness of the HgTe QW. Among the new proposals for a QSH system, the InAs/GaSb bilayer QW heterostructure is favored as it benefits from high mobility, easy fabrication, and most importantly the tunability of the band structure by an electric field [8][9][10][11][12][13][14][15][16][17][18]. Particularly, by application of dual gates on top and bottom of the heterostructure, the Fermi level and the alignment between InAs conduction and GaSb valence bands can be controlled independently in such a way that a continuous transition from trivial to brokengap nontrivial insulator is possible [8,15].In the early experiments on InAs/GaSb double QWs, the edge conduction was overshadowed by relatively large residual bulk conductance [9]. Subsequent efforts to suppress the bulk conductance via localization of bulk carriers incorporated the introduction of Si impurities at the interface between InAs and GaSb quantum wells [12][13][14], Be doping in the QW barrier [19,20], or using low purity Ga source material for the GaSb layer [21,22]. These studies confirmed robust edge conduction, however whether the conduction was due to helical or trivial edge states was not proven. On the other hand, more recent works demonstrated the presence of edge transport also in the trivial phase of these heterostructures [16,17,23]. The experiments with different sample geometries and edge lengths concluded that the ed...

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Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

Cited by 64 publications

References 101 publications

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

Analytical and numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity

Interacting topological edge channels

Localization of trivial edge states in InAs/GaSb composite quantum wells

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