Ginzburg-Landau Formalism Research Articles

Entropy-induced phase transitions in a hidden Potts model.

A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. We explore the q-state Potts model with extra r hidden states using the Ginzburg-Landau formalism in the mean-field limit. We analytically demonstrate that when 1<q≤2, the model exhibits a rich phase diagram comprising a variety of phase transitions such as continuous, discontinuous, two types of successive, and hybrid transitions; moreover, several characteristics such as critical point, critical endpoint, and tricritical point are identified. The critical line and critical endline merge in a singular form at the tricritical point. That supercritical behavior emerging at the tricritical point is, to the best our knowledge, novel. We microscopically investigate the origin of the discontinuous transition; it is induced by the competition between the interaction and entropy of the system in the Ising limit, whereas by the bistability of the hidden spin states in the percolation limit. Finally, we discuss the similarity and difference of the phase diagram generated in two types of Ising spins model.

Gravitational effects in a superconducting film struck by a laser pulse

We study the local interaction of the gravitational field with a superfluid condensate. To this end, we exploit the Ginzburg–Landau formalism with generalized Maxwell fields. The analysis shows that a slight local alteration of the gravitational field in a thin superconducting film can be achieved by laser pulses with particular characteristics.

Extended Ginzburg-Landau theory of superconductivity from generalized momentum operator and position-dependent mass

The concept of generalized momentum operator which is motivated from the generalized uncertainty principle has been extensively investigated in quantum mechanics and various aspects of theoretical and applied physics. In this study, we have applied this formalism to Ginzburg-Landau theory of superconductvity and Abrikosov vortex lattice in type II-superconductors. After deriving the extended Ginzburg-Landau equations, we have discussed several independent structures of the auxiliary function of position operator in the generalized momentum operator and we have analyzed their features in both Ginzburg-Landau and London theories. Comparable properties to the basic formalism have been obtained even without the presence of the cubic nonlinear term in Ginzburg-Landau equations. However, not all structures of the auxiliary function of position operator result on the exclusion of the magnetic field from a superconductor when it's below its critical temperature. But, only specific forms may succeed to eliminate the magnetic field. This approach has been generalized by considered a position-dependent mass of the electric charge. Amazingly, for a position-dependent mass of hyperbolic soliton-like structure, the extended Ginzburg-Landau wave function is identical to the result obtained in the conventional formalism and besides, for specific correlations between the auxiliary function of the position operator and position-dependent mass, the exclusion of the magnetic field is conceivable. We have also discussed the Abrikosov vortex lattice solution based on the extended Ginzburg-Landau formalism with position-dependent mass of the electric charge. It was observed that, for a specific structure of the position-dependent mass and for a quantum number n=0, a transition between a type-II and type-I superconductor takes place if the Ginzburg-Landau parameter is κ=121+257≈2.0634. For large n, the problem depends on the asymptotic form of the Hermite polynomial and periodicity occurs if the electric charge is quantized. Further details are obtained and analyzed.

Multiple-q current states in a multicomponent superconducting channel

It is well-established that multicomponent superconductors can host different nonstandard phenomena such as broken-time reversal symmetry (BTRS) states, exotic Fulde–Ferrell–Larkin–Ovchinnikov phases, the fractional Josephson effect as well as plenty of topological defects like phase solitons, domain walls and unusual vortex structures. We show that in the case of a two-component superconducting quasi-one-dimensional channel this catalogue can be extended by a novel inhomogeneous current state, which we have termed as a multiple-q state, characterized by the coexistence of two different interpenetrating Cooper pair condensates with different total momenta. Within the Ginzburg–Landau formalism for a dirty two-band superconductor with sizable impurity scattering treated in the Born-approximation we reveal that under certain conditions, the occurrence of multiple-q states can induce a cascade of transitions involving switching between them and the homogeneous BTRS (non-BTRS) states and vice versa leading this way to a complex interplay of homogeneous and inhomogeneous current states. We find that hallmarks of such a multiple-q state within a thin wire or channel can be a saw-like dependence of the depairing current and the existence of two distinct stable branches on it (a bistable current state).

