Conductance and persistent current in quasi-one-dimensional systems with grain boundaries: Effects of the strongly reflecting and columnar grains

It is shown that universal transport statistics in the ensembles of scattering matrices with the symmetry index β ∈ {1,2,4} can be found from a simple microscopic model. A stochastic Riccati equation for the reflection matrix in this model is mapped exactly to the Dorokhov-Mello-Pereyra-Kumar equation for all βs. The map is used to obtain transport statistics in a quasi-one-dimensional disordered conductor in a wide range of its parameters from ballistic to localizations regime. The conductance statistics, shot noise suppression, and transmission channel density are calculated and compared with available analytical results. Deviation from the universal statistics is also discussed.

Section: Introductionsupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universal conductance statistics in a backscattering model: Solving the Dorokhov-Mello-Pereyra-Kumar equation withβ=1, 2, and 4

Mil’nikov

Mori

2013

“…The compounded scattering matrix S ij = S i ⊗ S j can be calculated as [74][75][76] S ij = r i + t i r j (1 − r i r j ) −1 t i t i (1 − r j r i ) −1 t i t j (1 − r i r j ) −1 t i r j + t j r i (1 − r j r i ) −1 t j .…”

Section: (C2)mentioning

confidence: 99%

Robustness of persistent currents in two-dimensional Dirac systems with disorder

Ying

Lai

2017

We consider two-dimensional (2D) Dirac quantum ring systems formed by the infinite mass constraint. When an Aharonov-Bohm magnetic flux is present, e.g., through the center of the ring domain, persistent currents, i.e., permanent currents without dissipation, can arise. In real materials, impurities and defects are inevitable, raising the issue of robustness of the persistent currents. Using localized random potential to simulate the disorders, we investigate how the ensemble averaged current magnitude varies with the disorder density. For comparison, we study the nonrelativistic quantum counterpart by analyzing the solutions of the Schrödinger equation under the same geometrical and disorder settings. We find that, for the Dirac ring system, as the disorder density is systematically increased, the average current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents. The physical mechanism responsible for the robustness is the emergence of a class of boundary states -whispering gallery modes. In contrast, in the Schrödinger ring system, such boundary states cannot form and the currents diminish rapidly to zero with increase in the disorder density. We develop a physical theory based on a quasi one-dimensional approximation to understand the striking contrast in the behaviors of the persistent currents in the Dirac and Schrödinger rings. Our 2D Dirac ring systems with disorders can be experimentally realized, e.g., on the surface of a topological insulator with natural or deliberately added impurities from the fabrication process.

“…Our paper is organized as follows. In section II, resistance of wires with rough edges and wires with grains is calculated by means of the scattering-matrix approach [14,17,[19][20][21]. In section III we focus us on the single-particle states in clean metal rings.…”

Section: Introductionmentioning

confidence: 99%

Coexistence of diffusive resistance and ballistic persistent current in disordered metallic rings with rough edges: Possible origin of puzzling experimental values

Feilhauer

Moško²

2013

Self Cite

Typical persistent current (Ityp) in a mesoscopic normal metal ring with disorder due to rough edges and random grain boundaries is calculated by a scattering matrix method. In addition, resistance of a corresponding metallic wire is obtained from the Landauer formula and the electron mean free path (l) is determined. If disorder is due to the rough edges, a ballistic persistent current Ityp ≃ evF /L is found to coexist with the diffusive resistance (∝ L/l), where vF is the Fermi velocity and L ≫ l is the ring length. This ballistic current is due to a single electron that moves almost in parallel with the rough edges and thus hits them rarely (it is shown that this parallel motion exists in the ring geometry owing to the Hartree-Fock interaction). Our finding agrees with a puzzling experimental result Ityp ≃ evF /L, reported by Chandrasekhar et al. [Phys. Rev. Lett. 67, 3578 (1991)] for metallic rings of length L ≃ 100l. If disorder is due to the grain boundaries, our data reproduce theoretical result Ityp ≃ (evF /L)(l/L) that holds for the white-noise-like disorder and has been observed in recent experiments. Thus, result Ityp ≃ evF /L in a disordered metallic ring of length L ≫ l is as normal as result Ityp ≃ (evF /L)(l/L). Which result is observed depends on the nature of disorder. Experiments that would determine Ityp and l in correlation with the nature of disorder can be instructive.