Interaction and Disorder in Two Dimensions
Contact person: György Kriza,
Electron solid and vortex solid
Electrons confined to two dimensions undergo a quantum liquid to (Wigner) solid transition if a magnetic field is applied to suppress quantum fluctuations. Vortices in quasi-two dimensional type II superconductors show a classical vortex liquid to solid transition upon reducing the temperature to suppress thermal fluctuations. Both systems are subject to disorder imposed by the host material.
The electron system is composed of electrons or holes at epitaxial junctions between GaAs and GaAlAs, placed in a magnetic field perpendicular to the interface. They interact with one another through Coulomb forces and the random field derives from impurities and interface defects. The vortex system is set up in Bi2Sr2CaCu2O8+δ (BSCCO), one of the family of strongly type II high Tc cuprate layered superconductors but which is so anisotropic as to be quasi two-dimensional. A magnetic field perpendicular to the layers penetrates creates a set of quantised vortices which are coupled to one another within a layer by Magnus/Lorentz forces but are only weakly coupled between layers. The disorder field is constituted by defects to which they try to pin.
Transport in the magnetically induced Wigner solid phase is non-linear and shows three distinct regimes: activated transport at low current displaying a normal Hall effect, an intermediate current regime where the Hall voltage stagnates and a high current domain where a Hall effect reappears (Perruchot F., et al., 2000). The latter two regimes are seen as a consequence of depinning of the Wigner solid which is guided along a channel determined by the disorder configuration. As long as the Lorentz force is insufficient to push it transversely out of its channel, there is no Hall voltage. Once the Lorentz force is sufficient, the solid is no longer guided and behaves as a set of free charges with a Hall effect.
Transport in the vortex solid phase of the high Tc superconductors is also non-linear and is reputed to have vanishing Hall effect, even for depinned transport. This is a similar situation to the depinned Wigner solid, suggesting that there may be an unattained higher current regime where the vortex solid dechannels and a Hall effect expected for real free flux flow.appears. We have carried out a series of experiments with this eventuality in mind.
We have measured transport with low energy, high current pulses to avoid spurious effects from heating. In samples with low depinning threshold we have observed a Hall effect (characterised by transverse voltage which reverses sign when the magnetic field is reversed) to appear suddenly beyond a threshold current typically some 2 orders of magnitude higher than the depinning threshold (to be published). To give quantitative meaning to such transport results, however, requires knowing the force driving the vortices which requires in turn knowing the current distribution. To this end, multi-contact experiments were made on the position of the resistive depinning front as a function of current both along the face and in depth, the latter by lithographically etching a terrace along an edge (Pethes I., et al., 2003). This knowledge allowed us to compare the longitudinal resistance with the standard Bardeen-Stephen prediction: although the order of magnitude is correct, the field dependence for the in-plane resistivity was found to be ρab~H3/4 rather than ρab~H, while the c-axis resistivity ρc~H -3/4log2H (Pallinger A., et al., 2008). Another, more structural, aspect concerns the increase and peak in depinning threshold current with temperature for samples prepared by cooling in zero field before application of the measurement field and the instability of field cooled samples to small magnetic field variations. These features have been shown to be consequences of a metastability which results from progressive decoupling of the vortex pinning dynamics from the thermal bath (Pallinger A. et al., 2009).
