Condensed Matter Physics has grown from its roots in Solid State Physics and Low Temperature Physics to encompass the basic physics of the structure and properties of materials, from the atomic scale to the larger scales of familiar phenomena in the world around us. Over the past few decades an understanding has developed that the collective properties of the many strongly interacting particles comprising condensed matter systems are by no means a simple consequence of the basic laws of interactions between them, so that exotic new phenomena, such as new phases of matter, continue to be discovered. At the same time experimental advances now allow the direct investigation of single particles and excitations such as electrons and phonons within the solid state. An important feature of the discipline is the extraordinarily strong coupling between the experimental work and the associated theory, and the importance of technological advances, of lower temperatures, finer fabrication, and new materials etc., in setting the directions. The wide range of the field is amply demonstrated by the activities of the various components of the Caltech group.
The discovery of high-temperature superconducting oxides in 1986 has opened up a new era of intense research in the basic physics of superconductivity and opportunities for a broad range of device applications. Many applications of superconductivity are based on the unique magnetic properties of "type-II" superconductors. An external magnetic field between the lower and upper critical fields (HC1 and HC2, respectively) of a type-II superconductor does not penetrate uniformly through the sample. Rather, the magnetic field inside the sample becomes "quantized" into arrays of magnetic flux lines at temperatures below the zero-field superconducting transition temperature Tc. The positions of the flux lines form a periodic triangular lattice pattern; each flux line contains a flux quantum, and is surrounded by a vortex of currents which partially screens the magnetic interaction with neighboring flux lines, thereby lowering the free energy of the superconductor. Consequently, the "vortex state" enables type-II superconductors to sustain high magnetic fields and large applied current densities.
High-temperature superconductors (HTS) are "extreme" type-II superconductors. The combination of the high transition temperatures (Tc ~ 100 K, compared to Tc of 1 ~ 10 K in conventional superconductors), short superconducting coherence lengths, long magnetic penetration depths, and large electronic anisotropies in HTS results in a "soft" vortex-solid phase which is more susceptible to large thermal and disorder fluctuations. A new thermodynamic phase, the vortex-liquid, occurs between a low-temperature vortex-solid phase and the normal state. Despite interesting new physics properties associated with this vortex-liquid state and the phase transitions between the vortex-solid and vortex-liquid, the thermally-induced vortex motion in the vortex-liquid state results in dissipation which limits the usefulness of high-temperature superconductors to lower temperatures. Hence, for practical purposes such as device applications, it is essential to understand how to minimize vortex motion in high-temperature superconductors through the introduction of different types of pinning defects.
We have systematically investigated the effects of static disorder on the vortex dynamics of high-temperature superconductors. In the clean limit and for a constant magnetic field, the vortex-solid to liquid transition of YBa2Cu3O7 single crystals is consistent with a first-order melting transition. On the other hand, in the presence of significant static disorder, the vortex-solid phase becomes glassy, and the phase transition between the solid and liquid phases becomes second-order, with different universality classes associated with different types of static disorder. In addition to the variations in the universality classes of phase transitions, correlated static disorder also induces anisotropic vortex dynamics, as manifested by the changes in the angular dependent vortex phase transition temperatures
In addition to the important effects of symmetry-breaking and anisotropic vortex dynamics induced by static disorder, both the vortex-solid to liquid phase transition temperatures and the critical current densities are enhanced with the introduction of columnar defects. The physics knowledge derived from these investigations is being applied to improving microwave device performance and manufacturing high-temperature superconducting wires in research laboratories and industry worldwide.
With the modern invention of low-temperature scanning tunneling microscopy (STM), atomically-resolved images and spectroscopy of materials can be obtained. Currently the low-temperature scanning tunneling microscope in Professor Yeh's group can resolve atomic structures to fine details (~0.025 nm resolution). In addition to imaging, we have also used this spatially-resolved tool to investigate the directional tunneling spectroscopy and Andreev reflection of high-temperature superconducting YBa2Cu3O7single crystals along different k-vectors, to obtain the anisotropic superconducting energy gap on a YBa2Cu3O7 single crystal along the {100}, {001}, and {110} directions. By incorporating both the d-wave pairing symmetry and the two-dimensional tight-binding band structure, we are able to describe the features of the tunneling spectroscopy quantitatively. However, we find that along the {100} direction, the superconducting gap (28 +- 5 meV) derived from the theoretical fitting is larger than that along the {001} direction (20 +- 5 meV), suggesting that the interlayer coupling neglected in the two-dimensional band structure will have to be considered to fully account for the tunneling data. We plan to continue the STM studies on various families of high-temperature superconductors, in order to understand the dependence of the superconducting energy gap on the number of CuO2 layers per unit cell, the Fermi energy, and the k-vector. These systematic studies will help to unravel the pairing mechanism of high-temperature superconductors.