Boundary Effect and Critical Temperature of Two-Band Superconducting FeSe Films

Based on two-band Bogoliubov–de Gennes theory, we study the boundary effect of an interface between a two-gap superconductor FeSe and insulator (or vacuum). New boundary terms are introduced into two-band Ginzburg–Landau formalism, which modifies the boundary conditions for the corresponding order parameters of superconductor. The theory allows for a mean-field calculation of the critical temperature suppression with the decrease in FeSe film thickness. Our numerical results are in good agreement with the experimental data observed in this material.

Driven responses of periodically patterned superconducting films

We simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density ${J}_{\mathrm{c}}$, the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field $E(t)$ with a defect ``hopping'' frequency ${f}_{0}$, which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

Response of a θSOT sensor to the magnetic field's in-plane and out-of-plane components

Nano-sized three-junctions superconducting quantum interference device (θSOT) demonstrates tunable sensitivity to the multi-directional magnetic fields for its 3D unique structure. We report the magnetic properties of this device using the state-of-the-art 3D simulations within the Ginzburg–Landau formalism. The stability range of the Meissner state, in other words, the vortex nucleation point of the device for two fluxes (in the left and right loop), is studied in detail. Static properties such as the distribution of Cooper pairs and screening current density of θSOT device are observed. Response of the θSOT sensor to the magnetic field’s in-plane and out-of-plane components is investigated.

Effect of chemical disorder on Griffiths phase in weak itinerant ferromagnetic Ni92−xCuxCr8 alloy

We report magnetic and thermal properties of Cu substituted Ni92−xCuxCr8 polycrystalline alloys close to their critical concentration (xc~18%), where ferromagnetic order disappears. From the detailed analysis of field and temperature dependent magnetization data weak itinerant ferromagnetic character has been identified for the compositions below xc. Spin-fluctuations theory using the Ginzburg–Landau formalism further revealed the contributions of spin fluctuations, which increase near xc. Specific heat data shows unusual low-temperature variation with an enhanced Sommerfeld coefficient and non Fermi-liquid behavior due to strong magnetic fluctuations near xc. The magnetization data and the linear term of the specific heat follow the theoretical predictions of a ferromagnetic quantum critical point within the experimental uncertainties. The exponent of the power-law M(H) ∝Hλ fits to low-temperature magnetic isotherms and its variation with composition indeed suggests a possibility of quantum Griffiths phase in these alloy compositions. Finally, this study shows that the Cu substituted Ni-Cr system shows Griffiths phase at critical point even after the reduction of disorder.

Intricate interplay between superconductivity and topological surface states of c axis oriented MoTe2

The interaction between superconductivity and spin-polarized surface states of topological materials provides an exciting platform for the research and development of proximity induced coupling effects, Majorana fermions, spin valves, spintronics, etc. and so on. In this work, the inverse proximity effect observed exactly at the super conducting transition temperature of indium (3.5 K) demonstrates the complex interplay between robust 2D spin-polarized surface states observed in our (002n) oriented MoTe2 nanolayer sheets with that of superconducting states. Interestingly, our phenomenological model based on the Werthamer-Helfand-Hohenberg (WHH) model and Ginzburg–Landau formalism, invoked to validate the experimental observations, indicates a competition between superconductivity and topological order, marked by a close correspondence between the temperature of crossover (Tcr = 2.45 K) of their respective length scales, ξ and Lφ, and the saturation temperature in resistivity.

Sensitivity of SQUID-on-tip (SOT) to a magnetic nano-particle

Within the state-of-the-art 3D Ginzburg–Landau (GL) formalism, we investigate the static features of the most sensitive SQUID-on-tip (SOT) device placed on the top of a nano-particle. The SOT sensor’s free energy, Cooper pair density, and screening current density in the loop are investigated for the nano-particle’s various placements and sizes. The dynamic aspects of the device, such as its voltage–current characteristics, are evaluated in the presence of transport current using the two-dimensional (2D) time-dependent GL formalism. The sensitivity of the SOT is examined using quantum oscillations of the device’s depairing current as a function of the nano-particle’s size and location. The location of the nano-particle at the device’s center and closer to the device’s loop is required for optimal SOT sensitivity.

