Symmetry of two-terminal nonlinear electric conduction

Nonlinear Ballistic Response of Quantum Spin Hall Edge States

Topological edge states (TES) exhibit dissipationless transport, yet their dispersion has never been probed. Here we show that the nonlinear electrical response of ballistic TES ascertains the presence of symmetry breaking terms, such as deviations from nonlinearity and tilted spin quantization axes. The nonlinear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of TES and discuss experimental measurement.

Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device

We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that antisymmetric components of pairs of local and nonlocal conductances qualitatively match at energies below the superconducting gap, and we compare this finding with symmetry relations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional single-probe measurements in the search for Majorana zero modes.

How to measure the transmission phase through a quantum dot in a two-terminal interferometer

Measurement of the transmission phase through a quantum dot (QD) embedded in an arm of a two-terminal Aharonov-Bohm (AB) interferometer is inhibited by phase symmetry, i.e., the property that the linear response conductance of a two-terminal device is an even function of the magnetic field. It is demonstrated that in a setup consisting of an interferometer with a QD in each of its arms, with one of the QDs capacitively coupled to a nearby quantum point contact (QPC), phase symmetry is broken when a finite voltage bias is applied to the QPC. The transmission phase via the uncoupled QD can then be deduced from the amplitude of the odd component of the AB oscillations.

Conductance fluctuations and field asymmetry of rectification in graphene

We investigate conductance fluctuations as a function of carrier density n and magnetic field in diffusive mesoscopic samples made from monolayer and bilayer graphene. We show that the fluctuations' correlation energy and field, which are functions of the diffusion coefficient, have fundamentally different variations with n, illustrating the contrast between massive and massless carriers. The field dependent fluctuations are nearly independent of n, but the n-dependent fluctuations are not universal and are largest at the charge neutrality point. We also measure the second-order conductance fluctuations (mesoscopic rectification). Its field asymmetry, due to electron-electron interaction, decays with conductance, as predicted for diffusive systems.

Nonlinear conductance in a ballistic Aharonov-Bohm ring

The nonlinear electronic transport properties of a ballistic Aharonov-Bohm ring are investigated. It is demonstrated how the electronic interaction breaks the phase rigidity in a two-probe mesoscopic device as the voltage bias is increased. The possibility of studying interference effects in the nonlinear regime is addressed. The occurrence of magnetic field symmetries in higher order conductance coefficients is analyzed. The results are compared with recent experimental data.

Nonlinear magnetoconductance of a classical ballistic system

We study nonlinear transport through a classical ballistic system accounting for the Coulomb interaction between electrons. The joint effect of the applied bias V and magnetic field H on the electron trajectories results in a component of the nonlinear current I(V,H) which lacks the H-->-H symmetry: deltaI=alpha(cl)V(2)H. At zero temperature the magnitude of alpha(cl) is of the same order as that arising from the quantum interference mechanism. At higher temperatures the classical mechanism is expected to dominate due to its relatively weak temperature dependence.

Nonlinear magnetotransport in interacting chiral nanotubes

Nonlinear transport through interacting single-wall nanotubes containing a few impurities is studied theoretically. Extending the Luttinger liquid theory to incorporate trigonal warping and chirality effects, we derive the current contribution Ie even in the applied voltage V and odd in an orbital magnetic field B, which is nonzero only for chiral tubes and in the presence of interactions.

Asymmetry of nonlinear transport and electron interactions in quantum dots

The symmetry properties of transport beyond the linear regime in chaotic quantum dots are investigated experimentally. A component of differential conductance that is antisymmetric in both applied source-drain bias V and magnetic field B, absent in linear transport, is found to exhibit mesoscopic fluctuations around a zero average. Typical values of this component allow a measurement of the electron interaction strength.

Magnetic field symmetry and phase rigidity of the nonlinear conductance in a ring

We have performed nonlinear transport measurements as a function of a perpendicular magnetic field in a semiconductor Aharonov-Bohm ring connected to two leads. While the voltage-symmetric part of the conductance is symmetric in the magnetic field, the voltage-antisymmetric part of the conductance is not symmetric. These symmetry relations are compatible with the scattering theory for nonlinear mesoscopic transport. The observed asymmetry can be tuned continuously by changing the gate voltages near the arms of the ring, showing that the phase of the nonlinear conductance in a two-terminal interferometer is not rigid, in contrast with the case for the linear conductance.

Experimental investigation of the breakdown of the Onsager-Casimir relations

We use magnetoconductance fluctuation measurements of phase-coherent semiconductor billiards to quantify the contributions to the nonlinear electric conductance that are asymmetric under reversal of magnetic field. We find that the average asymmetric contribution is linear in magnetic field (for magnetic flux much larger than 1 flux quantum) and that its magnitude depends on billiard geometry. In addition, we find an unexpected asymmetry in the power spectrum of the magnetoconductance with respect to reversal of magnetic field and bias voltage.

Magnetic-field asymmetry of nonlinear transport in carbon nanotubes

We demonstrate that nonlinear electrical transport through a two-terminal nanoscale sample is not symmetric in the magnetic field B. More specifically, we have measured the lowest order B-asymmetric terms in single-walled carbon nanotubes. Theoretically, these terms can be used to infer both the strength of electron-electron interactions and the handedness of the nanotube. Consistent with theory, we find that at high temperatures the B-linear term is small and has a constant sign independent of Fermi energy, while at low temperatures it develops mesoscopic fluctuations. We also find surprising magnetoresistance at zero bias in the metallic regime.

Magnetoelectric anisotropy in diffusive transport

In this Letter we prove the existence of a new general diffusive transport phenomenon in crossed electric and magnetic fields: magnetoelectric anisotropy. For the specific case of diffusive electrical transport, we present a relativistic model to quantify this effect and present experimental evidence for its existence.

Magnetic-field asymmetry of nonlinear mesoscopic transport

We investigate departures of the Onsager relations in the nonlinear regime of electronic transport through mesoscopic systems. We show that the nonlinear current-voltage characteristic is not an even function of the magnetic field due only to the magnetic-field dependence of the screening potential within the conductor. We illustrate this result for two types of conductors: A quantum Hall bar with an antidot and a chaotic cavity connected to quantum point contacts. For the chaotic cavity we obtain through random matrix theory an asymmetry in the fluctuations of the nonlinear conductance that vanishes rapidly with the size of the contacts.