What Is Condensed Matter Physics

The Joy Of Condensed Matter Physics

A person presents a MagFly superconductor skate during the Science Festival on October 12, 2011 in… Paris, a ‘floating’ universal magnet system by German B.T. Innovation Company that allows a hundred-kilo person to levitate.

Why is condensed matter physics interesting? originally appeared on Quora – the knowledge sharing network where compelling questions are answered by people with unique insights.

Answer by Inna Vishik, Assistant Professor of Physics at UC Davis, on Quora:

I am drawn to condensed matter physics because it is simultaneously useful and fundamental, simultaneously mundane and fantastical, simultaneously large and small, and most of all, some of the phenomena that are observed in condensed matter systems are just flipping cool.

First, a definition of condensed matter. This field studies many-atom systems that are condensed but not too condensed . Condensed matter physics in its broadest definition encompasses many different subfields . For this piece, I will focus on solid-state physics with which I am most familiar.

With that disclaimer out of the way, back to our scheduled programming

A big thank you to Prof. Alexander F. Kemper, Dr. George Burkhard, and Noah Raman for helpful suggestions, improvements, and discussion on this piece.

Footnotes

Biomaterials And Soft Matter

Theoretical approaches include large scale molecular dynamics simulations, Monte Carlo simulations, parallel tempering and free energy methods, making use of the High-Performance Computing facilities at ACEnet and other Canadian computing consortia. Experimental techniques used at Memorial include NMR spectroscopy, laser scanning confocal microscopy, Raman microscopy, atomic force microscopy, electrochemistry, as well as chemical synthesis/purification techniques.

Faculty: Mike Morrow, Kris Poduska , Ivan Saika-Voivod, Stefan Wallin, John Whitehead, Anand Yethiraj. Other departments: Valerie Booth, Kaushik Nag

Discrete Spectra And Gap In Quantum Mechanics

Let me first remind that discretenes of energy levels plays a very important role in quantum mechanics, e.g., it explains the spectral lines of atoms, photoelectric effect, etc. When we are dealing with systems of many particles, their energy levels often merge in a band, but the discreteness of the spectrum still shows itself in the form of a gap. Alternatively, in some systems that are not characterized by a discrete spectrum, such as atomic liquids, a gap may appear as a result of interactions.

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What Is Theoretical Condensed Matter Physics And Why Is It Interesting

Condensed Matter Physics is the study of the structure and behaviour of the matter that makes up most of the usual stuff that surrounds us every day. It is not the study of the very small or of the very large but of the things in between. It takes for granted that most of these are made up of electrons and nuclei interacting according to the well-established laws of electromagnetism and quantum mechanics, and tries to explain their properties.

What makes it an interesting and fundamental branch of physics? It turns out that large assemblies of electrons and nuclei in a condensed state often exhibit so-called cooperative behaviour which is quite different from that of the individual parts. Superconductivity, for example. And the study of this new behaviour requires theoretical methods which can be every bit as sophisticated as those of particle theory or relativity. In fact, mathematically they often have a lot in common. But while there is only one `theory of everything’ which describes the building blocks of matter, at intermediate scales there are any number of `effective’ theories which account for the wealth of phenomena which we observe. Thus the subject is very diverse.

In condensed matter physics, experiment and observation play a key role. As compared with particle physics, most experiments are much easier to carry out, generally much more precise, and take far less time. So the link between experiment and theory is that much stronger.

Topological States Of Matter Group

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What Are We Doing In Condensed Matter Physics At Illinois

The University of Illinois maintains a distinguished tradition of focusing on the collective properties of matter and the emergence of novel and unusual states of matter, such as superconductivity and superfluidity.

Research in these areas has been recognized by numerous major awards, including Nobel Prizes to John Bardeen and Anthony Leggett. However, the university is also distinguished by its strong contributions to the development of technology emanating from condensed matter physics, especially in the area of semiconductor physics.

Today, the condensed matter group is the largest focus area in the department, with vibrant programs in both theory and experimental work. Every area of modern-day condensed matter physics is represented at Illinois, together with numerous cross-disciplinary programs in atomic, molecular and optical physics, materials science, and even biology.

