Interlayer Aharonov-Bohm Interference in Tilted Magnetic Fields in Quasi-One-Dimensional Organic Conductors

Abstract

Different types of angular magnetoresistance oscillations in quasi-one-dimensional layered materials, such as organic conductors (TMTSF)2X, are explained in terms of Aharonov-Bohm interference in interlayer electron tunneling. A two-parameter pattern of oscillations for generic orientations of a magnetic field is visualized and compared with the experimental data. Connections with angular magnetoresistance oscillations in other layered materials are discussed. AMRO [4,11,12] were formulated in terms of semiclassical electron trajectories on a cylindrical 3D Fermi surface. Then it was realized that AMRO can exist already for two layers [13,14,15], and they represent an Aharonov-Bohm interference effect in interlayer tunneling [16]. Some experimental evidence for AMRO in semiconducting bilayers has been found [17], but more systematic measurements are necessary.AMRO were also found in quasi-one-dimensional (Q1D) organic conductors with open Fermi surfaces, such as (TMTSF) 2 X [3]. These materials consist of parallel chains along the x axis, which form layers with the interlayer spacing d along the z axis and the interchain spacing b along the y axis, as shown in Fig. 1a. Origi- nally, three different AMRO were discovered in the Q1D conductors: the Lebed magic angles [18,19,20,21] for a magnetic field rotation in the (y, z) plane, the Danner, Kang, and Chaikin (DKC) oscillations in the (x, z) plane [22,23], and the third angular effect in the (x, y) plane [24,25,26]. Then Lee and Naughton [27] found combinations of all three effects for generic magnetic field rotations. It became clear that all types of AMRO in Q1D conductors have a common origin and should be explained by a single unified theory.In (TMTSF) 2 X, the in-plane tunneling amplitude between the chains, t b ∼ 250 K [22,23], is much greater than the inter-plane tunneling amplitude t c ∼ 10 K [3]. Thus, we can treat interlayer tunneling as a perturbation and study the interlayer conductivity σ c between just two layers for a tilted magnetic field B = (B x , B y , B z ), as shown in Fig. 1a. This bilayer approach [14,15] only assumes phase memory of interlayer tunneling within a decoherence time τ and does not require a well-defined momentum k z and a coherent 3D Fermi surface. It gives a simple and transparent interpretation of the most general Lee-Naughton oscillations [27] in terms of AharonovBohm interference in interlayer tunneling. The results are equivalent to other approaches based on the classical Boltzmann equation [25,26,27,28,29] and the quantum Kubo formula [30,31,32]. We calculate a contour plots of σ c as a function of two ratios B x /B z and B y /B z for models with one or several interlayer tunneling amplitudes [30,33]. This type of visualization clearly reveals agreement and disagreement between theory and experiment and allows to determine the electronic parameters of the Q1D materials. The results can be also applied to Q1D semiconducting bilayers consisting of quantum wires induced by an array parallel gates, as shown in Fig. 1a.Let us...

Interlayer interference in double wells in a tilted magnetic field

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Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor

“…In the latter case, AMRO arise from differences in Aharonov-Bohm phases acquired in hopping between layers for positions ϕ 1 and ϕ 2 on the FS 19 .…”

Pulsed magnetic field study of unconventional magnetoresistance of Q1D superconductors (TMTSF)2ClO4and (DMET)2I3

“…Some authors [1,2,3] have tried to apply quantum mechanics to understand the AMRO phenomena for the last several years, though semiclassical calculations starting from Boltzmann equation also reproduce the structure of each AMRO known as 'Lebed resonance', 'DannerKang-Chaikin oscillations, 'the third angular effect (TAE)' and 'Lee-Naughton oscillations (LNO)'. Especially some of the present authors claimed that a series of one-dimensional (1D) to two-dimensional (2D) crossovers are responsible for LNO [4], which are oscillations of the zaxis resistivity (ρ z * ) when the magnetic field (typically > 5 T) is rotated around an axis that is slightly ( 15 • ) tilted from the z*-axis.…”