We demonstrate that nonequilibrium nanoscopic systems with Majorana zero modes admit special kind of universality which cannot be classified as of strictly transport or strictly thermodynamic nature. To reveal such kind of Majorana universality we explore purely thermal nonequilibrium states of a quantum dot whose low-energy degrees of freedom are governed by Majorana zero modes. Specifically, the quantum dot is coupled to a topological superconductor, supporting Majorana zero modes, as well as to two normal metallic contacts with the same chemical potentials but different temperatures. It is shown that the Majorana universality in this setup is dual: it is stored inside both the response of the electric current, excited by exclusively the temperature difference, and the quantum dot compressibility. The latter is defined as the derivative of the quantum dot particle number with respect to the chemical potential and forms a universal Majorana ratio with a proper derivative of the electric current that flows in nonequilibrium states of purely thermal nature.
Nonequilibrium physics of random events, or fluctuations, is a unique fingerprint of a given system. Here we demonstrate that in noninteracting systems, whose dynamics is driven by Majorana states, the effective charge $e^*$, characterizing the electric current fluctuations, is fractional. This is in contrast to noninteracting Dirac systems with the trivial electronic charge, $e^*=e$. Quite the opposite, in the Majorana state we predict two different fractional effective charges at low and high energies, $e^*_l=e/2$ and $e^*_h=3e/2$, accessible at low and high bias voltages, respectively. We s…
Quantum finite frequency noise is one of fundamental aspects in quantum measurements performed during quantum information processing where currently Majorana bound states offer an efficient way to implement fault-tolerant quantum computation via topological protection from decoherence or unitary errors. Thus a detailed exploration of Majorana finite frequency noise spectra, preferably in a nonequilibrium device, is a timely challenge of fundamental importance. Here we present results on finite frequency differential noise that is the derivative of the noise with respect to the frequency. This …
Nonequilibrium states of a nanoscopic system may be achieved by both applying a bias voltage $V$ to its contacts and producing a difference $ΔT$ in their temperatures. Then the total current results from two competing flows, induced by $V$ and $ΔT$, respectively. Here we explore finite frequency quantum noise of this thermoelectric current flowing through a quantum dot whose low-energy dynamics is governed by Majorana degrees of freedom. We demonstrate that at finite frequency $ω$ Majorana zero modes induce a perfect universal symmetry between photon emission and absorption spectra and produce…
Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^>/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^>/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their …
We study the statistics of thermal energy transfer in the nonequilibrium (two-bath) spin-boson model. This quantum many-body impurity system serves as a canonical model for quantum energy transport. Our method makes use of the Majorana fermion representation for the spin operators, in combination with the Keldysh nonequilibrium Green's function approach. We derive an analytical expression for the cumulant generating function of the model in the steady state limit, and show that it satisfies the Gallavotti-Cohen fluctuation symmetry. We obtain analytical expressions for the heat current and its…
Our recent theoretical developments related to the nonrelativistic and relativistic fluctuation-electromagnetic interactions of bodies with different temperatures moving translationally and (or) rotationally relative to each other are briefly summarized. Three basic geometrical configurations and physical systems are discussed: "a small particle and a thick plate (i);"a small particle in radiation vacuum background" (ii), and "two thick plates in relative motion (iii) -classical Casimir-Lifshitz configuration with allowance for relative motion and different temperatures of plates. For the thir…
We present a new field-theoretic approach to anaylize non-equilirbium dynamics of two-level systems (TLS), which is based on a correspondence between a driven TLS and a Majorana fermion field theory coupled to bosonic fields. This approach allows us to calculate analytically properties of non-linear TLS dynamics with an arbitrary accuracy. We apply our method to analyze specific TLS dynamics under a monochromatic periodic drive that is relevant to the problem of decoherence in Josephson junction qubits. It is demonstrated that the method gives the precise positions of the resonance peaks in th…
The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of "quantum quench" to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${\cal L}(t)=| < ψ(0) | ψ(t) > |^2\sim t^{-α}$ for large times after the quench, with a universal critical exponent $α$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the exis…
The Majorana resonant level model (MRLM) describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga--Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only timescale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $Γ$, whatever the dot offset energy $Δ$, applied bias voltage or temperature. The voltage alone deter…
We study the transverse spin-Seebeck effect (SSE) on the surface of a three-dimensional topological insulator (TI) thin film, such as Bi$_2$Se$_3$, which is sandwiched between two normal metal leads. The temperature bias $ΔT$ applied between the leads generates surface charge current which becomes spin-polarized due to strong spin-orbit coupling on the TI surface, with polarization vector acquiring a component $P_x \simeq 60%$ {\em parallel to the direction of transport}. When the third nonmagnetic voltage probe is attached to the portion of the TI surface across its width $L_y$, pure spin cur…
Using the Schwinger-Keldysh approach and the drone (Majorana) fermion representation, we evaluate current distribution in a single-electron transistor in a regime where a total tunnel resistance is small. Nonequilibrium quantum fluctuations of charge induce a lifetime broadening of charge-state level, as well as renormalization of system parameters. We find that the lifetime broadening effect may suppress the probability of relatively large current.