Very low-loss superconducting niobium cavities, with the quality factor (Q) as high as Q ~ 1010 at T < 2 K, can be achieved by anealing the niobium cavity under ultra-high vacuum (~10-10 Torr) and at high temperatures (up to ~1800 oC). These high-Q superconducting cavities may be used as stable oscillators for precision clocks, frequency standards, and various microwave device components. Combined with modern microwave electronics and high-resolution thermometry (HRT) based on the SQUID (SUperconducting Quantum Interference Device) technology, the frequency stability of these oscillators can achieve up to one part in 1018. The high-resolution oscillators based on superconducting cavities can further achieve high accuracy in the frequency when compared with accurate atomic clocks. We are in the process of constructing and optimizing the superconducting cavity-based oscillators, in order to achieve state-of-the-art precision clocks for applications ranging from gravitational wave detection to space navigation.
As mentioned in the previous section, modern microwave technology combined with high-Q resonators can achieve frequency readout and control with a resolution up to one part in 1017 ~ 1018. Such high-resolution measurements are better than most experimental techniques, and therefore may be applied to research areas that require state-of-the-art precision. We have recently initiated a research project which aims at unraveling the fundamental nature of continuous phase transitions by studying the static and dynamic critical properties of condensed phases of helium near phase transitions with the use of various state-of-the-art technologies that can provide unprecedented precision. The basic concept is to utilize the unique capability of resolving the resonant frequencies of a helium-filled superconducting microwave cavity to extremely high precision (better than one part in 1017), in conjunction with the high-resolution thermometry (HRT) and high-resolution pressure control, to obtain precise measurements of the density and the phase transition temperatures of helium. The principle of using microwave techniques to perform precision density measurements of the helium in condensed phases is based on the Clausius-Massotti relation which relates the density of liquid helium to its dielectric constant. If we contain helium in a high-Q superconducting microwave cavity, the temperature-dependent dielectric constant of helium will couple to the electric field of the resonant modes in the cavity, yielding temperature-dependent frequency shifts relative to a reference resonant frequency. Even under the influence of gravity that gives rise to a gradient in the superfluid Lambda transition, our microwave techniques can deconvolve the gravity-induced density gradient, thereby yielding unprecedented precision of the helium density near the Lambda transition temperature. The precision can be further improved by at least two orders of magnitude under the microgravity environment. Similar measurements can be performed on He3 - He4 mixture, as well as on He4 near the solid/liquid transition.
Recent discovery of colossal negative magnetoresistance (CMR) in the perovskite manganites, Ln1-xMxMnO3 (Ln: trivalent are earth ions, M: divalent alkaline earth ions) has spurred intense research in understanding the origin and providing further improvement of the magnetoresistive effects. Our experimental studies, which involve measurements of the electrical transport, magnetic and optical properties, as well as tunneling spectroscopy using STM, have identified two important criteria for the occurrence of CMR in the manganites. One is the double-exchange interaction which gives rise to ferromagnetic interaction between adjacent Mn ions. The other is the lattice distortion associated with both the Jahn-Teller coupling and the deviation from the cubic structure as a result of the ionic size mismatch in the manganites. These two criteria result in a large exchange energy splitting between the majority and minority bands, hence complete spin polarization in the ferromagnetic state below the Curie temperature (TC). This phenomenon is known as half-metallic ferromagnetism, which is in contrast to typical ferromagnetic metals (such as Ni) where the energy splitting between the majority and minority carriers below TC is much smaller than the conduction bandwidth, yielding a small fraction of spin polarization. The half-metallicity has an important consequence on the electrical conduction. In the presence of magnetic domains below TC, any misalignment of the spins between two adjacent domains will result in a large energy barrier for the conducting carriers and therefore a large resistivity in the absence of an external magnetic field. The application of a magnetic field aligns the spins in different magnetic domains, thereby lowering the energy barrier for carriers and yielding colossal negative magnetoresistance.
