Quantum Materials: Where Many Paths Meet

NEWS & ANALYSIS MATERIALS NEWS Early promise Quantum materials: Arguably, it all began with superconductivity. It was recognized in the 1950s Where many paths meet that the ability of some materials to con- duct electricity without resistance is a By Philip Ball phenomenon that demands a quantum explanation. The theory put forward by ll matter, in the end, must be explained Aside from the matter of their intrinsic John Bardeen, Leon Cooper, and Robert A by quantum mechanics, which de- properties, however, what tends to unite Schrieffer (BCS) in 1957 invoked an scribes how atoms bind and electrons in- quantum materials is who is interested interaction between mobile conduction teract at a fundamental level. Typically, the in them. The community of researchers electrons, mediated by vibrations of the quantum behavior can be approximated that 20 years ago was grappling with crystal lattice that unites them into pairs, by a classical description, in which atoms high-temperature superconductivity is called Cooper pairs. These pairs can be become balls that stick together in well- likely today to be pondering topologi- considered as quasiparticles, which—in GH¿QHGDUUDQJHPHQWVYLDVLPSOHIRUFHV cal insulators and Weyl semimetals. A contrast to electrons themselves—be- and vibrate much like balls on springs. somewhat distinct community that used long to the fundamental class of particles Sometimes, however, that is not so. In to focus around the 1980s on the exotic called bosons, which have integer values some materials, the quantum aspects as- 2D phenomenon called the quantum Hall of quantum spin. sert themselves tenaciously, and the only HIIHFWLVQRZ¿QGLQJFRPPRQFDXVH$QG This makes all the difference. Particles way to fully understand how the material quantum materials draw inspiration from with half-integer spin (fermions), like behaves is to keep the quantum in view. a third direction too, apparently unlikely lone electrons, cannot occupy the same Such substances are now grouped togeth- at first flush: particle physics, within quantum state. However, bosons can, and er under the banner of TXDQWXPPDWHULDOV which some unusual types of fundamental so Cooper pairs can condense into a quan- The US Department of Energy (DOE) particles proposed around the mid-to-late tum state in which all the electrons can be describes quantum materials as “solids WKFHQWXU\DUHQRZ¿QGLQJDQDORJXHV described by a single quantum wave func- with exotic physical properties, arising in the quasiparticles of condensed matter. tion. In effect, they become a collective from the quantum mechanical proper- This is not a matter of leaping onboard entity, which is then immune to the dis- ties of their constituent electrons, that the latest fancy-titled bandwagon. Rather, turbing effects of electron scattering from KDYHJUHDWVFLHQWL¿FDQGRUWHFKQRORJL- LWLVDUHÀHFWLRQRIDFRPPRQH[SHULHQFH the crystal lattice—the source of energy cal potential.” It’s a diverse class of ma- in physics, whereby concepts developed dissipation and electrical resistance. But terials—so much so that some question to explore one phenomenon turn out to this collective state can only be sustained whether the designation is meaningful. It be a subset of more general principles. DWORZWHPSHUDWXUHVWRRPXFKWKHUPDO includes well-advertised materials such Quantum materials reveal that proper- noise, and the Cooper pairs are broken, as superconductors and graphene, along WLHVRQFHWKRXJKWWREHTXLUNVFRQ¿QHG and the material becomes a regular metal. with ones with less familiar names: top- WRH[RWLFFRQGLWLRQVDUHLQIDFWDVLJQL¿- Here, then, is a behavior dictated by ological insulators, Weyl semimetals, cant feature of the materials universe. quantum mechanical correlations be- quantum spin liquids, and spin ices. To turn those ideas into real materials, tween electrons: the trademark signature A collection of oddballs they may meanwhile, demands expertise from of many quantum materials. Yet BCS be, but quantum materials are both a RWKHU¿HOGVLQYROYLQJWKHVNLOOVRIV\Q- theory did not seem to work for the class treasure trove of interesting physics and thetic solid-state materials chemistry and of “high-temperature” superconductors a potential source of useful substances. crystal growth. This union of fundamental discovered by Georg Bednorz and K. And while the compositions and behav- physics and practical materials science is Alex Müller of IBM’s Zurich research iors of quantum materials cover a wide turning into one of the most vibrant areas laboratories in 1986, some of which spectrum, some common themes recur. of physical science today. Most of all, it proved to have superconducting transi- Many of them derive their properties from RIIHUVDSOD\JURXQGIRU¿QGLQJDQGH[- tion temperatures much higher than the reduced