Phase diagram of two interacting helical states

Santos, Raul A.; Gutman, D. B.; Carr, Sam T.

doi:10.1103/physrevb.93.235436

Cited by 13 publications

(14 citation statements)

References 35 publications

(71 reference statements)

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“…Going to a diagonal basis and bosonizing the system , the full Hamiltonian density

{scriptH}_{0} + {scriptH}_{int}

splits into two commuting parts

H = {scriptH}_{+} + {scriptH}_{-}

. The Hamiltonian density

H_{+}

is given by

{scriptH}_{+} = \frac{u_{+}}{2} [\frac{{(\partial_{x} φ_{+})}^{2}}{K} + {false(\partial_{x} θ_{+} false)}^{2} K],

with Luttinger parameter

K = \sqrt{false(v + g^{'} false) / false(v + g^{'} + 4 g false)}

, renormalized velocity

u_{+} = \sqrt{false(v + g^{'} false) false(v + g^{'} + 4 g false)}

and

g^{'} = a_{0} false(U_{0} - U false) / 2 π

.…”

Section: Two Coupled Helical Modesmentioning

confidence: 96%

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Interaction induced topological protection in one‐dimensional conductors

Kainaris

Santos

Gutman

et al. 2017

Fortschritte der Physik

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We discuss two one-dimensional model systems -the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder.

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“…Going to a diagonal basis and bosonizing the system , the full Hamiltonian density

{scriptH}_{0} + {scriptH}_{int}

splits into two commuting parts

H = {scriptH}_{+} + {scriptH}_{-}

. The Hamiltonian density

H_{+}

is given by

{scriptH}_{+} = \frac{u_{+}}{2} [\frac{{(\partial_{x} φ_{+})}^{2}}{K} + {false(\partial_{x} θ_{+} false)}^{2} K],

with Luttinger parameter

K = \sqrt{false(v + g^{'} false) / false(v + g^{'} + 4 g false)}

, renormalized velocity

u_{+} = \sqrt{false(v + g^{'} false) false(v + g^{'} + 4 g false)}

and

g^{'} = a_{0} false(U_{0} - U false) / 2 π

.…”

Section: Two Coupled Helical Modesmentioning

confidence: 96%

“…The first is a model of a single (spinful) channel quantum wire with Ising anisotropy . The second is two coupled quantum spin Hall helical edge states . In this case, it is important to note that the

Z_{2}

topological classification of the quantum spin Hall effect means that an even number of coupled edge states (i.e.…”

Section: Introductionmentioning

confidence: 99%

Interaction induced topological protection in one‐dimensional conductors

Kainaris

Santos

Gutman

et al. 2017

Fortschritte der Physik

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“…In ref. 27 , the authors propose a method to distinguish between the two which relies on the addition of two non-magnetic impurities in an other wise clean QSH sample. The occurrence of localized zero modes identifies the topological origin of the helical edge modes.…”

Section: Introductionmentioning

confidence: 99%

Probing helicity and the topological origins of helicity via non-local Hanbury-Brown and Twiss correlations

Mani

Benjamin

2017

Sci Rep

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Quantum Hall edge modes are chiral while quantum spin Hall edge modes are helical. However, unlike chiral edge modes which always occur in topological systems, quasi-helical edge modes may arise in a trivial insulator too. These trivial quasi-helical edge modes are not topologically protected and therefore need to be distinguished from helical edge modes arising due to topological reasons. Earlier conductance measurements were used to identify these helical states, in this work we report on the advantage of using the non local shot noise as a probe for the helical nature of these states as also their topological or otherwise origin and compare them with chiral quantum Hall states. We see that in similar set-ups affected by same degree of disorder and inelastic scattering, non local shot noise “HBT” correlations can be positive for helical edge modes but are always negative for the chiral quantum Hall edge modes. Further, while trivial quasi-helical edge modes exhibit negative non-local”HBT” charge correlations, topological helical edge modes can show positive non-local “HBT” charge correlation. We also study the non-local spin correlations and Fano factor for clues as regards both the distinction between chirality/helicity as well as the topological/trivial dichotomy for helical edge modes.

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“…Due to the finite tunneling between both subsystems, the edge states are energetically split around zero energy by E BBS defined in Eq. (29).…”

Section: Discussionmentioning

confidence: 99%

“…with E BBS and χ given in Eq. (29), and B > 0 denoting a real constant. For example at the Luther-Emery point, K s = 1/2, it is given by B = −2 cos Φ 0 s .…”

Section: B Region IImentioning

confidence: 99%

Transmission through a potential barrier in Luttinger liquids with a topological spin gap

2018

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We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy Luttinger liquid theory is gapped by interaction. This phase is of particular interest since it exhibits non-trivial interaction-induced topological properties. Using bosonization and an expansion in the tunneling strength, we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping the fractional spin the edge states can absorb or emit spinons and thus enable single electron tunneling across the impurity even though the bulk spectrum for these excitations is gapped. This results in a finite LDOS below the bulk gap and in a non-monotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase-which combines features of a topological spin insulator and a topological charge metal-in which the topology can be probed by measuring transport properties. arXiv:1709.08965v1 [cond-mat.str-el]

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Phase diagram of two interacting helical states

Cited by 13 publications

References 35 publications

Interaction induced topological protection in one‐dimensional conductors

Interaction induced topological protection in one‐dimensional conductors

Probing helicity and the topological origins of helicity via non-local Hanbury-Brown and Twiss correlations

Transmission through a potential barrier in Luttinger liquids with a topological spin gap

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