|BSCCO sample: approximately 800 µm long contacted along the middle of a face and along a terraced edge lithographically etched to 100nm below the face for investigation of depth behaviour of resistive front|
Dynamical normal modes of systems with translational symmetry are characterised by wavevector and frequency. They are seen as resonant maxima in the wavevector and frequency dependent susceptibility, the widths reflecting damping. The near field of an electromagnetic structure reflects its geometry: a periodic planar structure sets up a near field with like periodicity whose amplitude diminishes exponentially in the third dimension (Laplace). By coupling an open, planar, periodically shaped transmission line to a parallel two dimensional electron system one can probe its susceptibility by virtue of the near force field produced by the electromagnetic field of the structure: e.g. a meandering 10 μm strip transmission line with 10 μm between meanders sets up a near field potential of 20 μm periodicity at the frequency of the power transmitted by the line. Power is transferred to the physical system in proportion to the relevant susceptibility for that wavevector and frequency. Sweeping the frequency will reveal a resonance in transferred power as the frequency traverses the resonance in the susceptibility at the spatial Fourier components of the coupling field, corresponding to the normal mode frequencies for those wave vectors. A series of such resonances allows one to plot out the wavevector-frequency relation of the excitation branch.
|Diagram: Dispersion of propagating and near electromagnetic fields (green) and the dispersion of the excitation branch to be investigated (red). If they interact there is resonant power transfer at the crossing points (circles).|
We have used this technique with some success in the past to detect the appearance of a pinning mode and a transverse phonon mode in 2-d electron “Wigner” solids. It should be possible to do the same for quasi-two dimensional collective vortex modes. A variant of the technique has also been used to detect edge magneto-plasmons where the mode selection is imposed by the perimeter of the sample. It should be applicable to our new interest in the two-dimensional graphene electron system.
Five years ago, at the University of Manchester, it was discovered how to isolate, fix and contact a single layer of graphite by successive cleaving. Such a graphene sheet, apart from being the ultimate in two-dimensional systems, has very special electronic properties. Neutral, it has a filled conduction and empty valence band, but the bands meet at a point in momentum space corresponding to a linear (conical) crossing of bonding and anti bonding pi-orbital propagating states. Excess electrons may be transferred to it by making it one electrode of a capacitor and these excess electrons all propagate at a fixed speed regardless of the applied force and obey the same dynamics as would a charged neutrino or a massless Dirac electron. This new extreme relativistic dynamics confers new properties which have excited considerable interest world over. In collaboration with our Saclay (SPEC) colleagues – Glattli, Benaceur and Petkovic – we have been able to fabricate, contact and make transport measurements on the small 4 x 10 µm2 sample on a SiO2/Si substrate shown on the left. We hope to build on this to measure electronic excitations in the microwave and far infra-red frequencies, again in collaboration with our Saclay colleagues.
|Graphene: Scanning electron microscope photograph of graphene sample (dark) of about 4 x 10 μm2 contacted for transport measurements. The scale bar represents 5 μm.|
- NMR spectrometer: Pulse sequence, Fourier transform, wide line multifrequency spectrometer with 9 tesla field and 2-350 K sample temperature. (Bruker Avance III)
- Pulsed high current transport: balanced 1.5 A, 10 μs arbitrary pulse shape with low noise voltage detection (1.2 nV/√Hz), sample probe 5-300 K, 0-5 tesla.
- Access to SQUID magnetometer.
- Finite wavevector microwave spectrometer: 0.1 – 10 GHz, 20 mK – 100K sample space, 0-8 tesla field in house but designed to fit high magnetic field laboratory magnets to 30 tesla, 8 x 8 μm impedance matched meander strip line coupler, computer controlled superheterodyne low level detector TN=200 K (purpose made vector network analyzer), synthesized microwave sources for upgrade to 20 GHz and 40 GHz. The low temperature Joule-Thomson precooling dilution refrigerator insert, whose outside is shown on left and inside on the right, is also cabled for simultaneous low level AC, DC or pulse transport measurements. The lower section has 29 mm outer diameter over 750 mm with sample mounted inside the plastic, demountable dilution chamber 120 mm above the lower end.
