From SrTiO3 to Cuprates and Back to SrTiO3: A Way Along Alex Müller’s Scientific Career

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.

Ferroelectricity, Superconductivity, and SrTiO3—Passions of K.A. Müller

SrTiO3 is an insulating material which, using chemical doping, pressure, strain or isotope substitution, can be turned into a ferroelectric material or into a superconductor. The material itself, and the two aforementioned phenomena, have been subjects of intensive research of Karl Alex Müller and have been a source of inspiration, among other things, for his Nobel prize-winning research on high temperature superconductivity. An intriguing outstanding question is whether the occurrence of ferroelectricity and superconductivity in the same material is just a coincidence, or whether a deeper connection exists. In addition there is the empirical question of how these two phenomena interact with each other. Here we show that it is possible to induce superconductivity in a two-dimensional layer at the interface of SrTiO3 and LaAlO3 when we make the SrTiO3 ferroelectric by means of 18O substitution. Our experiments indicate that the ferroelectricity is perfectly compatible with having a superconducting two-dimensional electron system at the interface. This provides a promising avenue for manipulating superconductivity in a non centrosymmetric environment.

Unconventional Co-Existence of Insulating Nano-Regions and Conducting Filaments in Reduced SrTiO3: Mode Softening, Local Piezoelectricity, and Metallicity

Doped SrTiO3 becomes a metal at extremely low doping concentrations n and is even superconducting at n < 1020 cm−3, with the superconducting transition temperature adopting a dome-like shape with increasing carrier concentration. In this paper it is shown within the polarizability model and from first principles calculations that up to a well-defined carrier concentration nc transverse optic mode softening takes place together with polar nano-domain formation, which provides evidence of inhomogeneity and a two-component type behavior with metallicity coexisting with polarity. Beyond this region, a conventional metal is formed where superconductivity as well as mode softening is absent. For n ≤ nc the effective electron-phonon coupling follows the superconducting transition temperature. Effusion measurements, as well as macroscopic and nanoscopic conductivity measurements, indicate that the distribution of oxygen vacancies is local and inhomogeneous, from which it is concluded that metallicity stems from filaments which are embedded in a polar matrix as long as n ≤ nc.

Superconductivity in Compression-Shear Deformed Diamond

Diamond is a prototypical ultrawide band gap semiconductor, but turns into a superconductor with a critical temperature T_{c}≈4  K near 3% boron doping [E. A. Ekimov et al., Nature (London) 428, 542 (2004)NATUAS0028-083610.1038/nature02449]. Here we unveil a surprising new route to superconductivity in undoped diamond by compression-shear deformation that induces increasing metallization and lattice softening with rising strain, producing phonon mediated T_{c} up to 2.4-12.4 K for a wide range of Coulomb pseudopotential μ^{*}=0.15-0.05. This finding raises intriguing prospects of generating robust superconductivity in strained diamond crystal, showcasing a distinct and hitherto little explored approach to driving materials into superconducting states via strain engineering. These results hold promise for discovering superconductivity in normally nonsuperconductive materials, thereby expanding the landscape of viable nontraditional superconductors and offering actionable insights for experimental exploration.

Evolution of Electronic States and Emergence of Superconductivity in the Polar Semiconductor GeTe by Doping Valence-Skipping Indium

GeTe is a chemically simple IV-VI semiconductor which bears a rich plethora of different physical properties induced by doping and external stimuli. Here, we report a superconductor-semiconductor-superconductor transition controlled by finely-tuned In doping. Our results reveal the existence of a critical doping concentration x_{c}=0.12 in Ge_{1-x}In_{x}Te, where various properties, including structure, resistivity, charge carrier type, and the density of states, take either an extremum or change their character. At the same time, we find indications of a change in the In-valence state from In^{3+} to In^{1+} with increasing x by core-level photoemission spectroscopy, suggesting that this system is a new promising playground to probe valence fluctuations and their possible impact on structural, electronic, and thermodynamic properties of their host.

