Inelastic Relaxation Rate Research Articles

Microwave response of a superconductor beyond the Eliashberg theory

We review recent progress in the theory of electromagnetic response of dirty superconductors subject to microwave radiation. The theory originally developed by Eliashberg in 1970 and soon after that elaborated in a number of publications addressed the effect of superconductivity enhancement in the vicinity of the transition temperature. This effect originates from nonequilibrium redistribution of quasiparticles and requires a minimal microwave frequency depending on the inelastic relaxation rate and temperature. In a recent series of papers we generalized the Eliashberg theory to arbitrary temperatures T, microwave frequencies ω, dc supercurrent, and inelastic relaxation rates, assuming that the microwave power is weak enough and can be treated perturbatively. In the phase diagram (ω,T) the region of superconductivity enhancement occupies a finite area located near Tc. At sufficiently high frequencies and low temperatures, the effect of direct depairing prevails over quasiparticle redistribution, always leading to superconductivity suppression.

Role of electron-electron collisions for charge and heat transport at intermediate temperatures

Electric, thermal and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low- and high-temperature limits, while the experimentally important intermediate regime, in which elastic and inelastic scattering are both important, is less understood. To fill this gap, we provide comprehensive solutions of the Boltzmann equation in the presence of an electric field and a temperature gradient for two different cases: First, when electron-electron collisions are treated within the relaxation-time approximation while the full momentum dependence of electron-impurity scattering is included and, second, when the electron-impurity scattering is momentum-independent, but the electron-electron collisions give rise to a momentum-dependent inelastic scattering rate of the Fermi-liquid type. We find that for Fermi-liquid as well as for Coulomb interactions, both methods give the same results for the leading temperature dependence of the transport coefficients. Moreover, the inelastic relaxation rate enters the electric conductivity and the Seebeck coefficient only when the momentum dependence of the electron-impurity collisions, analytical or non-analytical, is included. Specifically, we show that inelastic processes only mildly affect the electric conductivity, but can generate a non-monotonic dependence of the Seebeck coefficient on temperature and even a change of sign. Thermal conductivity, by contrast, always depends on the inelastic scattering rate even for a constant elastic relaxation rate.

Edge states in lateral p−n junctions in inverted-band HgTe quantum wells

We investigate lateral p-n junctions, electrostatically defined in 14 nm-wide HgTe-based quantum wells (QWs) with inverted band structure. The p-n junctions resistances are close to $h/2e^2$, consistent with some previous experiments on 8-10 nm QWs, and the current-voltage characteristics are highly linear, indicating the transport via ballistic helical edge states. Shot noise measurements are performed in order to further verify the underlying transport mechanism. We discuss the role of unknown inelastic relaxation rates in the leads and in the edge channels for the correct interpretation of the noise data. Although the interpretation in favor of the helical edge states seems more consistent, a definite conclusion can not be drawn based on the present experiment. Our approach looks promising for the study of short quasi-ballistic edges in topological insulators (TIs) in suitable geometry.

Coulomb interaction in graphene: Relaxation rates and transport

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic-scattering rates as compared to the zero-temperature case. Focusing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing interference processes. We identify a hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a nonmonotonic energy dependence of the inelastic relaxation rates in clean graphene, which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly nonequilibrium setups.

Coherent Probing of Excited Quantum Dot States in an Interferometer

Measurements of elastic and inelastic cotunneling currents are presented on a two-terminal Aharonov-Bohm interferometer with a Coulomb-blockaded quantum dot embedded in each arm. Coherent current contributions, even in a magnetic field, are found in the nonlinear regime of inelastic cotunneling at a finite-bias voltage. The phase of the Aharonov-Bohm oscillations in the current exhibits phase jumps of pi at the onsets of inelastic processes. We suggest that additional coherent elastic processes occur via the excited state. Our measurement technique allows the detection of such processes on a background of other inelastic current contributions and contains qualitative information about the ratio of transport and inelastic relaxation rates.

Theory of microwave-induced oscillations in the magnetoconductivity of a two-dimensional electron gas

We develop a theory of magneto-oscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.

Theory of the oscillatory photoconductivity of a two-dimensional electron system

We develop a theory of magnetooscillations in the photoresistivity of a two-dimensional electron gas observed in recent experiments. According to our theory, the effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the DC field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.

