Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

Schulz, Α.; Martino, Alessandro De; Ingenhoven, P.; Egger, Reinhold

doi:10.1103/physrevb.79.205432

Cited by 47 publications

(47 citation statements)

References 60 publications

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“…A few years later, Schulz et al revisited this problem within one-loop RG, but treating the marginal backscattering interaction much more carefully. 33 Through this analysis, they obtained a Berezinskii-Kosterlitz-Thouless (BKT) phase diagram (as is the case without spin orbit 6 ), but with renormalized effective parameters, which depend crucially on the velocity difference. Importantly, if the velocity difference goes to zero, the bare backscattering parameters are not renormalized; which is an equivalent way of saying that the SOC may be gauged out.…”

Section: B Summary Of Previous Workmentioning

confidence: 99%

“…We follow a very similar approach to Ref. 33, but by integrating out the gapless charge sector, we treat exactly the forward scattering couplings between the spin and charge sectors before applying perturbative RG. Like Schulz et al, we also obtain a BKT phase diagram with renormalized parameters, but these renormalized param-eters can now be on either side of the phase boundary, meaning that under certain conditions (which are derived in this work), the spin-gap may appear and the SDW phase is realized.…”

Section: B Summary Of Previous Workmentioning

confidence: 99%

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Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

Kainaris

Carr

2015

Phys. Rev. B

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We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is then a two band model with a difference of Fermi velocities δv. Using bosonization and a two-loop renormalization group procedure we show that electron-electron interactions can open a gap in the spin sector of the theory when the interaction strength U is smaller than δv in appropriate units. For repulsive interactions, the resulting strong coupling phase is of the spin-density-wave type. We show that this phase has peculiar emergent topological properties. The gapped spin sector behaves as a topological insulator, with zero-energy edge modes with fractional spin. On the other hand, the charge sector remains critical, meaning the entire system is metallic. However, this bulk electron liquid as a whole exhibits properties commonly associated with the one-dimensional edge states of two-dimensional spin-Hall insulators, in particular, the conduction of 2e 2 /h is robust against nonmagnetic impurities. arXiv:1504.05016v2 [cond-mat.mes-hall]

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Section: B Summary Of Previous Workmentioning

confidence: 99%

Section: B Summary Of Previous Workmentioning

confidence: 99%

Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

Kainaris

Carr

2015

Phys. Rev. B

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“…Motivated by such prospects, there appeared several theoretical works concerned with a TLL in the presence of the SOIs. The SOIs mix the spin and charge sectors and a rich range of phenomena was predicted, from mild modifications to a breakdown of the TLL phase [20][21][22][23][24][25][26][27][28][29][30]. Despite active discussions in theory, there are only few experimental results about TLL physics in wires with strong SOIs.…”

Section: Introductionmentioning

confidence: 99%

Strong electron-electron interactions of a Tomonaga-Luttinger liquid observed in InAs quantum wires

et al. 2019

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We report strong electron-electron interactions in quantum wires etched from an InAs quantum well, a material known to have strong spin-orbit interactions. We find that the current through the wires as a function of the bias voltage and temperature follows the universal scaling behavior of a Tomonaga-Luttinger liquid. Using a universal scaling formula, we extract the interaction parameter and find strong electron-electron interactions, increasing as the wires become more depleted. We establish theoretically that spin-orbit interactions cause only minor modifications of the interaction parameter in this regime, indicating that genuinely strong electron-electron interactions are indeed achieved in the device. Our results suggest that etched InAs wires provide a platform with both strong electron-electron and strong spin-orbit interactions. * sato@meso.t.u-tokyo.ac.jp; Contributed equally to this work † matsuo@ap.t.u-tokyo.ac.jp; Contributed equally to this work

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“…One of the goals of this work is to compare the properties of our microscopic model to those of the popular LL models [26][27][28][29][30][31][32][33][34][35][36][37], specifically, the spiral LL and the helical LL. The spiral LL was first introduced by Braunecker et al [38,39] to describe a LL embedded in a lattice of nuclear spins.…”

Section: Introductionmentioning

confidence: 99%

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

et al. 2017

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We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

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Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

Cited by 47 publications

References 60 publications

Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

Strong electron-electron interactions of a Tomonaga-Luttinger liquid observed in InAs quantum wires

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

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