Evidence of Incoherent Carriers Associated with Resonant Impurity Levels and Their Influence on Superconductivity in the Anomalous Superconductor Pb_{1-x}Tl_{x}Te

We present a combined experimental and theoretical study of the evolution of the Fermi surface of the anomalous superconductor Pb_{1-x}Tl_{x}Te as a function of thallium concentration, drawing on a combination of magnetotransport measurements (Shubnikov-de Haas oscillations and the Hall coefficient), angle resolved photoemission spectroscopy, and density functional theory calculations of the electronic structure. Our results indicate that for Tl concentrations beyond a critical value, the Fermi energy coincides with resonant impurity states in Pb_{1-x}Tl_{x}Te, and we rule out the presence of an additional valence band maximum at the Fermi energy. A comparison to nonsuperconducting Pb_{1-x}Na_{x}Te implies that the presence of these impurity states at the Fermi energy provides the enhanced pairing interaction and thus also the anomalously high temperature superconductivity in this material.

Prospects and applications near ferroelectric quantum phase transitions: a key issues review

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T _c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

Topological Quantum Phase Transition and Superconductivity Induced by Pressure in the Bismuth Tellurohalide BiTeI

A pressure-induced topological quantum phase transition has been theoretically predicted for the semiconductor bismuth tellurohalide BiTeI with giant Rashba spin splitting. In this work, evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted topological quantum phase transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr, while resistivity at higher temperatures still exhibits semiconducting behavior. Theoretical calculations suggest that superconductivity may develop from the multivalley semiconductor phase. The superconducting transition temperature, T_c , increases with applied pressure and reaches a maximum value of 5.2 K at 23.5 GPa for BiTeI (4.8 K at 31.7 GPa for BiTeBr), followed by a slow decrease. The results demonstrate that BiTeX (X = I, Br) compounds with nontrivial topology of electronic states display new ground states upon compression.

Evidence for bulk superconductivity in pure bismuth single crystals at ambient pressure

At ambient pressure, bulk rhombohedral bismuth is a semimetal that remains in the normal state down to at least 10 millikelvin. Superconductivity in bulk bismuth is thought to be unlikely because of the extremely low carrier density. We observed bulk superconductivity in pure bismuth single crystals below 0.53 millikelvin at ambient pressure, with an estimated critical magnetic field of 5.2 microteslas at 0 kelvin. Superconductivity in bismuth cannot be explained by the conventional Bardeen-Cooper-Schrieffer theory because its adiabatic approximation does not hold true for bismuth. Future theoretical work will be needed to understand superconductivity in the nonadiabatic limit in systems with low carrier densities and unusual band structures, such as bismuth.

Isotope effect in superconducting n-doped SrTiO3

We report the influence on the superconducting critical temperature Tc in doped SrTiO3 of the substitution of the natural 16O atoms by the heavier isotope 18O. We observe that for a wide range of doping this substitution causes a strong (~50%) enhancement of Tc. Also the magnetic critical field Hc2 is increased by a factor ~2. Such a strong impact on Tc and Hc2, with a sign opposite to conventional superconductors, is unprecedented. The observed effect could be the consequence of strong coupling of the doped electrons to lattice vibrations (phonons), a notion which finds support in numerous optical and photo-emission studies. The unusually large size of the observed isotope effect supports a recent model for superconductivity in these materials based on strong coupling to the ferroelectric soft modes of SrTiO3.

Heat-Treatment-Induced Switching of Magnetic States in the Doped Polar Semiconductor Ge1-xMnxTe

Cross-control of a material property - manipulation of a physical quantity (e.g., magnetisation) by a nonconjugate field (e.g., electrical field) - is a challenge in fundamental science and also important for technological device applications. It has been demonstrated that magnetic properties can be controlled by electrical and optical stimuli in various magnets. Here we find that heat-treatment allows the control over two competing magnetic phases in the Mn-doped polar semiconductor GeTe. The onset temperatures Tc of ferromagnetism vary at low Mn concentrations by a factor of five to six with a maximum Tc ≈ 180 K, depending on the selected phase. Analyses in terms of synchrotron x-ray diffraction and energy dispersive x-ray spectroscopy indicate a possible segregation of the Mn ions, which is responsible for the high-Tc phase. More importantly, we demonstrate that the two states can be switched back and forth repeatedly from either phase by changing the heat-treatment of a sample, thereby confirming magnetic phase-change-memory functionality.

