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Register a new userApplications of nonequilibrium Kubo formula to the detection of quantum noise
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The Kubo fluctuation-dissipation theorem relates the current fluctuations of a system in an equilibrium state with the linear AC-conductance. This theorem holds also out of equilibrium provided that the system is in a stationary state and that the linear conductance is replaced by the (dynamic) conductance with respect to the non equilibrium state. We provide a simple proof for that statement and then apply it in two cases. We first show that in an excess noise measurement at zero temperature, in which the impedance matching is maintained while driving a mesoscopic sample out of equilibrium, it is the nonsymmetrized noise power spectrum which is measured, even if the bare measurement, i.e. without extracting the excess part of the noise, obtains the symmetrized noise. As a second application we derive a commutation relation for the two components of fermionic or bosonic currents which holds in every stationary state and which is a generalization of the one valid only for bosonic currents. As is usually the case, such a commutation relation can be used e.g. to derive Heisenberg uncertainty relationships among these current components.
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Current quantum noise can be pictured as a sum over transitions through which the electronic system exchanges energy with its environment. We formulate this picture and use it to show which type of current correlators are measurable, and in what measurement the zero point fluctuations will play a role (the answer to the latter is as expected: only if the detector excites the system.) Using the above picture, we calculate and give physical interpretation of the finite-frequency finite-temperature current noise in a noninteracting Landauer-type system, where the chemical potentials of terminals 1 and 2 are $mu+eV/2$ and $mu-eV/2$ respectively, and derive a detailed-balance condition for this nonequilibrium system. Finally, we derive a generalized form of the Kubo formula for a wide class of interacting nonequilibrium systems, relating the differential conductivity to the current noise.
The Smrcka-Streda version of Kubos linear response formula is widely used in the literature to compute non-equilibrium transport properties of heterostructures. It is particularly useful for the evaluation of intrinsic transport properties associated with the Berry curvature of the Bloch states, such as anomalous and spin Hall currents as well as the damping-like component of the spin-orbit torque. Here, we demonstrate in a very general way that the widely used decomposition of the Kubo-Bastin formula introduced by Smrcka and Streda contains an overlap, which has lead to widespread confusion in the literature regarding the Fermi surface and Fermi sea contributions. To remedy this pathology, we propose a new decomposition of the Kubo-Bastin formula based on the permutation properties of the correlation function and derive a new set of formulas, without an overlap, that provides direct access to the transport effects of interest. We apply these new formulas to selected cases and demonstrate that the Fermi sea and Fermi surface contributions can be uniquely addressed with our symmetrized approach.
When current flows through a magnetic tunnel junction (MTJ), there is spin accumulation at the electrode-barrier interfaces if the magnetic moments of the two ferromagnetic electrodes are not aligned. Here we report that such nonequilibrium spin accumulation generates its own characteristic low frequency noise (LFN). Past work viewed the LFN in MTJs as an equilibrium effect arising from resistance fluctuations ($S_R$) which a passively applied current ($I$) converts to measurable voltage fluctuations ($S_{V}=I^{2}S_{R}$). We treat the LFN associated with spin accumulation as a nonequilibrium effect, and find that the noise power can be fitted in terms of the spin-polarized current by $S_{I}f=aIcoth(frac{I}{b})-ab$, resembling the form of the shot noise for a tunnel junction, but with current now taking the role of the bias voltage, and spin-flip probability taking the role of tunneling probability.
We present a new scheme to detect the quantum shot noise in coupled mesoscopic systems. By applying the noise thermometry to the capacitively coupled quantum point contacts (QPCs) we prove that the noise temperature of one QPC is in perfect proportion to that of the other QPC which is driven to non-equilibrium to generate quantum shot noise. We also found an unexpected effect that the noise in the source QPC is remarkably suppressed possibly due to the cooling effect by the detector QPC.
When an electric current passes across a potential barrier, the partition process of electrons at the barrier gives rise to the shot noise, reflecting the discrete nature of the electric charge. Here we report the observation of excess shot noise connected with a spin current which is induced by a nonequilibrium spin accumulation in an all-semiconductor lateral spin-valve device. We find that this excess shot noise is proportional to the spin current. Additionally, we determine quantitatively the spin-injection-induced electron temperature by measuring the current noise. Our experiments show that spin accumulation driven shot noise provides a novel means of investigating nonequilibrium spin transport.
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