Inelastic electron relaxation rates caused by spin-M/2Kondo impurities

We study a spin S=M/2--Kondo system coupled to electrons in an arbitrary nonequilibrium situation above Kondo temperature. Coupling to hot electrons leads to an increased inverse lifetime of pseudo particles, related to the Korringa width. This in turn is responsible for the increased inelastic relaxation rates of the electronic system. The rates are related to spin--spin correlation functions which are determined using a projection operator formalism. The results generalize recent findings for S=1/2--Kondo impurities which have been used to describe energy relaxation experiments in disordered mesoscopic wires.

Low-temperature transport, thermal, and optical properties of single-grain quasicrystals of icosahedral phases in the Y-Mg-Zn and Tb-Mg-Zn alloy systems

We present a comprehensive series of results of electrical transport ~electrical conductivity, magnetoconductivity, Hall effect!, thermal ~specific heat!, and optical ~reflectivity ! measurements in varying temperature ranges between 1.5 and 300 K on high-quality single-grain quasicrystals of icosahedral Y-Mg-Zn. This data set is augmented by the specific-heat and optical-reflectivity data obtained from a single-grain quasicrystal of icosahedral Tb-Mg-Zn. For Y-Mg-Zn, both the electrical conductivity s(T) and magnetoconductivity ds(H) may be described by calculations considering quantum interference effects. A detailed comparison of the weak-localization contributions to s(T) and ds(H) with our experimental data provides estimates of the inelastic and spin-orbit relaxation rates. The inelastic relaxation rate is found to be proportional to T 3 . The dominant contributions to the optical conductivity s 1(v) spectrum, obtained from the reflectivity R(v) data in the frequency range between 16 and 9.7310 4 cm 21 , are a strong Drude feature at low frequencies and a prominent absorption signal centered at approximately 6 310 3 cm 21 . A comparison of the spectral weight of the Drude contribution to s 1(v) with the magnitude of the linear-in-T term gT of the low-temperature specific heat Cp(T) yields the itinerant charge-carrier density ni57.62310 21 cm 23 or 0.13 charge carriers per atom. The low ni value is corroborated by the results of the Hall effect measurements. For Tb-Mg-Zn, the optical conductivity s 1(v) spectrum reveals features similar to those of Y-Mg-Zn. The low-temperature specific heat Cp(T) of Tb-Mg-Zn is strongly influenced by a spin-glass-type freezing of Tb moments and by crystalelectric-field effects.

Nonequilibrium phenomena in superconducting double-barrier structure Nb/Nb'/Nb

We report the first experimental data indicating on the influence of the nonequilibrium quasiparticles with the energy near gap in SDBS in the case when the injection rate of the quasiparticles with the higher energy exceeds the inelastic relaxation rate.

Weak localization and anharmonicity of phonons.

The problem of localization of phonons in disordered materials is studied in the framework of the weak-localization theory. Quantum correction to phonon diffusion is calculated by the resummation technique of maximally crossed diagrams in two and three dimensions. The strong energy dependence of the elastic mean free path---the Rayleigh-Klemens scattering---is responsible for the existence of a threshold frequency ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$ where the diffusion constant vanishes. The value of ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$ depends only on the local fluctuation of masses and on the Debye frequency in three dimensions. This threshold describes the phenomenon of localization of phonon density fluctuations or second sound. The self-energies of the phonons are strongly affected by this quantum correction via the anharmonic interactions. The two basic anharmonic couplings contribute to the one-phonon renormalization and provide shortening of the mean lifetime as well as excess of spectral density in the vicinity of the threshold. In two dimensions, as for the electrons, the dynamical quantum correction diverges logarithmically when the frequency goes to zero. A procedure of convergence is used by cutting off the low-frequency contributions at the inelastic relaxation rate. Renormalization of phonons are obtained in a self-consistent way. Finally a tentative application of the previous results to the low-temperature properties of glasses is discussed. In particular the existence of a plateau in thermal conductivity accompanied by excess specific heat in all the glasses measured so far could be understood as the manifestation of localization of acoustic-phonon density at the critical threshold ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$. .AE