arXiv subjects

T. Kühn

Publications and source records attributed to T. Kühn.

10 recordsLinked to original sources

arXiv2010

Temperature Profile for Ballistic and Diffusive Phonon Transport in a Suspended Membrane with a Radial Symmetric Heat Source

We have calculated the temperature profiles for phonon heat transport in a suspended membrane with a radially symmetric heat source in the two extreme cases of either fully ballistic or fully diffusive transport. Theoretical results confirm that it is possible to distinguish these two transport mechanisms from the radial temperature profiles alone. Models are also compared to experimental data measured with 40 nm thick, free standing silicon nitride membranes below 1 K by using tunnel junction (SINIS) thermometers. The measured temperature profile is qualitatively in agreement with the ballistic model.

cond-mat.mes-hall↗

arXiv2009

Effects of charging energy on SINIS tunnel junction thermometry

We have investigated theoretically the effects of the charging energy to the normal metal--insulator--superconductor (NIS) tunnel junction used as a thermometer. We demonstrate by numerical calculations how the charging effects modify NIS thermometry, and how the voltage--to--temperature response and the responsivity $|dV/dT|$ of a current biased thermometer are affected. In addition, we show that the responsivity of the thermometer can be modulated with an additional gate electrode. The maximum responsivity is achieved when the Coulomb blockade is maximal, i.e. with a closed gate.

cond-mat.mes-hall↗

arXiv2008

Method for finding the critical temperature of the island in a SET structure

We present a method to measure the critical temperature of the island of a superconducting single electron transistor. The method is based on a sharp change in the slope of the zero-bias conductance as a function of temperature. We have used this method to determine the superconducting phase transition temperature of the Nb island of an superconducting single electron transistor with Al leads. We obtain $T_\mathrm{c}^\mathrm{Nb}$ as high as 8.5 K and gap energies up to $Δ_\mathrm{Nb}\simeq 1.45$ meV. By looking at the zero bias conductance as a function of magnetic field instead of temperature, also the critical field of the island can be determined. Using the orthodox theory, we have performed extensive numerical simulations of charge transport properties in the SET at temperatures comparable to the gap, which match very well the data, therefore providing a solid theoretical basis for our method.

cond-mat.mes-hall↗

arXiv2007

Interaction of two level systems in amorphous materials with arbitrary phonon fields

To describe the interaction of the two level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this new model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a $6\times 6$ symmetric tensor of deformation potential parameters, $[R]$. Taking into account the isotropy of the amorphous solid, we deduce that $[R]$ has only two independent parameters. We show how these two parameters can be calculated from experimental data and we prove that for any amorphous bulk material the average coupling of TLSs with longitudinal phonons is always stronger than the average coupling with transversal phonons (in standard notations, $γ_l>γ_t$).

cond-mat.dis-nn↗

arXiv2007

Maximizing phonon thermal conductance for ballistic membranes

At low temperatures, phonon scattering can become so weak that phonon transport becomes ballistic. We calculate the ballistic phonon conductance G for membranes using elasticity theory, considering the transition from three to two dimensions. We discuss the temperature and thickness dependence and especially concentrate on the issue of material parameters. For all membrane thicknesses, the best conductors have, counter-intuitively, the lowest speed of sound.

cond-mat.mes-hall↗

arXiv2007

The tensor of interaction of a two-level system with an arbitrary strain field

The interaction between two-level systems (TLS) and strain fields in a solid is contained in the diagonal matrix element of the interaction hamiltonian, $δ$, which, in general, has the expression $δ=2[γ]:[S]$, with the tensor $[γ]$ describing the TLS ``deformability'' and $[S]$ being the symmetric strain tensor. We construct $[γ]$ on very general grounds, by associating to the TLS two objects: a direction, $\hat\bt$, and a forth rank tensor of coupling constants, $[[R]]$. Based on the method of construction and on the invariance of the expression of $δ$ with respect to the symmetry transformation of the solid, we conclude that $[[R]]$ has the same structure as the tensor of stiffness constants, $[[c]]$, from elasticity theory. In particular, if the solid is isotropic, $[[R]]$ has only two independent parameters, which are the equivalent of the Lamé constants. Employing this model we calculate the absorption and emission rates of phonons on TLSs and show that in isotropic solids, on average, the longitudinal phonons interact stronger with the TLSs than the transversal ones, as it is observed in experiments. We also show that in isotropic solids, a transversal wave leaves unperturbed all the TLSs with the direction contained in one of the two planes that are perpendicular either to the wave propagation direction or to the polarization direction and that a longitudinal strain applied to the solid polarises the TLS ensemble.

cond-mat.dis-nn↗

arXiv2007

Interaction of Lamb modes with two-level systems in amorphous nanoscopic membranes

Using a generalized model of interaction between a two-level system (TLS) and an arbitrary deformation of the material, we calculate the interaction of Lamb modes with TLSs in amorphous nanoscopic membranes. We compare the mean free paths of the Lamb modes with different symmetries and calculate the heat conductivity $κ$. In the limit of an infinitely wide membrane, the heat conductivity is divergent. Nevertheless, the finite size of the membrane imposes a lower cut-off for the phonons frequencies, which leads to the temperature dependence $κ\propto T(a+b\ln T)$. This temperature dependence is a hallmark of the TLS-limited heat conductance at low temperature.

cond-mat.mes-hall↗

arXiv2007

Optimal operation of transition-edge sensors on ballistic membranes

We calculate the operating parameters of a transition edge sensor that is mounted on a thin dielectric membrane with the assumption that the phononic heat transport in the membrane is ballistic. Our treatment uses the correct phonon modes from elasticity theory (Lamb-modes), and spans the transition from 3D to 2D behavior. The phonon cooling power and conductance have a global minimum as function of membrane thickness, which leads to an optimal value for the membrane thickness with respect to noise equivalent power at a fixed operating temperature. The energy resolution of a calorimeter will not be affected strongly, but, somewhat counterintuitively, the effective time constant can be reduced by decreasing the membrane thickness in the 2D limit.

cond-mat.mes-hall↗

arXiv2006

Quantization of the elastic modes in an isotropic plate

We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion relations are manifested in low temperature experiments in ultra-thin membranes.

cond-mat.mtrl-sci↗

arXiv2004

Heat transport in ultra-thin dielectric membranes and bridges

Phonon modes and their dispersion relations in ultrathin homogenous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the modes with different polarizations. We compute the heat capacity of membranes and the heat conductivity of narrow bridges cut out of such membranes, in a temperature range where the dimensions have a strong influence on the results. In the high temperature regime we recover the three-dimensional bulk results. However, in the low temperature limit the heat capacity, $C_V$, is proportional with $T$ (temperature), while the heat conductivity, $κ$, of narrow bridges is proportional to $T^{3/2}$, leading to a thermal cut-off frequency $f_c=κ/C_V\propto T^{1/2}$.

cond-mat.mes-hall↗