The complete spin polarization due to the half-metallic ferromagnetism in the manganites has a great promise for exploring new physics and for device applications. For instance, we may consider injecting completely spin-polarized electrons from the manganites into a high-temperature superconductor via epitaxial thin film growth of Ln1-xMxMnO3 on top of a high-temperature superconductor (e.g., YBa2Cu3O7) film. By injecting a current through the manganites, polarized carriers will diffuse into the superconductor underneath, resulting in Cooper-pair breaking and the suppression of superconductivity. Thus, the superconducting critical current may be controlled by varying the magnitude of the magnetic current. This concept can be used to develop low-noise, high-gain three-terminal devices for a wide range of applications, and is an example of advancing technology from understanding of fundamental physics.
The cobaltites Ln1-xMxCoO3 are interesting magnetic materials particularly because of the coexistence of multiple spin configurations in the Co ions. For x=0.18 ~ 0.6, these cobaltites are ferromagnetic at low temperatures. It is known that clusters of high-spin Co ions form better conducting regions imbedded in the less conducting matrix consisting of low-spin Co-ions. We have recently discovered giant spontaneous Hall effects in La1-xCaxCoO3 epitaxial films with x=0.2, 0.3, 0.5. The giant ferromagnetic Hall effect is most significant near the ferromagnetic percolation threshold and at temperatures slightly below TC. The spontaneous Hall effect then vanishes for x=0.1, below the percolation threshold. For all ferromagnetic La1-xCaxCoO3, the spontaneous Hall resistivity is found to be larger than any known single-phase ferromagnets. Although to date there is lack of quantitative theoretical understanding to account for the magnitude of the giant spontaneous Hall effect, our studies have identified two important criteria for the enhancement of the ferromagnetic Hall effect. One is the large spin-orbit scattering due to the presence of magnetic clusters in the cobaltites, the other is the presence of magnetic percolating process.
The giant ferromagnetic Hall effect in the cobaltites may be used as sensitive magnetometers for operation at temperatures significantly higher than liquid helium temperatures. The sensitive change in the Hall resistivity due to very small magnetic fields may be considered for making low-field magnetometers. The device specifications based on these cobaltites may be particularly useful for lower-cost magnetometers in unmanned space missions, such as for magnetic field detection on the surface of Mars.
M. L. Roukes Group
"Nanotechnology", i.e. the ability to mass produce atomic-scale machines, was first publicly envisioned by Richard Feynman here in Pasadena, at a lecture almost 40 years ago. We are exploring the frontiers of nanotechnology in a number of areas, a few of which are listed below.
Nanoelectromechanical Systems (NEMS)
NEMS are three-dimensional structures and machinery with dimensions at the 10-100 nanometer scale. We are investigating the basic physics of motion at these small scales, applying NEMS as high-sensitivity detectors, employing NEMS in fluid environments for biology applications, and making single-molecule resonators out of carbon nanotubes.
Magnetic Resonance Force Microscopy
Magnetic resonance force microscopy (MRFM) combines the three-dimensional imaging capabilities of magnetic resonance imaging with the high sensitivity and resolution of atomic force microscopy. By employing advanced NEMS techniques, we hope to push toward achieving atomic-scale resolution.
Heat Transport in Nanoscale Systems
Crucial to the operation of electronic devices is the dissipation of heat, but very little is known about thermal transport at the nanoscale. Fabrication of 3D suspended nanostructures with integrated heaters and thermometers allows us to study this regime by measuring the heat flow across nanometer-scale structures.
Spin Transport
In the new field of "spintronics" electronic devices will control the spin of electrons in addition to their charge. We have recently begun making and studying some of the first all-semiconductor spintronic devices.
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Nanomechanical resonators |
Thermal transport measurement device |
Selected Publications
Atoms adsorbed on a surface can move around, interact with one another, and generally behave like 2-dimensional matter. Two-dimensional (2D) matter has phases and phase transitions like 3D matter: solid, liquid and gas, and also other phenomena that are unique to the adsorbed state.
Recent work at Caltech has focussed on multilayer films of methane, argon and krypton adsorbed on graphite. The purpose has been to investigate the transition between 2D and 3D behavior. It has been found that the first molecular layer forms 2D matter, undergoing a rich variety of behavior at various different temperatures and amounts adsorbed. When a second layer is adsorbed on top of the first layer, the first layer becomes an essentially inert substrate, and the second layer undergoes a whole new set of 2D phases and phase transitions. The same happens all over again in the third and fourth layers, but the third and fourth layers are no longer independent of one another. Their phases and phase transitions become linked together in phenomena that indicate the beginning of the formation of the bulk interface as the film grows thicker.
These investigations have been made possible by a new, automated scanning ratio calorimeter that has been built in the Sloan laboratory. With this instrument, data of unprecedented resolution may be acquired rapidly over a wide range of thermodynamic conditions. The initial studies of methane, argon and krypton that have been completed on the graphite substrate raise a variety of questions of fundamental importance to be investigated in the future.