A research group, the Institute for Condensed Matter Theory , was to establish a highly interactive research environment that encourages members to take on the most challenging, long-term research issues.

Iiiapplications Of Molecular Beam Epitaxy To Semiconductors

The first materials to be grown with the molecular beam epitaxy technique were the IIIV semiconductors, and device technology was the primary driving force behind its development. GaAs was of particular interest and remains a major use for MBE. In the Si industry, techniques exist to fabricate layered structures without resort to UHV, such as chemical vapor deposition . CVD reactors employ relatively high gas pressures and involve much shorter growth times, with the result that minimum contamination is introduced into the material.

GaAs, on the other hand, relies heavily on MBE. In order to grow high-quality IIIV materials, a relatively high flux of the group V elements is required since the sticking coefficients are much lower. The group III element is then directed onto the substrate in a molecular beam and the substrate temperature is critically adjusted to ensure correct stoichiometry by group V element incorporation. This method has been optimized over a number of years and is now commonly used for all IIIV and IIVI compounds.

FIGURE 6. A diagram showing the relationship between the lattice spacing and band gap of group IIIV and IV semiconductors.

Cliff Hooker, in, 2011

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What Is Meant In Condensed Matter Physics By A Gap And Why Is It So Important

I come from a HEP background and moved to condensed matter physics. I keep seeing the word gap being thrown around a lot: this system has a gap, this is a gapless system, the spectrum is gapped, energy gap, band gap etc.

They seem to be closely related to each other, quoting Wikipedia:

In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes.

whereas

In many-body physics, most commonly within condensed-matter physics, a gapped Hamiltonian is a Hamiltonian for an infinitely large many-body system where there is a finite energy gap separating the ground space from the first excited states. A Hamiltonian that is not gapped is called gapless.

and so on. Furthermore, what is the physical significance of all these gaps?

• 1$\begingroup$Quick analogy: to produce a electron-positron pair you need to provide energy above the rest energy of the electron. To produce an conduction electron in a semiconductor you need to provide enough energy to create an electron-hole pair.$\endgroup$

Research And Adjunct Faculty

Jifeng Liu, Assistant Professor focuses on the design of optoelectronic materials and devices for both solar cells and energy-efficient information technologies.

Francesco Ticozzi, Adjoint Visiting Assistant Professor focuses on quantum control theory, information encoding and communication in quantum systems, and information-theoretic approaches to control systems.

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Cosmology And General Relativity

• Problem of time: In quantum mechanics time is a classical background parameter and the flow of time is universal and absolute. In general relativity time is one component of four-dimensional spacetime, and the flow of time changes depending on the curvature of spacetime and the spacetime trajectory of the observer. How can these two concepts of time be reconciled?
• Cosmic inflation: Is the theory of cosmic inflation in the very early universe correct, and, if so, what are the details of this epoch? What is the hypothetical inflatonscalar field that gave rise to this cosmic inflation? If inflation happened at one point, is it self-sustaining through inflation of quantum-mechanical fluctuations, and thus ongoing in some extremely distant place?
• Horizon problem: Why is the distant universe so homogeneous when the Big Bang theory seems to predict larger measurable anisotropies of the night sky than those observed? Cosmological inflation is generally accepted as the solution, but are other possible explanations such as a variable speed of light more appropriate?
• Cosmological constant problem: Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

Solar Fullerenes And Carbon Nanotubes

Fullerenes and carbon nanotubes have become a major field in condensed matter physics and chemistry. However, the large-scale production of these materials with high yield and selectivity is still a crucial problem. Conventional methods for the synthesis of fullerenes, such as electric arc discharge and laser ablation, fail when the process is being scaled up to higher power levels. The solar vaporization process seems to be more promising using the solar reactor shown in Fig. 17, in which a graphite rod contained under vacuum pressure behind a hemispherical quartz window is directly irradiated with peak solar concentration ratios exceeding 7000 suns and the vaporized carbon is swept out by Ar, quenched, and collected in a filter bag. The key parameters characterizing this process are the carbon soot mass flow rate and the desired product yield. The former is a function of the target temperature, whereas the latter is a function of specific reactor variables such as fluid flow patterns, residence times, concentration of the carbon vapor in the carrier gas, target temperature, and temperature distribution in the cooling zone.