Contact person: Mónika Bokor,
We study the relations between the hydration properties and the solvent accessible surface of proteins. Our aim is the detailed characterization of the hydration of intrinsically disordered, amyloid forming, and globular proteins. We have developed a procedure based on wide-line NMR spectrometry, nuclear relaxation rate measurements and DSC for this purpose. This interdisciplinary experimental approach can be applied for the determination of the disordered/ordered nature of novel proteins concerning their secondary structure. These experiments also enable one to map the differences between the protein classes intrinsically disordered, amyloid forming and globular. We focus on
- setting up characteristic hydration values and thermal trends for the different protein types,
- characterization of the solvent accessible surface of the protein molecule in terms of homo/heterogeneity in the interactions with water molecules and co-solutes (e.g. ions, buffer agents),
- the setting up a general nuclear relaxation model for hydration water including each relevant relaxation channel (e.g. dipolar, quadrupolar, paramagnetic), and
- determination of the thermodynamic parameters of the hydrated protein.
The mobile water molecules within the hydrate layer of proteins can be qualitatively and quantitatively characterized by wide-line 1H NMR (Balázs et al., 2009; Bokor et al., 2005; Bokor et al., 2010; Csizmók et al., 2005, Szőllősi et al., 2008; Tompa et al., 2006; Tompa et al., 2009; Tompa et al., 2010). We proposed a novel method for the quantitative measurement of water molecules in the hydration shell directly based on 1H NMR intensity data for aqueous protein solutions (Tompa et al., 2006; Tompa et al., 2010).
Ubiquitin NMR structure [Source: Protein Database]
The protein molecules and their hydration water form one phase in the thermodynamic sense and the specific heat of the protein+hydration water can be estimated accordingly by a proper combination of NMR and DSC methods (Bokor et al., 2010; Tompa et al., 2009; Tompa et al., 2010). We have found that the endothermic peak due to the eutectic phase transition of the NaCl-water system, detected calorimetrically, can be used as a direct indicator for the interactions between the protein and the Na+ and Cl– ions (Tompa et al., 2006; Kamasa et al. 2007).
Our results provide important evidence for the process required to assign a novel protein as intrinsically disordered. The technique enables the characterization of intrinsically disordered proteins, showing their significantly larger hydration than globular proteins as the evidence for their open and largely solvent-exposed nature (Balázs et al., 2009; Bokor et al., 2005; Csizmók et al., 2005, Szőllősi et al., 2008; Tompa et al., 2006; Tompa et al., 2009; Tompa et al., 2010).
The information provided by these NMR techniques is complementary to that obtained by other, more often used methods (homo- and heteronuclear Overhauser effect, nuclear magnetic relaxation dispersion, and spin-spin relaxation).
The study of metal-hydrogen systems has both theoretical and practical importance. To investigate these systems, proton NMR spectroscopy (PMR), electric transport and bulk susceptibility measurements, X-ray diffraction and UPS have been used at temperatures between 4 and 350 K for binary Zr-Ni and ternary Zr-Ni-Cu amorphous alloys charged with hydrogen.
The simultaneous measurements of line-shift and bulk susceptibility enabled us to separate the Knight-shift and the chemical shift contributions to the proton line-shift and thus have given some hints to understand how the electrons arrange themselves around protons in metals. On the basis of spin-spin relaxation mechanism dominant in the high temperature range and from the temperature dependence of the electrical resistivity, the activation energy and correlation time of hydrogen diffusion could be determined as the function of hydrogen and the third component (Cu) content. In contrary to the commonly accepted models, both the hydrogen and the copper content influence the correlation time but do not affect the activation energy. The UPS spectra of ternary systems show Cu, Ni-, and Zr derived states both before and after hydrogenation. It is found that hydrogen had the greatest effect in the region of Cu-derived states. The effect was ascribed to a hydrogen induced phase separation.
Conventional in situ DC resistivity measurement is used for monitoring the H content during absorption and desorption processes and also for the determination of diffusion parameters. Simultaneously, the maximum hydrogen storage capacity in the amorphous Ni1-xZrx alloys was determined. Electrochemical measurements have also been performed on these alloys in order to characterize their behaviour with regard to their potential applications as metal hydride battery electrode materials.