Dilution Refrigerator Temperatures Research Articles

Instrumentation for cryogenic microwave cavity resonance measurements

We describe instrumentation and measurement procedures for performing microwave measurements on small metallic samples at dilution refrigerator temperatures using the microwave cavity perturbation technique. The quality factor Q of the lead-plated cavity was of order of 105 at temperatures below the superconducting transition temperature of lead. Microwaves were coupled into and out of the resonator through two room-temperature positionable semirigid coaxial lines, each terminated in a small-loop antenna. We describe in detail the arrangement of the apparatus used to tune to, and lock onto, a cavity resonance and the strategy used to categorize various resonance modes. One of the main features of this microwave spectrometer is the application of the FM detection method to measure changes in both the frequency and the quality factor of the sample-loaded cavity. The procedures for converting these quantities to the real and imaginary components of the surface impedance are described. As an application of the methodology used, we present some results of measurements on the superconducting response of a heavy fermion superconductor, UBe13, which can be fitted with the Mattis–Bardeen theory.

Spin polarization of xenon films at low-temperature induced by [formula omitted

We have measured the 129 Xe spin-lattice relaxation time T 1 for xenon films adsorbed on silica gel in an 8 T magnetic field at dilution refrigerator temperatures, both with and without 3 He filling the sample cell. Without 3 He , T 1 increases rapidly as the temperature is lowered. With 3 He , T 1 is considerably shortened, and is consistent with temperature-independent quantum relaxation. Using this technique, it is possible to brute-force polarize large quantities of xenon in high B/ T conditions.

Quantum theory of bilayer quantum Hall smectics

Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states, in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled-Luttinger-liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled-Luttinger-liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer backscattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which rescales time and length along but not transverse to the stripes. With interlayer backscattering interactions present the Luttinger-liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by backscattering interactions are summarized in Fig. 11 by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance. We predict that the bilayer will form incompressible isotropic interlayer phase-coherent states for small layer separations, say $d<~1.5\mathcal{l}.$ At larger interlayer spacings, however, the bilayer will tend to form one of several different anisotropic states depending on the layer charge balance, which we parametrize by the fractional filling factor $\ensuremath{\nu}$ contributed by one of the two layers. For large charge imbalances $(\ensuremath{\nu}$ far from $1/2),$ we predict states in which anisotropic Wigner crystals form in each of the layers. For $\ensuremath{\nu}$ closer to $1/2,$ we predict stripe states that have spontaneous interlayer phase-coherence and a gap for charged excitations. These states should exhibit the quantum Hall effect for current flowing within the layers and also the giant interlayer tunneling conductance anomalies at low bias voltages that have been observed in bilayers when the $N=0$ Landau level is partially filled. When the gaps produced by backscattering interactions are sufficiently small, the phenomenology observed at typical dilution fridge temperatures will be that of a smectic metal, anisotropic transport without a quantum Hall effect. For stripe states in the $N=2$ Landau level, this behavior is expected over a range of bilayer charge imbalances on both sides of \ensuremath{\nu}=1/2.

Electron Transport in Metallic Grains

We discuss electron transport in individual nanometer-scale metallic grains at dilution refrigerator temperatures. In the weak coupling regime, the grains exhibit Coulomb blockade and discrete energy levels. Electron-electron interactions lead to clustering and broadening of quasiparticle states. Magnetic field dependences of tunneling resonances directly reveal Kramers degeneracy and Lande g-factors. In grains of Au, which have strong spin-orbit interaction, g-factors are strongly suppressed from the free electron value. We have recently studied grains in the strong coupling regime. Coulomb blockade persists in this regime. It leads to a suppression in sample conductance at zero bias voltage at low temperatures. The conductance fluctuates with the applied magnetic field near zero bias voltage. We present evidence that the fluctuations are induced by electron spin. This paper reviews the evolving progress in interpreting these observations.

Hole transport in coupled SiGe quantum dots for quantum computation

We describe transport measurements on double quantum dot structures formed by trench isolation in a SiGe:Si heterostructure. Three different device geometries are described, and a number of phenomena are observed. Transport measurements at 4.2 K reveal a carrier energy filtering effect accompanying a period doubling in Coulomb oscillations, showing that tunnel barriers can be raised and lowered by application of a gate voltage. Peak splitting in Coulomb oscillations is also observed at 4.2 K, indicating interdot capacitive coupling. The stability diagram for a double dot is mapped out at dilution refrigerator temperatures. In another device, single hole electrometers are fabricated 50 nm away from a double quantum dot, and the ability to measure a single excess charge on the double dot is demonstrated at dilution refrigerator temperatures.