Figure 17. Scheme of a solar reactor for fullerene synthesis. Source: Institut de Science et de Génie des Matériaux et Prodédés, Centre National de la Recherche Scientifique, Font-Romeu, France.

Figure 18. Scheme of a solar reactor for CFC production. Source: Paul Scherrer Institute, Villigen, Switzerland.

Sajeev John, … Kurt Busch, in, 2003

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List Of Unsolved Problems In Physics

The following is a list of notable unsolved problems grouped into broad areas of physics.

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

There are still some questions beyond the Standard Model of physics, such as the strong CP problem, neutrino mass, matterantimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itselfthe Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions .

Advent Of Quantum Mechanics

Drude’s classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the FermiDirac statistics. Using this idea, he developed the theory of paramagnetism in 1926. Shortly after, Sommerfeld incorporated the FermiDirac statistics into the free electron model and made it better to explain the heat capacity. Two years later, Bloch used quantum mechanics to describe the motion of an electron in a periodic lattice.:366368 The mathematics of crystal structures developed by , Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935.Band structure calculations was first used in 1930 to predict the properties of new materials, and in 1947 John Bardeen, Walter Brattain and William Shockley developed the first semiconductor-based transistor, heralding a revolution in electronics.

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Soft Materials Research Center

Research is directed toward understanding and using the properties of condensed phases, ranging from experiments on the fundamental physics of phase transitions and chirality in liquid crystals, to the importance of liquid crystal ordering in the self-assembly of DNA and its role in the evolution of life in a pre-biotic earth, to the development of liquid crystal electro-optic light valves.

History Of Condensed Matter Physics

Heike Kamerlingh OnnesJohannes van der Waalsheliumliquefactor

One of the first studies of condensed states of matter was by EnglishchemistHumphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity. This indicated that the atoms in John Dalton‘s atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as nitrogen and hydrogen could be liquefied under the right conditions and would then behave as metals.

In 1823, Michael Faraday, then an assistant in Davy’s lab, successfully liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and oxygen. Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases, and Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.:3538 By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively.

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Gapped And Gapless Systems

From the point of view of the theory of critical phenomena, the presence/absence of the gap characterizes different phases of a system. Thus, semiconductors/insulators differ from metals by the fact that in the former the lowest energy excitations are gapped, while in the latter the excitations are gapless. This creates a huge difference between these types of materials . Why some systems are insulators while others conductors is known as metal-insulator transition . Similarly, appearance of a gap often characterizes other phenomena, such as the emergence of superconductivity.

ExampleAn example was discussed in the comments which nicely illustrates the different meanings of a gap. Let us consider a model of multi-level sites coupled via tunneling:$$H=\sum_\alpha\left$$Diagonalizing this Hamiltonian will give us something like$$\bar=\sum_\epsilon_\alpha \bar_,\bar_=\bar_^\dagger \bar_,\\\epsilon_=h_\alpha+2\lambda_\alpha\cos$$We see that every level has transformed into a band of width $\lambda\alpha$, centered at the original level energy $\h_\alpha$.

Band overlap: gap in the density-of-statesDepending on the values of $h\alpha$ and $\lambda_\alpha$ the bands may or may not overlap, even though the original levels were non-degenerate. Thus, if we calculate the density-of-states, it may or may not have regions where it is zero, which will affect many properties of the material, such as optical absorption, electric conductance, etc.

Crudely speaking…

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The Conformational Free Energy

Consider a solution of very long ideal polymer chains concentration of repeat units c,cb3 1. The ideal-gas translational free energy of long chains is negligible hence the free energy of the homogeneous solution does not depend on concentration and can be set equal to zero. Let us find the free energy F of the system in an inhomogeneous state with concentration profile c such a state may correspond to an equilibrium in the presence of an external potential field due to solid particles or confining surfaces.

It is convenient to consider the simplest Gaussian chain model: point-like beads connected by elastic springs , Figure 12. To calculate the free energy F

Jeremy J. Ramsden, in, 2011