Random Rashba spin-orbit coupling at the quantum spin Hall edge

Geißler, Florian; Crépin, François; Trauzettel, Björn

doi:10.1103/physrevb.89.235136

Cited by 55 publications

(71 citation statements)

References 24 publications

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“…The interest in such systems is motivated by potential applications in spintronics [31][32][33] and quantum computation [34,35]. The properties under consideration are most often related to transport, partially because the explanation of the weak temperature dependence of the non-perfectly quantized conductance in long samples still represents an open and challenging issue, even though several scattering mechanisms have been inspected [36][37][38][39][40][41][42][43][44][45][46]. Much less emphasis has, on the other hand, been devoted to its local properties [47].…”

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confidence: 99%

Charge and spin density in the helical Luttinger liquid

Ziani¹,

Fleckenstein²,

Crépin³

et al. 2016

EPL

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-The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are not able to modify the electron density, while only magnetic impurities can pin the planar spin density wave. editor's choice Copyright c EPLA, 2016Introduction. -One-dimensional gapless quantum systems are characterized by a peculiar behavior: if (arbitrarily weak) inter-particle interaction is present, the low-energy excitations have a collective nature and are described by the Luttinger liquid theory [1][2][3]. Experimental evidence of the validity of the Luttinger liquid theory in fermionic systems has been achieved in a number of different devices, ranging from carbon nanotubes [4,5] and quantum wires [6,7], to Bechgaard salts [8] and edges of quantum Hall bars [9][10][11]. Exotic behaviors related to the Luttinger liquid, like spin charge separation [12] and charge fractionalization [13,14], have also been observed. Moreover, the Luttinger liquid picture is able to capture the low-energy properties of gapless one-dimensional bosonic [15] and spin systems [16]. In addition to its wide range of applicability, the Luttinger liquid picture has another important technical advantage: its Hamiltonian describes a collection of free bosons, and the fundamental field operators (right and left movers) of the theory can also be expressed by means of the creation and annihilation operators of such bosons, so that the correlation functions can very often be calculated analytically [2]. As a direct consequence of its wide range of validity, the relation between the fundamental field operators of the Luttinger liquid and the observables do depend on the system under consideration. Even though the thermodynamics of all the Luttinger liquid pictures of various systems is

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confidence: 99%

Charge and spin density in the helical Luttinger liquid

Ziani¹,

Fleckenstein²,

Crépin³

et al. 2016

EPL

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confidence: 99%

“…(2) has been termed "random RSOC" in previous studies [30,31]. Unlike backscattering (random mass) disorder in a spinless Luttinger liquid, short-range correlated random RSOC is irrelevant in the RG sense for an edge Luttinger parameter K > 1/2 [31]. Both the random RSOC and one-particle umklapp interaction can be simultaneously irrelevant, and map to similar operators in bosonization [28,30,39].…”

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confidence: 99%

“…A crucial theoretical task is to identify and understand mechanisms that might weaken topological protection and suppress the conductance at finite and zero T [3,20,[27][28][29][30][31]. Although irrelevant, the one-particle umklapp interaction can be the dominant source of inelastic backscattering for k B T much less than the bulk gap in an isolated HLL, leading to T -dependent corrections to the edge conductance [20,[27][28][29].…”

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Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

Xie

Chou

et al. 2016

Phys. Rev. Lett.

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The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrabilitybreaking terms. The edge states of a quantum spin Hall (QSH) insulator realize a time-reversal symmetric helical Luttinger liquid (HLL): Two counterpropagating modes possess opposite spins and hence form a Kramers doublet [1][2][3][4][5][6][7]. Owing to the nontrivial bulk Z 2 topology, the HLL provides an alternative realization for a quantum wire with strong spin-orbit coupling and an odd number of channels [8], distinct from (e.g.) carbon nanotubes [9][10][11][12][13][14]. In an ideal QSH insulator, the S z component of the electron spin is conserved. Elastic backscattering of HLL edge carriers off of impurities is prohibited by the combination of spin U(1) and time-reversal symmetries; only forwardscattering potential disorder is allowed. The combination of pure potential disorder and Luttinger liquid interactions bosonizes [15,16] to a trivial free theory, leading to the prediction that edge electrons exhibit ballistic transport at any temperature [5]. These conclusions obtain in a fixed realization of the disorder, a robust version of topological protection that also applies to the surface states of 3D topological superconductors [17][18][19].

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“…Long edges on the other hand are characterized by a reduced conductance. Even though a comprehensive theoretical understanding of the scattering sources causing the reduction of the conductance of the edge is still lacking, the role of electron-phonon interactions[11], of magnetic [12] and nonmagnetic impurities [13,14], in the presence of random Rashba disorder [15,16], of breaking of axial symmetry in combination with electronelectron interactions and impurities [17,18], of tunneling among the edges and charge puddles in the bulk of the 2DTI [19], and of the coupling between opposite edges [20,21] has been theoretically elucidated. The mathematical tool allowing for most of such calculations is bosonization [22,23], a procedure that enables us to recast the Hamiltonian of the interacting electrons on the edges into a Hamiltonian of free bosonic excitations, representing charge density waves, and to express the Fermi operator in terms of the creation and annihilation bosonic operators.…”

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confidence: 99%

Fractional Wigner Crystal in the Helical Luttinger Liquid

2015

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The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they instead represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we show that the state characterized by such fractional oscillations still bears the signatures of spin momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a non trivial spin texture. [7][8][9] (2DTI). Particular emphasis has been devoted to the investigation of the transport properties of 2DTI: topological protection of the edge states facilitates the observation of conductance quantization [5,6,10] in short samples. Long edges on the other hand are characterized by a reduced conductance. Even though a comprehensive theoretical understanding of the scattering sources causing the reduction of the conductance of the edge is still lacking, the role of electron-phonon interactions[11], of magnetic [12] and nonmagnetic impurities [13,14], in the presence of random Rashba disorder [15,16], of breaking of axial symmetry in combination with electronelectron interactions and impurities [17,18], of tunneling among the edges and charge puddles in the bulk of the 2DTI [19], and of the coupling between opposite edges [20,21] has been theoretically elucidated. The mathematical tool allowing for most of such calculations is bosonization [22,23], a procedure that enables us to recast the Hamiltonian of the interacting electrons on the edges into a Hamiltonian of free bosonic excitations, representing charge density waves, and to express the Fermi operator in terms of the creation and annihilation bosonic operators. The physical meaning of the bosonization technique can be understood within the framework of Luttinger liquid theory [24], that is the one dimensional counterpart of the Fermi liquid theory for one dimensional gapless systems. More precisely, the exactly solvable Luttinger model [25][26][27], a strictly linear theory of interacting one dimensional fermions with infinite bandwidth in the single particle dispersion is usually employed. The validity of the Luttinger model as a basis for the description of interacting electrons has a number of experimental demonstrations, ranging from spin charge separation [28], to charge fractionalization [29,30], and to anomalous tunneling [31,32]. On the other hand, the Luttinger model alone fails in predicting a reasonable behavior of local observables [33][34][35][36], such as the electron density and the density-density correlation functions when electron-electron interactions are strong. In particular, the Luttinger model is not able to capture the transition between a weakly correlated state dominated by Fri...

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Random Rashba spin-orbit coupling at the quantum spin Hall edge

Cited by 55 publications

References 24 publications

Charge and spin density in the helical Luttinger liquid

Charge and spin density in the helical Luttinger liquid

Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

Fractional Wigner Crystal in the Helical Luttinger Liquid

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