The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_{4}$. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.
The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La1.92Sr0.08CuO4. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.
In the vicinity of continuous quantum phase transitions (QPTs), quantum systems become scale-invariant and can be grouped into universality classes characterized by sets of critical exponents. We have found that despite scale-invariance and universality, the experimental data still contain information related to the microscopic processes and scales governing QPTs. We have found that for many systems, the scaled data near QPTs can be approximated by the generic exponential dependence introduced in the scaling theory of localization; this dependence includes as a parameter a microscopic seeding scale of the renormalization group, L0. We have also conjectured that for interacting systems, the temperature cuts the renormalization group flow at the length travelled by a system-specific elementary excitation over the life-time set by the Planckian time, τP=ℏ/kBT. We have adapted this approach for QPTs in several systems and showed that L0 extracted from experiment is comparable to physically-expected minimal length scales, namely (i) the mean free path for metal-insulator transition in doped semiconductor Si:B, (ii) the distance between spins in Heisenberg and Ising chains, (iii) the period of an optical lattice for cold atom boson gases, and (iv) the period of a moiré superlattice for the Mott QPT in dichalcogenide bilayers. The metal-insulator transition in Si:P has been explained using a non-interacting version of the model. In two companion papers, we show that in superconducting systems, L0 is comparable to superconducting coherence length, and in quantum Hall systems, to the magnetic length. The developed new method of data analysis identifies microscopic processes leading to QPTs and quantitatively explains and unifies a large body of experimental data.
Over the past four decades, experimental studies of quantum phase transitions (QPTs) have been primarily focused on identifying these transitions in various materials and determining the critical exponents and universality classes associated with them. Since the critical exponents originate from the scale invariance, they are not explicitly tied to the microscopic physics of QPTs, which remains poorly understood for many systems. We have developed a model of QPTs, which addresses this deficiency. The model is based on the experimentally supported conjecture that the scaled data across a QPT depend, in a universal manner, on two system-specific length scales: the microscopic scale, L0, typically known from general considerations (e.g., mean-free path, lattice constant) and the dephasing length, ${L}_{\ensuremath{\varphi}}(T)$. Using this model, we have found that experimental data in the quantum critical regime of 18 distinct material classes can be quantitatively described by assuming that ${L}_{\ensuremath{\varphi}}(T)$ is determined by the distance traveled by system-specific excitations during the Planckian time, ${\ensuremath{\tau}}_{P}=\ensuremath{\hbar}/{k}_{B}T$. In this work, we demonstrate how the model explains microscopic physics of QPTs in doped semiconductors and amorphous alloys, materials with Ising and Heisenberg spin chains, cold boson gases in optical traps, and the Mott transitions in organic semiconductors. The dynamics of excitations is determined by parameters such as the effective mass and diffusion coefficient, D, of the corresponding noninteracting or weakly renormalized system. For doped semiconductors and amorphous alloys, the noncritical behavior of D in the quantum critical regime sharply contrasts with zero-temperature diffusion coefficient, which goes to zero at the transition. We also analyze the results of numerical studies of the Mott transition with dynamical mean-field theory, interpreting them as if they were experimental data. For these results, we find that, as expected, the microscopic scale matches the dimensionless lattice constant, ${L}_{0}\ensuremath{\sim}1$. Finally, we report that the metal-insulator transition in Si:P, Ge:Sb, and Ge:As can be explained using a noninteracting version of the model.
The main objective of this paper is to provide a systematic theoretical study on quantum phase transitions associated with the Bose-Einstein condensates, the superfluidity and the su-perconductivity. First, we indicate that there are only two types of phase transitions: dynamical phase transitions and topologi-cal phase transitions (TPTs). A TPT refers to the transition in its topological structure in the physical space of the system, and quantum phase transitions (QPTs) belong to the category of TPTs. Second, the basic physical characteristics of a QPT are precisely formulated. In particular, a QPT is a transition between quantum states, which are described by the wave functions ψ, and the control parameters are non-thermal. Third, we derive the topological structure equations for QPTs, so that the basic geometric theory of incompressible flows can be readily applied. In particular, a topo-logical index for the supercurrent can be defined, leading to precise information on the topological structure and its transitions in the physical space for the underlying system. Fourth, we derive then the basic theory for different TPTs, leading to transparent physical pictures of various condensates. Finally, we derive the microscopic mechanism for the Meissner effect of superconductivity: below the critical temperature, under the applied magnetic field, spin J = 1 Cooper pairs reversely parallel to the applied field can form and are stable, and the total magnetic moment of all Cooper pairs, together with the surface supercurrent, can cancel out the magnetism induced by the applied field and resists the applied field from entering its body.
Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition between quantum fluctuations and mutual interactions among constituents of the system, not by thermal fluctuations; hence they can occur even at zero temperature. Examples of quantum phase transitions in many-body physics may be found in systems ranging from high-temperature superconductors to topological insulators. A quantum phase transition usually can be characterized by nonanalyticity/discontinuity in certain order parameters or divergence of the ground state energy eigenvalue and/or its derivatives with respect to certain physical quantities. Here in a circular one-dimensional spin model with Heisenberg XY interaction and no magnetic field, we observe critical phenomena for the n0=1/N→0 Mott insulator caused by a qualitative change of the boundary condition. We demonstrate in the vicinity of the transition point a sudden change in ground-state properties accompanied by an avoided level-crossing between the ground and the first excited states. Notably, our result links conventional quantum phase transitions to microscopic boundary conditions, with significant implications for quantum information, quantum control, and quantum computing.
This study has a look at investigates quantum phase transitions (QPTs) in low-dimensional substances, focusing at the outcomes of disorder, electron interactions, and outside fields. Theoretical frameworks, which includes the Hubbard and Ising models, have been employed to analyze essential behaviors, at the same time as renormalization organization strategies furnished insights into scaling near quantum critical points. Experimental observations of conductivity below varying magnetic fields and ultra-low temperatures showed segment transitions between steel, insulating, and superconducting states. These findings were in addition verified via computational simulations using Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) methods, which correctly mapped phase diagrams and important temperatures. The effects underscore the transformative potential of QPTs in quantum technologies, in particular in the development of solid qubits and green nanoelectronics gadgets. Future research will awareness on refining theoretical fashions, enhancing experimental setups, and exploring new quantum levels to increase quantum and nano technology.