We propose a nonequilibrium Monte Carlo (MC) approach to explore nonequilibrium dynamical ferromagnetism of interacting single molecule magnets (SMMs). Both quantum spin tunneling and thermally activated spin reversal are successfully implemented in the same MC simulation framework. Applied to a typical example, this simulation method satisfactorily reproduces experimental magnetization curves with experimental parameters. Our results show that both quantum and classical effects are essential to determine the hysteresis behaviors. This method is effective and reliable to gain deep insights int…
We theoretically investigate electronic transport through a junction where a quantum dot (QD) is tunnel coupled on both sides to semiconductor nanowires with strong spin-orbit interaction and proximity-induced superconductivity. The results are presented as stability diagrams, i.e., the differential conductance as a function of the bias voltage applied across the junction and the gate voltage used to control the electrostatic potential on the QD. A small applied magnetic field splits and modifies the resonances due to the Zeeman splitting of the QD level. Above a critical field strength, Major…
We study nonequilibrium transport in various open quantum systems whose systems and leads/baths are made of topological superconductors (TSs), semiconductors, and metals. Using quantum Langevin equations and Green's function method, we derive exact expressions for steady-state electrical, thermal, and spin current at the junctions between a system and leads. We validate these current expressions by comparing them with the results from direct time-evolution simulations. We then show how an electrical current injected in TS wires divides into two parts carried by single electronic excitations an…
We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [1-3], we obtain a completely positive and trace preserving Lindblad master equation for the combined dot-qubit dynamics, describing relaxation and decoherence processes beyond the rotating-wave approximation. This approach is applicable to a wide range of weakly coupled environments representing experimentally relevant readout devices. We study i…
In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protect…
We analyze the nonequilibrium transport properties of a parallel double quantum dot in terms of its full counting statistics (FCS). The parameters of the setup are assumed to be such that both subsystems are driven into the Kondo regime. After a series of transformations the Hamiltonian is then mapped onto a Majorana resonant level model, which effectively describes the Toulouse point of the respective double impurity two-terminal Kondo model. Its FCS is then obtained at arbitrary constellation of voltage, temperature, and local magnetic fields. We identify two different transport processes co…
We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and ARPES as probes of isolated out-of-equilibrium quantum systems, and examine the crucial role played by the nonequilibrium distribution function. As an example, we focus on the induced topological time-periodic (Floquet) phase in a 2D $p+ip$ superfluid, following an instantaneous quench of the coupling strength. The post-quench Cooper pairs occupy a linear combination of "ground" and "excited" Floquet states, with coefficients determined by the distribution function. While the Floquet bandstructure exhibits…
Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
L.D. Landau Institute for Theoretical Physics（列夫·朗道理论物理研究所）；Kirensky Institute of Physics, Federal Research Center KSC SB RAS（基连斯基物理研究所，俄罗斯科学院西伯利亚分院克拉斯诺亚尔斯克科学中心联邦研究中心）；Laboratory for Condensed Matter Physics, HSE University（高等经济大学凝聚态物理实验室）
The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface-states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by the TI…
We theoretically investigate laser induced quantum transport in a two-level quantum dot attached to electric contacts. Our approach, based on nonequilibrium Green function technique, allows to include thermal effects on the photon-induced quantum transport and excitonic coherent dynamics. By solving a set of coupled integrodifferential equations, involving correlation and propagator functions, we obtain the photocurrent and the dot occupations as a function of time. The characteristic coherent Rabi oscillations are found in both occupations and photocurrent, with two distinct sources of decohe…
Transport properties of ultrasmall quantum dots with a single unpaired electron are commonly modeled by the nonequilibrium Kondo model, describing the exchange interaction of a spin-1/2 local moment with two leads of noninteracting electrons. Remarkably, the model possesses an exact solution when tuned to a special manifold in its parameter space known as the Toulouse limit. We use the Toulouse limit to exactly calculate the adiabatically pumped spin current in the Kondo regime. In the absence of both potential scattering and a voltage bias, the instantaneous charge current is strictly zero fo…
Semiconductor-superconductor hybrid systems have outstanding potential for emerging high-performance nanoelectronics and quantum devices. However, critical to their successful application is the fabrication of high-quality and reproducible semiconductor-superconductor interfaces. Here, we realize and measure axial Al-Ge-Al nanowire heterostructures with atomically precise interfaces, enwrapped by an ultrathin epitaxial Si layer further denoted as Al-Ge/Si-Al nanowire heterostructures. The heterostructures were synthesized by a thermally induced exchange reaction of single-crystalline Ge/Si cor…
