In this work we address the recent experiment of Altimiras and collaborators, where an electron distribution function at the quantum Hall (QH) edge at filling factor 2 has been measured with high precision. It has been reported that the energy of electrons injected into one of the two chiral edge channels with the help of a quantum point contact (QPC) is equally distributed between them, in agreement with earlier predictions, one being based on the Fermi gas approach, and the other utilizing the Luttinger liquid theory. We argue that the physics of the energy relaxation process at the QH edge may in fact be more rich, providing the possibility for discriminating between two physical pictures in experiment. Namely, using the recently proposed non-equilibrium bosonization technique we evaluate the electron distribution function and find that the initial "double-step" distribution created at a QPC evolves through several intermediate asymptotics, before reaching eventual equilibrium state. At short distances the distribution function is found to be asymmetric due to non-Gaussian current noise effects. At larger distances, where noise becomes Gaussian, the distribution function acquires symmetric Lorentzian shape. Importantly, in the regime of low QPC transparencies T the width of the Lorentzian scales linearly with T, in contrast to the case of equilibrium Fermi distribution, whose width scales as square root of T. Therefore, we propose to do measurements at low QPC transparencies. We suggest that the missing energy paradox may be explained by the nonlinear dispersion of the spectrum of edge states.
Relaxation in driven integer quantum Hall edge states
一个高度非热的电子分布时，产生的量子霍尔边缘态源在不同的电位满足量子点接触。在最近的实验中已经观察到这种分布作为接触下游距离的函数而松弛成静止形式[Phys. Rev. Lett. 105，056803（2010）]。在这里，我们提出了一个精确的治疗的极小模型的系统填充因子为ν=2，与结果，以及帐户的观察。
Quantum Hall states can be characterized by their chiral edge modes. Upon softening the edge potential, the edge has long been known to undergo spontaneous reconstruction driven by charging effects. In this paper we demonstrate a qualitatively distinct phenomenon driven by exchange effects, in which the ordering of the edge modes at $ν=3$ switches abruptly as the edge potential is made softer, while the ordering in the bulk remains intact. We demonstrate that this phenomenon is robust, and has many verifiable experimental signatures in transport.
We numerically investigate the second-order nonlinear Hall transport properties of a four-terminal system with time-reversal symmetry and broken inversion symmetry. Within the nonequilibrium Green's function formalism, the second-order nonlinear conductances are derived, where the internal Coulomb potential in response to external voltages is explicitly included to guarantee the gauge invariance. For the system with single mirror symmetry Mx, nonlinear Hall properties are only observable in the y direction and contributed solely from the second-order nonlinear effect. From the symmetry point o…
We investigate the coupling between quantum Hall (QH) edge channels (ECs) located at opposite sides of a 50-um-wide Hall bar by exciting a charged wavepacket in one EC and detecting time-dependent current in the other EC. In a QH state, the current shows a peak followed by a dip, demonstrating the existence of capacitive coupling across the incompressible two-dimensional electron system (2DES). The observed magnetic field dependence of the amplitude and time delay of the current suggests that the capacitance is affected by the presence of localized states. We also show that the dominant manner…
Integrability of electron dynamics in one dimension is manifested by the non-equilibrium stationary states. They emerge near a point contact coupling two quantum Hall edges with different chemical potentials. I use the non-equilibrium bosonization technique to show that the effective temperature of such states at the fractional quantum Hall edges has a universal linear dependence on the current through the contact. In contrast, the temperature at eventual equilibrium scales as the square root of the power dissipating at the point contact. I propose to use this distinction to detect these intri…
We study quantum spin Hall insulators with local Coulomb interactions in the presence of boundaries using dynamical mean field theory. We investigate the different influence of the Coulomb interaction on the bulk and the edge states. Interestingly, we discover an edge reconstruction driven by electronic correlations. The reason is that the helical edge states experience Mott localization for an interaction strength smaller than the bulk one. We argue that the significance of this edge reconstruction can be understood by topological properties of the system characterized by a local Chern marker…
Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one dimensional (1D) ballistic modes was predicted, and experimentally demonstrated, to have a universal value for bosons, fermions, and fractionally charged anyons. A fraction of this value is expected in non-abelian states. Nevertheless, open questions about energy relaxation along the propagation length in 1D modes remain. Here, we introduce a novel experimental setup that measures the energy relaxation in chiral 1D modes of the quantum Hall eff…
The one-dimensional, chiral edge channels of the quantum Hall effect are a promising platform in which to implement electron quantum optics experiments; however, Coulomb interactions between edge channels are a major source of decoherence and energy relaxation. It is therefore of large interest to understand the range and limitations of the simple quantum electron optics picture. Here we confirm experimentally for the first time the predicted relaxation and revival of electrons injected at finite energy into an edge channel. The observed decay of the injected electrons is reproduced theoretica…
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal r…
The nuclear spin-lattice relaxation time T1 of the nu = 2 quantum Hall ferromagnet (QHF) formed in a gate-controlled InSb two-dimensional electron gas has been characterized using a pump-probe technique. In contrast to a long T1 of quantum Hall states around nu = 1 that possesses a Korringa-type temperature dependence, the temperature-independent short T1 of the nu = 2 QHF suggests the presence of low energy collective spin excitations in a domain wall. Furthermore, T1 of this ferromagnetic state is also found to be filling- and current-independent. The interpretation of these results as compa…
Extrinsic Orbital Hall Effect and Orbital Relaxation in Mesoscopic Devices
Universidade Federal Rural de Pernambuco（巴西联邦农村大学）；Pohang University of Science and Technology (POSTECH)（韩国科学技术院）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Physics Center of Minho and Porto Universities (CF-UM-UP)（米尼奥与波尔图大学物理中心）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）
The understanding of the characteristics of a magnetic layer in a different environment is crucial for any spintronics application. Before practical applications, thorough scrutiny of such devices is compulsory. Here we study such a potential Hall device of MgO-capped Hf/GdFeCo bilayer (FeCo-rich) for magnetization relaxation around nucleation fields at different voltage probe line widths and dc sensing currents. The device is characterized by anomalous Hall measurements in transverse and longitudinal Hall geometries for two different probe widths A (5 micrometer) and B (1 micrometer). The coe…
We theoretically investigate the evolution of the peak height of an energy resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor $ν=2$. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energy. We investigate this quantity assuming a short range capacitive coupling between the edges. Moreover, we also take into account phenomenologically the possibility of energy dissipation towards additional degrees of freedom both linear and quadratic in the injection e…
We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange a…
In the quantum anomalous Hall effect, chiral edge modes are expected to conduct spin polarized current without dissipation and thus hold great promise for future electronics and spintronics with low energy consumption. However, spin polarization of chiral edge modes has never been established in experiments. In this work, we theoretically study spin polarization of chiral edge modes in the quantum anomalous Hall effect, based on both the effective model and more realistic tight-binding model constructed from the first principles calculations. We find that spin polarization can be manipulated b…
Employing the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As shown by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of n=1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions which are well localized at the system edge and independent of the Fermi energy. On t…
We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions $(ν_{\text{top}},ν_{\text{bottom}})=(1,1)$ and $(1/3,2)$, motivated by a recent approach to engineering artificial edges~\cite{2018NatPh..14..411R}. We show that random tunneling and strong repulsive interactions within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, slowly decaying correlations on the edge become predominantly superconducting. We discuss the resulting ob…
