Tuning the many-body interactions in a helical Luttinger liquid

Abstract

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter K, characterising the competition between the electrons’ kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state’s dielectric environment. This is reflected in a tunability of the Luttinger parameter K, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunnelling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

A Gate‐Tunable Ambipolar Quantum Phase Transition in a Topological Excitonic Insulator

“…Alternatively, one might expect CDW order to reemerge in the presence of translational symmetry-breaking or a spin polarization along the edge. [25,44] Indeed, we believe that the absence of translational invariance at the edge could explain periodic modulations previously observed [40] in the charge density along the crystal edges of WTe 2 monolayers, reflecting CDW order. As we show in Figure S3 (Supporting Information), a fast Fourier Transform (FFT) of the energy-dependent LDOS seems to confirm this notion as the modulations have a periodicity of q ≃ 1 6 2𝜋 a , and are non-dispersive.…”

“…Further, as shown in Figure 4, we clearly observe the expected enhanced LDOS on the crystal's edges (black curves) reflecting a metallic boundary mode, regardless of the position of the Fermi level. The pseudo-gap like suppression seen in the edge state's LDOS, has previously been shown to arise from a helical Tomonaga-Luttinger liquid (TLL) ground state, [40][41][42] and is seen to remain strictly centered at E F regardless of doping (Figure 4b). From fits to a TLL model we extract a Luttinger parameter K ≈ 0.3-0.4, consistent with previous work.…”

“…MBE Growth: Monolayer crystals of 1T'-WTe 2 were synthesized by molecular-beam epitaxy (MBE) on monolayer graphene, exfoliated on SiO 2 (300 nm)/Si in an Omicron Lab10 ultra-high vacuum (UHV) MBE chamber [40,51] (base pressure below 1 × 10 −10 mbar). The freshly exfoliated monolayer graphene substrates were annealed in UHV at 400 °C slowly (ramping rate of (≈2 °Cmin -1 ) followed by electrical contact formation by micro-soldering with indium [52] in an Ar-filled glove box.…”

WS2 Band Gap Renormalization Induced by Tomonaga Luttinger Liquid Formation in Mirror Twin Boundaries

“…The latter has been realized in both nanotubes and transition metal dichalcogenides (TMDs). [6][7][8][9][10][11][12][13][14][15][16][17] These quasi particle excitations not only host new condensed matter physics phenomena but hold the promise to become major pillars of quantum electronics and quantum information applications. 18 We show the capability to controllably create 1D confined systems and to directly observe TLL formation at its native length scale, which is key to understanding the governing principles behind such a stronglycorrelated system.…”

WS$_2$ Band Gap Renormalization Induced by Tomonaga Luttinger Liquid Formation in Mirror Twin Boundaries

“…The latter has been realized in both nanotubes and transition metal dichalcogenides (TMDs). [6][7][8][9][10][11][12][13][14][15][16][17] These quasi particle excitations not only host new condensed matter physics phenomena but hold the promise to become major pillars of quantum electronics and quantum information applications. 18 We show the capability to controllably create 1D confined systems and to directly observe TLL formation at its native length scale, which is key to understanding the governing principles behind such a stronglycorrelated system.…”