Griffiths phase in diluted magnetic semiconductors

We study the effects of disorder in the vicinity of the ferromagnetic transition in a diluted magnetic semiconductor in the strongly localized regime. We derive an effective polaron Hamiltonian, which leads to the Griffiths phase above the ferromagnetic transition point. The Griffiths-McCoy effects yield nonperturbative contributions to the dynamic susceptibility. We explicitly derive the long-time susceptibility, which has a pseudoscaling form, with the dynamic critical exponent being expressed through the percolation indices.     

Quantum information processing with large nuclear spins in GaAs semiconductors

We propose an implementation for quantum information processing based on coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We describe theoretically an NMR method which involves multiphoton transitions and which exploits the nonequidistance of nuclear spin levels due to quadrupolar splittings. Starting from known spin anisotropies we derive effective Hamiltonians in a generalized rotating frame, valid for arbitrary I, which allow us to describe the nonperturbative time evolution of spin states generated by magnetic rf fields. We identify an experimentally observable regime for multiphoton Rabi oscillations. In the nonlinear regime, we find Berry phase interference.     

Fluctuation conductivity of thin films and nanowires near a parallel-field-tuned superconducting quantum phase transition

We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to a normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive "Aslamazov-Larkin" contribution, the negative "density of states" contribution, and the "Maki-Thompson" interference contribution are all of the same order and the total correction is negative. Further, we show that, based on how the quantum critical point is approached, there are three regimes that show different temperature and field dependencies which should be experimentally accessible.     

Two mode photon bunching effect as witness of quantum criticality in circuit QED

We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an experimentally accessible physical implementation, a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line resonator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two magnetic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally independent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus, the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.     

Thermodynamic properties of the superconductivity in quasi-two-dimensional Dirac electronic systems

The thermodynamic properties of superconducting Dirac electronic systems is analyzed in the vicinity of quantum critical point. The system is characterized by a quantum critical point at zero doping, such that the critical temperature vanishes below some finite value of interaction strength. It is found that the specific heat jump of the system largely deviates from the conventional BCS theory value in the vicinity of quantum critical point. We investigated the region of applicability of the mean-field theory using the Ginzburg-Landau functional.     

Ferromagnetic quantum critical fluctuations in YbRh2(Si0.95Ge0.05)2

The bulk magnetic susceptibility chi(T,B) of YbRh(2)(Si(0.95)Ge(0.05))(2) has been investigated close to the field-induced quantum critical point at B(c) = 0.027 T. For B < or= 0.05 T a Curie-Weiss law with a negative Weiss temperature is observed at temperatures below 0.3 K. Outside this region, the susceptibility indicates ferromagnetic quantum critical fluctuations, chi(T) proportional, variantT-0.6 above 0.3 K. At low temperatures the Pauli susceptibility follows chi(0) proportional, variant(B-B(c))(-0.6) and scales with the coefficient of the T(2) term in the electrical resistivity. The Sommerfeld-Wilson ratio is highly enhanced and increases up to 30 close to the critical field.     

Critical phenomena and the quantum critical point of ferromagnetic Zr(1-x)NbxZn2

We present a study of the magnetic properties of Zr(1-x)NbxZn2, using an Arrott plot analysis of the magnetization. The Curie temperature Tc is suppressed to zero temperature for Nb concentration xc = 0.083+/-0.002, while the spontaneous moment vanishes linearly with Tc as predicted by the Stoner theory. The initial susceptibility chi displays critical behavior for x or= xc we find that chi(-1) = chi0(-1) + aT(4/3), where chi0(-1) vanishes as x-->xc. The resulting magnetic phase diagram shows that the quantum critical behavior extends over the widest range of temperatures for x=xc, and demonstrates how a finite transition temperature ferromagnet is transformed into a paramagnet, via a quantum critical point.     

Andreev tunneling in strongly interacting quantum dots

We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and nonlinear transport in the nonperturbative regime. New effects associated with the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the I–V characteristics depends on the relative size of the gap energy and the Kondo temperature.     

Direct observation of the scaling relation between density of states and pairing gap in a dirty superconductor

Theories and experiments on dirty superconductors are complex but important in terms of both theoretical fundamentals and practical applications. These activities are even more challenging when magnetic fields are present because the field distribution, electron density of states, and superconducting pairing potentials become nonuniform. Here, we present tunneling microspectroscopic experiments on Nb C single crystals and demonstrate that Nb C is a homogeneous dirty superconductor. When applying magnetic fields to the samples, we found that the zero-energy local density of states and the pairing energy gap followed the explicit scaling relation proposed by de Gennes for homogeneous dirty superconductors in high magnetic fields. More significantly, our experimental findings indicate that the validity of the scaling relation extends to magnetic field strengths far below the upper critical field, calling for a new nonperturbative understanding of this fundamental property in dirty superconductors. On the practical side, we used the observed scaling relation to derive a simple and straightforward experimental scheme for estimating the superconducting coherence length of a dirty superconductor in magnetic fields.     

Reentrant Orbital Effect against Superconductivity in the Quasi-Two-Dimensional Superconductor NbS2

JETP Letters - We derive an integral equation for the superconducting gap, which takes into account the quantum nature of electron motion in a parallel magnetic field in a quasi-two-dimensional...     

