Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator

Abstract

Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against singleparticle backscattering (SPB). However, as twoparticle scattering is not forbidden by TRS [1], the existence of electronic interactions at the edge and their notoriously strong impact on 1D states may lead to an intriguing interplay between topology and electronic correlations. In particular, it is directly relevant to the question in which parameter regime the quantum spin Hall effect (QSHE) expected for 2D-TIs becomes obscured by these correlation effects that prevail at low temperatures [2]. Here we study the problem on bismuthene on SiC(0001) which has recently been synthesized and proposed to be a candidate material for a room-temperature QSHE [3]. By utilizing the accessibility of this monolayer-substrate system on atomic length scales by scanning tunneling microscopy/spectroscopy (STM/STS) we observe metallic edge channels which display 1D electronic correlation effects. Specifically, we prove the correspondence with a Tomonaga-Luttinger liquid (TLL), and, based on the observed universal scaling of the differential tunneling conductivity (dI/dV ), we derive a TLL parameter K reflecting intermediate electronic interaction strength in the edge states of bismuthene. This establishes the first spectroscopic identification of 1D electronic correlation effects in the topological edge states of a 2D-TI.The topological protection of the 1D metallic edge channels in 2D-TIs against elastic SPB by TRS [4,5] leads to quantized, i.e. dissipationless transport which is reflected in the QSHE. Moreover, the property of spin-momentum locking renders 2D-TIs promising candidate materials for applications in spintronics. To date, the QSHE has only been measured in three material systems that are all characterized by small bandgaps (E gap ≤ 55 meV) of which the quantum well (QW) structures of three-dimensional semiconductors, such as *

A tied Fermi liquid to Luttinger liquid model for the explanation of nonlinear transport in conducting polymers

“…systems, including metallic carbon nanotubes [15][16][17] , nanowires 18 , and edge states in 2D systems, have been reported as LLs and show good agreement with theory 19,20 . Although isolated polymer chains have quasi-1D structures, their films are usually in condensed 2D or 3D forms, and these undoubtedly raised questions on whether the conducting polymer could be treated as collections of pure 1D LL systems without considering their detailed condensed forms on the molecular scale.…”

Coherent spin transport through helical edge states of topological insulator

“…Taking into account, the electron-electron interaction makes it also possible to construct effective two-qubit computational schemes in two coupled interferometers based on conventional materials 35,36 , on edge states of the integer quantum Hall effect 37,38 and on helical states 34 . Signatures of electron-electron interaction in HES was already observed experimentally 39,40 .…”

“…For the first time, quantum spin Hall effect was observed in structures based on HgTe/CdTe 53 and InAs/GaSb 54 , which had a rather narrow bulk gap, <100 K. Substantially large values were observed recently in WTe 2 , where gap of the order of 500 K was observed 55 , and in bismuthene grown on a SiC (0001) substrate, where a bulk gap of about 0.8 eV was demonstrated 56,57 (see also recent discussion in ref. 39 ). Thus, recent experimental studies unambiguously indicate the possibility of transport through HES at room temperature, when the condition Δ b ≫ T ≫ Δ, needed for applicability of our theory, can be easily satisfied.…”

A Short Review on One Dimensional Wigner Crystallization

“…Interestingly, the Luttinger liquid also applies to bosonic [21], and spin one-dimensional systems [22,23], thus providing a very powerful tool. The experimental consequences of the Luttinger liquid behavior of fermionic systems can be found in very different contexts, ranging from Bechgaard salts [24,25], to quantum wires [26][27][28][29], quantum Hall edges [30][31][32], quantum spin Hall edges [33,34], and carbon nanotubes [35], even in the presence of mechanical vibrations [36,37]. Interestingly, strongly out of equilibrium scenarios can also be inspected within this framework [38][39][40][41][42][43][44][45][46][47][48][49].…”