Thermal Conductivity of Normal Liquid 3He in Aerogel

We report thermal conductivity measurements for normal phase liquid 3He inside 98 and 95% aerogels at dilution refrigerator temperatures (5 to 50 mK). In our measurements we use cylindrical samples of aerogel which have been fabricated inside quartz tubes. Each tube is enclosed at one end by a small chamber to which a known heat input is applied at a measured temperature. The other end is in an open volume of helium which is heat sunk to the refrigerator. Vibrating wire thermometry is used to measure the helium temperatures. The thermal conductivity measurements show clearly the effects of quasiparticle-“impurity” scattering, from which values of the mean free path are derived. These are 92 nm for the 98% aerogel and 56 nm for the 95% sample.

High pressure hydrogen loading cell for photoconductivity measurements down to the milliKelvin regime

A gas loading cell has been developed to load rare earth thin film samples with hydrogen at pressures up to 200 bars at room temperature. A miniature valve closes the gas inlet, after which the cell is suspended from the cold tail of a He3 flow cryostat into the bore of a 16 T superconducting magnet. An ultraviolet stroboscope outside the cryostat illuminates the sample by way of an optical fiber to a window in the cell. Electrical feedthroughs permit photoconductivity and magnetotransport measurements over three decades in temperature. Extension to other materials, different gas atmospheres, and helium dilution refrigerator temperatures is straightforward.

Temperature dependence of critical currents in Nb/InAs/Nb Josephson junction arrays

We study extreme geometries in the field of 2DEG-coupled Josephson Junctions, at dilution refrigerator temperatures. The 2DEG is a continuous layer of InAs that contacts an overlying array of niobium stripes. The temperature dependence of other S–Semi–S systems has been studied in relatively small geometries. Our junctions are in a new regime with widths to 1 mm and lengths of 1.5 μm . We find temperature-dependences of the critical current, I c, that are difficult to fit consistently with theories used for other InAs-based junctions.

High magnetic field corrections to resistance thermometers for low temperature calorimetry

We present a general analytical method of correcting for magnetic-field-induced changes in both the apparent temperature and the sensitivity of resistive thermometers at dilution refrigerator temperatures. With this method, we are able to reduce magnetic field induced errors in temperature to a level limited only by our ability to regulate the temperature in the absence of a magnetic field. We illustrate the application of our method to two resistive sensors in magnetic fields up to 18 T: a custom-made AuxGe1−x thin film sensor used in calorimetry and a commercially available ruthenium–oxide thick film resistor used in thermometry.

Fine structure in the energy spectra of ultrasmall Au nanoparticles

We have studied tunneling into individual Au nanoparticles of estimated diameters 2-5 nm, at dilution refrigerator temperatures. The I-V curves indicate resonant tunneling via discrete energy levels of the particle. Unlike previously studied normal metal particles of Au and Al, in these samples we find that the lowest energy tunneling resonances are split into clusters of 2-10 subresonances. Such effects appear to be increasingly important in smaller grains, as might be expected from the larger characteristic energies.

Tunneling Through Metallic Quantum Dots

We discuss single-electron tunneling measurements at dilutionrefrigerator temperatures on metallic grains, sufficientlysmall that the quantum levels of the conduction electrons canbe resolved. These measurements directly reveal the energyeigenvalues of the electrons in a grain that typicallycontains a few thousand conduction electrons. Suchmeasurements were first carried out a few years ago by Ralph,et al. on nanograins of Al. More recently, this workhas been extended to measurements on nanoparticles of theheavy metal Au by Davidovic and on nanoparticles ofalloys of Al and Au by Salinas, et al. This morerecent work has pointed up the need to go beyond the simplestindependent-electron model, to include the Coulomb interactionbetween electrons and also nonequilibrium electronpopulations. These interactions cause the energy levels tomerge into a continuum above the Thouless energy and can causea single quasiparticle level to show up as a cluster ofresonances. The strong spin-orbit interaction in Au cancause levels to split in magnetic fields with a g-factor of∼0.3, instead of the free electron g=2. In addition,there is evidence for a proliferation of low-lying energylevels suggestive of system spin values greater than1/2 induced by the exchangeinteraction. This paper will review the evolving progress thathas been made in interpreting these observations.

Coulomb oscillations in partially open quantum dots

We report tunneling measurements of the Coulomb blockade in a single quantum dot at zero magnetic field and dilution refrigerator temperatures with weak tunneling from the dot to one lead (the ‘closed’ lead, conductance G closed ) and strong tunneling to the other lead (the ‘open’ lead, conductance G open ). We observe suppression of the Coulomb oscillations with G open ≈2 e 2/ h, and then see the oscillations return for G open >2 e 2/ h. The oscillations show a strikingly lower threshold temperature at G open ≈2 e 2/ hthan for greater or lesser G open .

