Symmetry of Two-Terminal Nonlinear Electric Conduction

Abstract

The well-established symmetry relations for linear transport phenomena cannot, in general, be applied in the nonlinear regime. Here we propose a set of symmetry relations with respect to bias voltage and magnetic field for the nonlinear conductance of two-terminal electric conductors. We experimentally confirm these relations using phase-coherent, semiconductor quantum dots.

Experimental Investigation of the Breakdown of the Onsager-Casimir Relations

“…At zero magnetic field, it is well known that the absence of spatial symmetry leads to nonlinear terms in the conductance that are asymmetric in V [3]. Only very recently has a distinct nonlinear term attracted attention that leads to an asymmetry of the conductance in the presence of both finite B and V [4,5]. The contribution of electron-electron interaction to this asymmetry was calculated to lowest order for disordered [6] and ballistic [7] phase-coherent conductors for a magnetic flux smaller than one flux quantum Φ o = h/e, and for bias voltages, V smaller than the characteristic energy scale of the system (typically µeV in semiconductor billiards).…”

“…Billiards were defined using electron beam lithography and deep wet-etching of the 2-dimensional electron gas (2DEG) formed in a GaInAs/InP heterostructure (Fermi energy = 35 meV) [10]. This system was chosen for its high shape fidelity in billiard definition [5,10] and because previous studies have shown it exhibits negligible circuit-induced asymmetry ('selfgating'), permitting careful control of device and conductance symmetry [4,5]. Device dimensions were made to be smaller than the electron mean free path such that transport within the billiard was ballistic (see Table 1).…”

“…Transport was phase coherent (see Table 1), leading to magnetoconductance fluctuations (MCF) arising from quantum interference effects. MCF are an excellent tool for probing transport symmetries in the nonlinear regime [5] since they are extremely sensitive to electron scattering configurations [11] and have a high degree of reproducibility. Two-terminal magnetoconductance measurements were made in four-point geometry using lock-in techniques.…”

Scanning-gate-induced effects in nonlinear transport through nanostructures

“…Interestingly, general properties can be inferred from symmetry considerations. Onsager's relations for linear response [34][35][36] and their generalization to the nonlinear regime [37][38][39] determine the symmetry of the response functions. For a leftright symmetric device in the absence of a magnetic field, the I -V characteristics is odd, i.e., I (−V ) = −I (V ) and g (0) 2 = 0.…”

Pumping charge with ac magnetic fluxes and the dynamical breakdown of Onsager symmetry

“…38 Several recent works have been devoted to the study of mechanisms for breaking Onsager symmetry in the nonlinear conductance theoretically 39 as well as in several experimental settings. 40,41 In most of these cases, the source for the asymmetric behavior of the current as a function of dc was identified to be the effective voltage profile induced along the biased structure as a consequence of the Coulomb interaction. In the case of rings threaded by dc fluxes while biased by ac voltages, there are also experimental results, which are supported by semiclassical theoretical arguments, indicating that the Onsager-Casimir relations are in general not valid for the conductance associated to the rectified current.…”