Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

Guigou, M.; Martin, Thierry; Crépieux, Adeline

doi:10.1103/physrevb.80.045420

Cited by 12 publications

(12 citation statements)

References 55 publications

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“…1] is a direct probe of the locally available electronic states in the TLL, assuming the density of states in the STM tip to be a constant. In a TLL wire the STM current has been shown to vary as a power of the bias voltage: dI/dV ∝ ρ(ω) ∝ ω ∆−1 , with the TDOS exponent ∆ depending on the strength of the e-e interaction strength [41][42][43][44][45][46][47]. The TDOS exponent in a spinless two wire junction tuned to the connected (or a single wire without impurity) [5 and 48] and disconnected fixed points (single wire with impurity) [5,[49][50][51], are known to be ∆ = (g + g −1 )/2 and ∆ = 1/g respectively, where g denotes the TLL interaction parameter.…”

Section: Introductionmentioning

confidence: 99%

Enhancement of tunneling density of states at a Y junction of spin-12Tomonaga–Luttinger liquid wires

Mardanya

Agarwal

2015

Phys. Rev. B

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We calculate the tunneling density of states (TDOS) in a dissipationless three wire junction of interacting spin-1/2 electrons, and find an anomalous enhancement of the TDOS in the zero bias limit, even for repulsive interactions for several bosonic fixed points. This enhancement is physically related to the reflection of holes from the junction for incident electrons, and it occurs only in the vicinity of the junction (x < vmin/2ω where vmin is the minimum of the velocity of charge or spin excitations and ω is the bias frequency), crossing over to the bulk value which is always suppressed, at larger distances. The TDOS exponent can be directly probed in a STM experiment by measuring the differential tunneling conductance as a function of either the bias voltage or temperature as done in C. Blumenstein et al., Nat. Phys. 7, 776 (2011).

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Section: Introductionmentioning

confidence: 99%

Enhancement of tunneling density of states at a Y junction of spin-12Tomonaga–Luttinger liquid wires

Mardanya

Agarwal

2015

Phys. Rev. B

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“…The calculation of the non perturbative Green's functions associated to H 0 : G θθ j , G φθ j , G θφ j ,G φφ j , and G ϕϕ σ is presented in detail in Ref. 8, and the calculation of the mixed Green's functions is done in Sec. IV.…”

Section: A Tunnel Current Definitionmentioning

confidence: 99%

“…There, we developed general expressions for the Dyson equations, which allowed to derive non perturbatively the Greens functions of the bosonic fields which are needed to obtain the spectral function of the wire. The tunneling density of states was shown to be enhanced (reduced) for large (weak) Coulomb interaction 8 .…”

Section: Introductionmentioning

confidence: 99%

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Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. II. Transport properties

Guigou

Martin²,

Crépieux³

2009

Phys. Rev. B

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We study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations nonperturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the amplitude of the tunnel transfer; the profile of the tunneling current is strongly modified by the presence of screening. The zero-frequency noise is modified in a similar way but the Fano factor remains unchanged. We also consider the effect of the screening on the asymmetry of the finite-frequency nonsymmetrized noise and on the conductance.The total Hamiltonian we consider is H = H 0 + H V , where H 0 is the unperturbed Hamiltonian and H V is the perturbation PHYSICAL REVIEW B 80, 045421 ͑2009͒

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“…Spectral properties and fractionalization phenomena of 1D systems can be detected via scanning tunneling spectroscopy [80][81][82]. In particular, charge partitioning in Luttinger liquid wires [83][84][85] has been highlighted, showing that for an infinite nanotube, fractional charges can be identified through the measurement of both the autocorrelation noise and the cross correlation noise, measured at the extremities of the nanotube [86][87][88][89][90][91]. Experimental results of tunneling spectroscopy of topological insulators [92][93][94][95] have also been recently reported.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of interacting helical channels driven by Lorentzian pulses

et al. 2019

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Precise shaping of coherent electron sources allows the controlled creation of wavepackets into a one dimensional (1D) quantum conductor. Periodic trains of Lorentzian pulses have been shown to induce minimal excitations without creating additional electron-hole pairs in a single non-interacting 1D electron channel. The presence of electron-electron (e-e) interactions dramatically affects the non-equilibrium dynamics of a 1D system. Here, we consider the intrinsic spectral properties of a helical liquid, with a pair of counterpropagating interacting channels, in the presence of timedependent Lorentzian voltage pulses. We show that peculiar asymmetries in the behavior of the spectral function are induced by interactions, depending on the sign of the injected charges. Moreover, we discuss the robustness of the concept of minimal excitations in the presence of interactions, where the link with excess noise is no more straightforward. Finally, we propose a scanning tunneling microscope setup to spectroscopically access and probe the non-equilibrium behavior induced by the voltage drive and e-e interactions. This allows a diagnosis of fractional charges in a correlated quantum spin Hall liquid in the presence of time-dependent drives.

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Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

Cited by 12 publications

References 55 publications

Enhancement of tunneling density of states at a Y junction of spin-12Tomonaga–Luttinger liquid wires

Enhancement of tunneling density of states at a Y junction of spin-12Tomonaga–Luttinger liquid wires

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. II. Transport properties

Spectral properties of interacting helical channels driven by Lorentzian pulses

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