Fundamental Critical Relations

We consider systems which exhibit typical critical dependence of the specific heat: <artwork name="GPHT31001ei1">) where γ, γ ′ are critical exponents (γ = α for <artwork name="GPHT31001ei2"> for <artwork name="GPHT31001ei3">), as well as, the case when <artwork name="GPHT31001ei4">, uniaxial ferroelectrics; a = 1, liquid He⁴). Starting from the critical behaviour of the specific heat we can exactly find the asymptotic form of the Gibbs (Helmholtz) potential in the vicinity of the critical point for each case separately. We derive in this way many exact critical relations in the limit T → T_C which remain the same for each particular case. They define a new class of universal critical relations independent from the underlying microscopic mechanism and the symmetry of these systems. It, however, means that they are independent from the critical indices, characterizing each particular material. The derived relations are valid for magnetic, ferroelectric and superconducting materials, as well as, for liquid He⁴ and they have very important consequences concerning the mutual relations between critical amplitudes of many thermodynamical quantities near the critical point and therefore can be important and interesting from the experimental and technological point of view.     

Possible Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in CeCoIn5

We report specific heat measurements of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical field H(c2), with magnetic fields in the [110], [100], and [001] directions, and at temperatures down to 50 mK. The superconducting phase transition changes from second to first order for fields above 10 T for H parallel [110] and H parallel [100]. In the same range of magnetic fields, we observe a second specific heat anomaly within the superconducting state. We interpret this anomaly as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. We obtain similar results for H parallel [001], with the FFLO state occupying a smaller part of the phase diagram.     

Nonperturbative expansion in QCD

The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β-function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.     

Fermi problem with artificial atoms in circuit QED

We propose a feasible experimental test of a 1D version of the Fermi problem using superconducting qubits. We give an explicit nonperturbative proof of strict causality in this model, showing that the probability of excitation of a two-level artificial atom with a dipolar coupling to a quantum field is completely independent of the other qubit until signals from it may arrive. We explain why this is in perfect agreement with the existence of nonlocal correlations and previous results which were used to claim apparent causality problems for Fermi's two-atom system.     

Spin decoherence in superconducting atom chips

Using a consistent quantum-mechanical treatment for the electromagnetic radiation, we theoretically investigate the magnetic spin-flip scatterings of a neutral two-level atom trapped in the vicinity of a superconducting body. We derive a simple scaling law for the corresponding spin-flip lifetime for such an atom trapped near a superconducting thick slab. For temperatures below the superconducting transition temperature Tc, the lifetime is found to be enhanced by several orders of magnitude in comparison to the case of a normal conducting slab. At zero temperature the spin-flip lifetime is given by the unbounded free-space value.     

Quantum critical scaling in graphene

We show that the emergent relativistic symmetry of electrons in graphene near its quantum critical point (QCP) implies a crucial importance of the Coulomb interaction. We derive scaling laws, valid near the QCP, that dictate the nontrivial magnetic and charge response of interacting graphene. Our analysis yields numerous predictions for how the Coulomb interaction will be manifested in experimental observables such as the diamagnetic response and electronic compressibility.     

Avoided antiferromagnetic order and quantum critical point in CeCoIn5

We measured the specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field H(c2)=5 T and 9 T, with the field in the [001] direction, and at temperatures down to 50 mK. At 5 T the data show a non-Fermi liquid (NFL) behavior down to the lowest temperatures. At the field above 8 T the data exhibit a crossover from the Fermi liquid to a non-Fermi liquid behavior. We analyzed the scaling properties of the specific heat and compared both the resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is due to incipient antiferromagnetism (AFM) in CeCoIn5 with the quantum critical point in the vicinity of H(c2). Below H(c2) the AFM phase which competes with the paramagnetic ground state is superseded by the superconducting transition.     

Superconducting quantum interference devices made of Sb-doped Bi2Se3 topological insulator nanoribbons

We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi₂Se₃ topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a magnetic field perpendicular to the SQUID loop, revealing that the periodicity corresponds to the superconducting flux quantum. Our experimental observations can be useful to explore Majorana bound states (MBS) in TI NR, promising for developing topological quantum information devices.     

Anisotropy-induced quantum critical behavior of magnetite nanoparticles at low temperatures

The classical, thermally driven transition from ferrimagnets to superparamagnets in Fe₃O₄ nanoparticles can be converted into another quantum phase by a transverse microwave magnetic field or by a strong internal anisotropic field. These fields, perpendicular to the Ising axis, can destroy the magnetic long-range order to quantum paramagnets as the fields exceed some critical values. We have exploited the spin resonance spectrometer to determine the dynamic spin susceptibility and the critical exponent γ, which is a power-law dependent spanning of the quantum critical point. Quantum phase transition observed at low temperatures for small magnetite nanoparticles induced by strong surface anisotropic field illustrates the fascinating interplay between thermal and quantum fluctuations in the vicinity of a quantum critical point.     

Activated scaling of classical and quantum spin glasses

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a "critical rounding," chi(1) proportional to chi(3) proportional to [T ln(t/tau(0)')/K](gamma/b phi) exp - [Tt(g)(phi b)ln(t/tau(0)'/K)](nu/b) (T=temperature, t=time, K=barrier constant, t(g) = 1 - T(SG)/T, and T(SG) = transition temperature; gamma>0 for chi(3) and <0 for chi(1)). This model, also valid in the presence of resonant tunneling states at energies K(0) < K [provided that K is replaced by K(0)+2T ln (1/Gamma(0)), where Gamma(0)(2) proportional, variant tunnel splitting of a spin S=1], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system LiHo(x)Y(1-x) seems to follow this model.