Phonon mechanism in the most dilute superconductor n-type SrTiO3

Superconductivity of n-doped SrTiO3, which remained enigmatic for half a century, is treated as a particular case of nonadiabatic phonon pairing. Motivated by experiment, we suggest the existence of the mobility edge at some dopant concentration. The itinerant part of the spectrum consists of three conduction bands filling by electrons successively. Each subband contributes to the superconducting instability and exhibits a gap in its energy spectrum at low temperatures. We argue that superconductivity of n-doped SrTiO3 results from the interaction of electrons with several longitudinal (LO) optical phonons with frequencies much larger than the Fermi energy. Immobile charges under the mobility edge threshold increase the "optical" dielectric constant far above that in clean SrTiO3 placing control on the electron-LO phonon interaction. TC initially grows as density of states at the Fermi surface increases with doping, but the accumulating charges reduce the electrons-polar-phonon interaction by screening the longitudinal electric fields. The theory predicts maxima in the TC-concentration dependence indeed observed experimentally. Having reached a maximum in the third band, the transition temperature finally decreases, rounding out the TC (n) dome, the three maxima with accompanying superconducting gaps emerging consecutively as electrons fill successive bands. This arises from attributes of the LO optical phonon pairing of electrons. The mechanism of LO phonons opens the path to increasing superconducting transition temperature in bulk transition-metal oxides and other polar crystals, and in charged 2D layers at the LaAaO3/SrTiO3 interfaces and on the SrTiO3 substrates.

Superconducting group-IV semiconductors

Despite the amount of experimental and theoretical work on doping-induced superconductivity in covalent semiconductors based on group IV elements over the past four years, many open questions and puzzling results remain to be clarified. The nature of the coupling (whether mediated by electronic correlation, phonons or both), the relationship between the doping concentration and the critical temperature (T(c)), which affects the prospects for higher transition temperatures, and the influence of disorder and dopant homogeneity are debated issues that will determine the future of the field. Here, we present recent achievements and predictions, with a focus on boron-doped diamond and silicon. We also suggest that innovative superconducting devices, combining specific properties of diamond or silicon with the maturity of semiconductor-based technologies, will soon be developed.

Superconductivity in heavily boron-doped silicon carbide

The discoveries of superconductivity in heavily boron-doped diamond in 2004 and silicon in 2006 have renewed the interest in the superconducting state of semiconductors. Charge-carrier doping of wide-gap semiconductors leads to a metallic phase from which upon further doping superconductivity can emerge. Recently, we discovered superconductivity in a closely related system: heavily boron-doped silicon carbide. The sample used for that study consisted of cubic and hexagonal SiC phase fractions and hence this led to the question which of them participated in the superconductivity. Here we studied a hexagonal SiC sample, free from cubic SiC phase by means of x-ray diffraction, resistivity, and ac susceptibility.

An insight into what superconducts in polycrystalline boron-doped diamonds based on investigations of microstructure

The discovery of superconductivity in polycrystalline boron-doped diamond (BDD) synthesized under high pressure and high temperatures [Ekimov, et al. (2004) Nature 428:542-545] has raised a number of questions on the origin of the superconducting state. It was suggested that the heavy boron doping of diamond eventually leads to superconductivity. To justify such statements more detailed information on the microstructure of the composite materials and on the exact boron content in the diamond grains is needed. For that we used high-resolution transmission electron microscopy and electron energy loss spectroscopy. For the studied superconducting BDD samples synthesized at high pressures and high temperatures the diamond grain sizes are approximately 1-2 mum with a boron content between 0.2 (2) and 0.5 (1) at %. The grains are separated by 10- to 20-nm-thick layers and triangular-shaped pockets of predominantly (at least 95 at %) amorphous boron. These results render superconductivity caused by the heavy boron doping in diamond highly unlikely.