Quantum Hall effect from finite-frequency studies

An overview is given of two finite frequency ( f ≈ 10–100 MHz and 0.2–14 GHz) experiments on the two-dimensional electron system (2DES) in GaAs/ Al x Ga 1− x As heterostructures at dilution refrigerator temperatures in the quantum Hall effect regime. In the lower frequency experiment, Re σ xx and Im σ x are simultaneously measured in a high mobility sample and a giant dielectric constant is observed in the insulating phase reentrant around the 1 5 fractional quantum Hall effect liquid. The data provide new evidence for Wigner crystal order in the insulator, where the crystal is strongly pinned by residual impurities in close proximity to the 2DES. In the high-frequency experiment, Re σ xx is measured in an ƒ range that can be continuously tuned from well-below to well-above kT/h of the sample. Dynamic scaling was observed in the plateau to plateau transition of integer quantum Hall effect in a low mobility sample.

The vibrating sample magnetometer: Experiences of a volunteer (invited)

On its 40th anniversary, I describe how the vibrating sample magnetometer (VSM) was developed and, later, how the very low frequency VSM, a flux-integration device, was developed. The important features of the moving sample technique, detection coil symmetry, calibration, sensitivity, and image effects are discussed briefly. Some VSM adaptations discussed include operation at 3He and dilution refrigerator temperatures, at high hydrostatic pressures, in superconducting, high-power water-cooled and hybrid magnets, for very low frequency ac susceptibility, and with SQUID detectors.

The decay of induced eddy currents in a two-dimensional electron system

Large long-lived eddy currents are induced in a two-dimensional electron system as the magnetic field is swept through the almost dissipationless states associated with the quantum Hall effect. We have measured the temperature dependence of the decay times of these currents in a GaAs/AlGaAs single heterojunction, using a torque magnetometer at dilution refrigerator temperatures. At Landau-level filling factor ν = 4, the decay time is less than a minute at T = 40 mK, whereas at ν = 1 and 2 we observe a decay time of about 4 hours which follows a short initial decay of the order of minutes. We discuss the possible mechanisms for decay of the currents and conclude that the energy is stored predominantly in the Hall electric field between the edge and the centre of the sample. At T = 40 mK we estimate a 2D resistivity of the order of 10 −14 Ω □ for ν = 1 and 2 and 10 −11 Ω p[ for ν = 4.

Exciton luminescence in the quantum hall and electron solid regimes

Optical studies in the regime of the quantum Hall effect (QHE) reveal complex behavior related to the strongly interacting 2D electron system. In the following we review our recent investigations of exciton luminescence in high-mobility GaAs electron systems. Several novel phenomena are observed, including additional exciton peaks at high magnetic fields, intensity variations and energy shifts coincident with the quantum Hall effect, strongly suppressed recombination at ν = 1 and ν = 1 3 , and peak splitting in the electron solid regime. The experiments were made using picosecond time-resolved PL measurements, dilution refrigerator temperatures ( T > 0.05 K), and high magnetic fields ( B ⩽ 20 T).

A rotating dilution cryostat to study quantum liquids

A rotating cryostat, under examination, to study quantum liquids at dilution refrigerator temperatures is described. The specific features include continuous operation with 3He J-T precooled dilution refrigerator and very smooth rotation for the study of quantum liquids such as submonolayer 4He films in well defined porous glasses.

Optical spectroscopy of GaAs in the extreme quantum limit: integer and fractional quantum Hall effect, and onset of the electron solid

Our recent optical detection of the integer and fractional quantum Hall effects in GaAs, by intrinsic band-gap photoluminescence at dilution refrigerator temperatures, is reviewed. This work has been extended to the extreme quantum limit where a photoluminescence peak develops close to Landau level filling factor v = 1 5 which correlates both with the onset of threshold behaviour in current-voltage characteristics of the two-dimensional electron system and a resonant radio-frequency absorption; the latter are quantitatively accounted for by a model of crystalline electronic structure broken up into domains. Preliminary mK transport experiments in intense, pulsed magnetic fields are also described, which establish a basis to access the electron solid phase transition in a hitherto unattainable region of the ( B, T) plane.

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe13, URu2Si2 and U6Fe. The magnetic field penetration depth in the superconducting state of UBe13 is greater than 10000 A, as no increase in the transverse field relaxation rate is observed belowTc. A sharp increase in the precession frequency is seen, starting atTc. This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu2Si2 show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu2Si2 show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U6Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atTc=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.

Platinum NMR thermometry in high magnetic fields

A platinum nuclear magnetic resonance (NMR) thermometer has been developed for use in high magnetic fields (10 T) at low dilution refrigerator temperatures (10 mK). The design consists of fine platinum wires cooled by a heat exchanger of pressed silver powder. Nuclear magnetic heat capacity, thermal and magnetic relaxation times and inhomogeneous line broadening are quantitatively addressed. A version of the thermometer that fits within a 1 mm diameter tube has been used to measure temperatures down to 7.9 mK in a dilute 3He– 4He solution in an 8 T field.