Phase transitions and critical phenomena in condensed matter systems have been an extraordinarily active area of research for the past 25 years. Examples of such transitions include the onset of magnetism in materials such as Iron and Nickel, the demixing of binary fluids, and the condensation and freezing of liquids and solids. With the advent of renormalization group methods and other powerful theoretical tools, detailed predictions of the behavior at and near such transitions can be made. Motivated by ever more sophisticated experiments at lower and lower temperatures, a new branch of this field has recently come into being: that of quantum phase transitions. These are transitions that take place in the ground state wavefunction of quantum mechanical systems at zero temperature. The corresponding behavior of classical systems tends to be trivial and uninteresting since they are completely frozen and motionless at zero temperature. In contrast, zero temperature quantum systems are some of the most mobile known, displaying such phenomena as superfluidity and superconductivity.
Some of the phenomena being studied in at Caltech include the onset of superfluidity in "dirty" systems, such as 4He in porous media and packed powders, the onset of superconductivity in amorphous thin films, and spin glass transitions in quantum magnets. Related topics include the behavior of high temperature superconductors in strong magnetic fields and moderate temperatures where the Abrikosov flux lattice undergoes a melting transition. This classical phase transition, under certain conditions, can be mapped onto a zero temperature boson superfluidity problem in which the flux lines become the imaginary-time world lines of the bosons. Experimental work in this area is being performed at Caltech by the group of Nai-Chang Yeh.
A host of nonzero temperature transitions are also under investigation. These include nuclear ferromagnetism in thin 3He films, the effects of gravitational rounding on the classic 4He lambda transition, layering transitions in thin film growth experiments being performed at Caltech by David Goodstein's group, and classical magnetic tricritical phenomena.
There are also many physical phenomena that, at first sight, lie far from what one would ordinarily consider to be phase transitions, but nevertheless benefit greatly from theoretical ideas and techniques developed in the latter field. Two such phenomena that are under active study in the group are the thermodynamics of large-scale vortex structures in ideal two-dimensional fluid flow, and the classic problem of turbulence in strongly driven three- dimensional fluids. The former problem is fascinating because it involves a system that can be treated using the classic methods of statistical mechanics, but contains very long-ranged Coulomb interactions, and an infinite number of conservation laws. The combination of these two features leads to an enormously rich, yet theoretically tractable thermodynamic behavior. The latter problem is one of the oldest in physics, but has yet to submit to a proper theoretical understanding. We are gaining new insight by applying new theoretical techniques based on the 1/N-expansion in critical phenomena. The technique has the potential of being the first to provide a detailed, systematic description of the turbulent state. Turbulent phenomena occur also in such varied situations as nonequilibrium surface growth, and wind generated waves on the ocean surface. We are beginning to apply similar ideas to these phenomena as well.
Physical systems may be driven "far from equilibrium" by the continuous addition and subtraction of energy, for example the passage of a heat current through a fluid system, or the continuous pumping of chemical constituents to give a chemical reaction that never "runs down". The usual unifying principles of thermodynamics and statistical mechanics do not apply to these systems, and novel phenomena develop. Two particular phenomena of interest are the formation of spatial structures ("pattern formation") in nonequilibrium systems ranging from fluids (e.g. Rayleigh-Benard convection) through crystal growth to chemical reactions (the "Turing Patterns"), and chaotic dynamics. (Turbulence, described above, is another). A particularly challenging question being studied is the combination of these two, known as "spatiotemporal chaos" - the chaotic dynamics of spatially extended systems showing patterns or coherent structures. Topics investigated here include methods of characterization, the role conservation laws and the control of spatiotmeporal chaos.
Methods used are a combination of the tools developed for equilibrium phase transitions, perturbation methods of Applied Mathematics, and large scale computations. A close regard of experimental work is a vital feature in this area where the strong nonlinearity of the theoretical description makes our intuition based on the study of linear systems unreliable. As the basic understanding of the phenomena becomes clearer from detailed experiments and theory on well controlled physical systems, the focus of the work is evolving to include the application to a diverse range of natural phenomena including plastic deformation in solids, the climate, and the modelling of chemical and biological phenomena.
Graduate student Malissa Midzor in the Nanofabrication lab.
Atomic imaging of superconductor NbSe2 taken at 4.2 K using a low-temperature scanning tunneling microscope in Prof. Yeh's group. The distance between consecutive atoms is 0.35 nm.
Graduate student William Weber.