Metal-to-insulator transition and superconductivity in boron-doped diamond

The experimental discovery of superconductivity in boron-doped diamond came as a major surprise to both the diamond and the superconducting materials communities. The main experimental results obtained since then on single-crystal diamond epilayers are reviewed and applied to calculations, and some open questions are identified. The critical doping of the metal-to-insulator transition (MIT) was found to coincide with that necessary for superconductivity to occur. Some of the critical exponents of the MIT were determined and superconducting diamond was found to follow a conventional type II behaviour in the dirty limit, with relatively high critical temperature values quite close to the doping-induced insulator-to-metal transition. This could indicate that on the metallic side both the electron-phonon coupling and the screening parameter depend on the boron concentration. In our view, doped diamond is a potential model system for the study of electronic phase transitions and a stimulating example for other semiconductors such as germanium and silicon.

Superconductivity in doped cubic silicon

Although the local resistivity of semiconducting silicon in its standard crystalline form can be changed by many orders of magnitude by doping with elements, superconductivity has so far never been achieved. Hybrid devices combining silicon's semiconducting properties and superconductivity have therefore remained largely underdeveloped. Here we report that superconductivity can be induced when boron is locally introduced into silicon at concentrations above its equilibrium solubility. For sufficiently high boron doping (typically 100 p.p.m.) silicon becomes metallic. We find that at a higher boron concentration of several per cent, achieved by gas immersion laser doping, silicon becomes superconducting. Electrical resistivity and magnetic susceptibility measurements show that boron-doped silicon (Si:B) made in this way is a superconductor below a transition temperature T(c) approximately 0.35 K, with a critical field of about 0.4 T. Ab initio calculations, corroborated by Raman measurements, strongly suggest that doping is substitutional. The calculated electron-phonon coupling strength is found to be consistent with a conventional phonon-mediated coupling mechanism. Our findings will facilitate the fabrication of new silicon-based superconducting nanostructures and mesoscopic devices with high-quality interfaces.

Intervalley gap anomaly of two-dimensional electrons in silicon

We report here a systematic study of the energy gaps at the odd-integer quantum Hall states nu = 3 and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley splitting is independent of the in-plane fields. However, the nu = 3 valley gap differs by about a factor of 3 (Deltav approximately 0.4 vs 1.2 K) on different sides of the coincidence. More surprisingly, instead of reducing to zero, the energy gaps at nu = 3 and 5 rise rapidly when approaching the coincidence angles. We believe that such an anomaly is related to strong couplings of the nearly degenerate Landau levels.

Superconductivity in diamond

Diamond is an electrical insulator well known for its exceptional hardness. It also conducts heat even more effectively than copper, and can withstand very high electric fields. With these physical properties, diamond is attractive for electronic applications, particularly when charge carriers are introduced (by chemical doping) into the system. Boron has one less electron than carbon and, because of its small atomic radius, boron is relatively easily incorporated into diamond; as boron acts as a charge acceptor, the resulting diamond is effectively hole-doped. Here we report the discovery of superconductivity in boron-doped diamond synthesized at high pressure (nearly 100,000 atmospheres) and temperature (2,500-2,800 K). Electrical resistivity, magnetic susceptibility, specific heat and field-dependent resistance measurements show that boron-doped diamond is a bulk, type-II superconductor below the superconducting transition temperature T(c) approximately 4 K; superconductivity survives in a magnetic field up to Hc2(0) > or = 3.5 T. The discovery of superconductivity in diamond-structured carbon suggests that Si and Ge, which also form in the diamond structure, may similarly exhibit superconductivity under the appropriate conditions.