dimensionality, in particular from ploring new physics. But there could be boiling point of liquid nitrogen (77 K). FRQ¿QHPHQWRIHOHFWURQVWRWZRGLPHQ- SUDFWLFDOEHQH¿WVWRRQHZHOHFWURQLFGH- These materials are not metals but ceram- sional (2D) sheets. In many, magnetism vices, and, in particular, new possibilities ics: metal oxides with a characteristic lay- and electronic structure interact in curious for building quantum computers, which ered structure, of which the paradigmatic ways. In particular, they tend to be materi- would exploit the rules of quantum me- example was lanthanum copper oxides. als in which electrons cannot be consid- chanics to achieve computational power Despite several decades of work, ered as independent particles but act as far in excess of anything the classical there is still no fully satisfactory con- collective states dubbed quasiparticles. computers of today can attain. sensus view of how high-temperature Philip Ball, [email protected] 698 MRS BULLETIN VOLUME 42 OCTOBER 2017 www.mrs.org/bulletin NEWS & ANALYSIS MATERIALS NEWS superconductors work. “The complexity of the materials has made arriving at sim- SOHPRGHOVGLI¿FXOW´VD\VSK\VLFLVW'DYLG Ceperley of the University of Illinois at Urbana-Champaign. All the same, most researchers agree that the electron correlations that must surely lie at the root of the phenomenon are related to both the Ȁ layered, quasi-2D crystal structure of the Ȁ' materials and to their magnetic behavior. Meanwhile, another strand of exotic quantum properties was evolving in a dif- ferent arena. In 1980, Klaus von Klitzing showed that at low temperatures, the Hall effect—an effect known for a century, in which a voltage across an electrical FRQGXFWRULVFUHDWHGE\WKHLQÀXHQFHRI DPDJQHWLF¿HOGRQWKHHOHFWURQSDWKV² can become quantized. That’s to say, the conductance of a thin, quasi-2D conduc- tor may change in stepwise jumps as the Figure 1. The band structure of graphene. The valence (blue/green) and conduction (red/yellow) VWUHQJWKRIDWUDQVYHUVHPDJQHWLF¿HOG bands touch at points K and K' in momentum space. is increased: the quantum Hall effect (QHE). Qualitatively, this quantization is the result of electrons in the 2D material Kissing cones EHLQJFRQ¿QHGWRGLVFUHWHORRSLQJRUELWV The connections between high-tempera- Konstantin Novoselov of The University not unlike those postulated for simple ture superconductors, the QHE, and 2D of Manchester in the UK were awarded theories of the quantum atom, but much electron gases are, in retrospect, clear the 2010 Nobel Prize in Physics. larger in size. These electron states owe enough: in particular, the reduced dimen- From a chemist’s point of view, the their stability to the topological properties sionality, interaction of electronic and extended network of conjugated bonds in of the electronic band structure in the ma- magnetic or electron-spin properties, and the graphene sheet creates pathways for terial. They are in some ways analogous the importance of electron correlations and mobile electrons that give graphene its to the topological defects that may appear quasiparticle descriptions. electrical conductivity. To the solid-state in crystal structures, such as screw dislo- These aspects all come together in physicist, more used to describing elec- cations, which, like the whorled crown of the much-vaunted “wonder material” tronic structure in terms of band theory, hairs on your head, are irreducible con- graphene, which is also perhaps the most the picture is more complex. The pecu- sequences of shape. These structures are familiar and celebrated quantum material liarity of graphene is that it has the fully said to be “topologically protected.” today. These 2D sheets of pure carbon, ¿OOHGYDOHQFHEDQGDQGHPSW\FRQGXFWLRQ Von Klitzing won the 1985 Nobel Prize the atoms united into hexagonal rings band of a semiconductor, but with a band- in Physics for his work (it went to Bednorz long familiar from the mundane parent gap between these states that falls to zero and Müller in 1987), and, subsequently, material graphite, have been proposed— at a particular value of electron momen- more exotic variants of the QHE were some would say hyped—as a fabric for the WXP7KDWLVWKHGH¿QLQJFKDUDFWHULVWLFRI discovered. Robert B. Laughlin, Horst next generation of electronic circuitry and a semimetal. L. Störmer, and Daniel C. Tsui won the touchscreens. That graphene should be a gapless 1998 physics Nobel for showing that un- While the real value of graphene in semiconductor has been recognized since der certain conditions, electrons in a 2D that applied arena remains to be seen, LWVHOHFWURQLFEDQGVWUXFWXUHZDV¿UVWFDOFX- material that are free to move more or less few physicists would dispute that, as a lated in 1947—well before graphene

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