Linear and nonlinear transport in a small charge-tunable open quantum ring

Hernández, F. G. G.; Gusev, G. M.; Kvon, Z. D.; Portal, J. C.

doi:10.1103/physrevb.84.075332

Cited by 7 publications

(4 citation statements)

References 31 publications

(56 reference statements)

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“…In AharonovBohm interferometers with conserved electron current this symmetry is displayed by the "phase rigidity" of the (linear) conductance oscillations with the magnetic field B, G 1 (B) = G 1 (−B) 27,28 . Beyond linear response, the phase symmetry of the conductance is not enforced, and several experiments 29,30,[32][33][34][35][36][37] have demonstrated its breakdown. Supporting theoretical works have elucidated the role of many-body interactions in the system [38][39][40][41][42] , typically approaching the problem by calculating the screening potential within the conductor in a self-consistent manner, a procedure often limited to low-order conduction terms 38,40,41 .…”

Section: Introductionmentioning

confidence: 99%

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

2013

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The probe technique is a simple mean to incorporate elastic and inelastic processes into quantum dynamics. Using numerical simulations, we demonstrate that this tool can be employed beyond the analytically tractable linear response regime, providing a stable solution for the probe parameters: temperature and chemical potential. Adopting four probes: dephasing, voltage, temperature, and voltage-temperature, mimicking different elastic and inelastic effects, we focus on magnetic field and gate voltage symmetries of charge current and heat current in Aharonov-Bohm interferometers, potentially far-from-equilibrium. Considering electron current, we prove analytically that in the linear response regime inelastic scattering processes do not break the Onsager symmetry. Beyond linear response, even (odd) conductance terms obey an odd (even) symmetry with the threading magnetic flux, as long as the system acquires a spatial inversion symmetry. When spatial asymmetry is introduced particle-hole symmetry assures that nonlinear conductance terms maintain certain symmetries with respect to magnetic field and gate voltage. These analytic results are supported by numerical simulations. Analogous results are obtained for the electron heat current. We also demonstrate that a double-dot Aharonov-Bohm interferometer acts as a rectifier when two conditions are met: (i) many-body effects are included, here in the form of inelastic scattering, and (ii) time reversal symmetry is broken.

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Section: Introductionmentioning

confidence: 99%

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

2013

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“…Magnetic field symmetry of the electric conduction in the non-linear regime was addressed in several experiments : on quantum dots 14,17,37 , carbon nanotubes 38 , mesoscopic 2D metallic rings 18,[39][40][41][42] and monolayer graphene sheets 43 . Motivated by the early experiments, the first theoretical works on ballistic 15 and diffusive 16 quantum dots were completed by investigating the role of dephasing, thermal smearing, etc [28][29][30]44 .…”

Section: Introductionmentioning

confidence: 99%

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

Texier

Mitscherling

2018

Phys. Rev. B

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We study the non-linear conductance G ∼ ∂ 2 I/∂V 2 |V =0 in coherent quasi-one-dimensional weakly disordered metallic wires. Our analysis is based on the scattering approach and includes the effect of Coulomb interaction. The non-linear conductance correlations can be related to integrals of two fundamental correlation functions : the correlator of functional derivatives of the conductance and the correlator of injectivities (the injectivity is the contribution to the local density of states of eigenstates incoming from one contact). These correlators are obtained explicitly by using diagrammatic techniques for weakly disordered metals. In a coherent wire of length L, we obtain rms G 0.006 E −1 Th (and G = 0), where E Th = D/L 2 is the Thouless energy of the wire and D the diffusion constant ; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal : the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, rms Ga 0.001 (gE Th ) −1 , where g 1 is the dimensionless (linear) conductance of the wire. In a weakly coherent wire (i.e. Lϕ L, where Lϕ is the phase coherence length), the non-linear conductance is of the same order than the result G0 of a free electron calculation (although screening again strongly reduces the dimensionless prefactor) : we get G ∼ G0 ∼ (Lϕ/L) 7/2 E −1 Th , while the antisymmetric part (at high magnetic field) now behaves as Ga ∼ (Lϕ/L) 11/2 (gE Th ) −1 G. The effect of thermal fluctuations is studied : when the thermal length LT = D/kBT is the smallest length scale, LT Lϕ L, the free electron result G0 ∼ (LT /L) 3 (Lϕ/L) 1/2 E −1 Th is negligible and the dominant contribution is provided by screening, G ∼ (LT /L)(Lϕ/L) 7/2 E −1 Th ; in this regime, the antisymmetric part is Ga ∼ (LT /L) 2 (Lϕ/L) 7/2 (gE Th ) −1 . All the precise dimensionless prefactors are obtained. Crossovers from zero to strong magnetic field regimes are also analysed.

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“…21 However, only Keyser et al 33 have been able to show this experimentally by studying a semiconducting ring with less than ten electrons. Very recently, Hernandez et al 34 reported measurements on a 20-40electron ring but they were only able to observe the Φ 0 and Φ 0 /2 oscillations. As the effect seems to be elusive in experiments, it is necessary to study which additional factors could complicate the experimental observation of fractional periodicity.…”

Section: Introductionmentioning

confidence: 99%

Fractional periodicity of persistent current in coupled quantum rings

Ijäs

Harju

2012

Phys. Rev. B

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We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as asymmetry. In the weakly coupled case, we find fractional periodicity at all electron fillings at sufficiently high Hubbard U, similar to isolated rings. For strongly coupled rings, on the contrary, fractional periodicity is only observed at sufficiently large negative gate voltages and high interaction strengths. This is explained by the formation of a bound correlated state in the ring that is effectively weakly coupled to the lead

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Linear and nonlinear transport in a small charge-tunable open quantum ring

Cited by 7 publications

References 31 publications

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

Fractional periodicity of persistent current in coupled quantum rings

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