Static properties of superconducting pyramidal STM tip in the presence of a vortex

Stationary properties of a superconducting STM tip are studied in the presence of a vortex by applying three-dimensional Ginzburg-Landau formalism. The free energy of the tip is studied in detail to analyze different vortex states. Cooper pairs and corresponding screening current density are studied in the different positions of the tip. Obtained results are important to comprehend the static phenomenon of the STM tip in real-life applications.

Pauli paramagnetism of triplet Cooper pairs in a nematic superconductor

We investigate the response of a doped topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ with spin-triplet nematic superconductivity to external magnetization. We calculate the Zeeman part of the magnetic susceptibility for nematic and chiral superconducting phases near ${T}_{c}$ in the Ginzburg-Landau formalism. The superconducting order parameter from the ${E}_{u}$ representation has nontrivial coupling with the transversal Zeeman field that results in a paramagnetic response to magnetization. The topology of a Fermi surface has a strong influence on magnetic susceptibility. The Lifshitz transition from a closed to open Fermi surface eventually leads to a phase transition from the nematic to chiral phase. At the transition point, magnetic susceptibility diverges. Also, we study the effects of the electron-electron interaction on the competition between nematic and chiral phases. We find that in a real system, electron-electron interaction can drive the nematic to chiral phase only in the vicinity of the phase transition. We compare our results with the existing experimental data.

Molecular response for nematic superconducting media in a hollow cylinder: a numerical approach

In the context of the Ginzburg–Landau formalism proposed by Barci et al. in 2016 for nematic superconductivity, and by performing a numerical treatment based on the shooting method, we analyze the behaviour of the radial distribution of the nematic order parameter when the superconducting order parameter reaches the typical non-trivial saddle point. We consider the cases of a hollow cylindrical domain, with a disk or an annular domain as its cross section, whether the order parameter is subjected to Neumann or Dirichlet boundary conditions. We conclude that depending on the corresponding situation a non trivial solution holds if certain relations between the radii are satisfied. Moreover, we observe a saturation effect on each instance that constitutes a purely geometrical consequence on the relation between the typical sizes and shapes of the samples. These conclusions can be useful for further experimental realizations and extensions to the interaction of the nematic (superconducting) order parameters with electromagnetic fields.

Analysis of Charge Order in the Kagome Metal AV_{3}Sb_{5} (A=K,Rb,Cs).

Motivated by the recent discovery of unconventional charge order, we develop a theory of electronically mediated charge density wave formation in the family of kagome metals AV_{3}Sb_{5} (A=K,Rb,Cs). The intertwining of van Hove filling and sublattice interference suggests a three-fold charge density wave instability at T_{CDW}. From there, the charge order forming below T_{CDW} can unfold into a variety of phases capable of exhibiting orbital currents and nematicity. We develop a Ginzburg Landau formalism to stake out the parameter space of kagome charge order. We find a nematic chiral charge order to be energetically preferred, which shows tentative agreement with experimental evidence.

Phase diagram of vortices in the polar phase of spin-1 Bose-Einstein condensates

The phase diagram of lowest-energy vortices in the polar phase of spin-1 Bose-Einstein condensates is investigated theoretically. Singly quantized vortices are categorized by the local ordered state in the vortex core and three types of vortices are found as lowest-energy vortices, which are elliptic AF-core vortices, axisymmetric F-core vortices, and N-core vortices. These vortices are named after the local ordered state, ferromagnetic (F), antiferromagnetic (AF), broken-axisymmetry (BA), and normal (N) states apart from the bulk polar (P) state. The N-core vortex is a conventional vortex, in the core of which the superfluid order parameter vanishes. The other two types of vortices are stabilized when the quadratic Zeeman energy is smaller than a critical value. The axisymmetric F-core vortex is the lowest-energy vortex for ferromagnetic interaction, and it has an F core surrounded by a BA skin that forms a ferromagnetic-spin texture, as exemplified by the localized Mermin-Ho texture. The elliptic AF-core vortex is stabilized for antiferromagnetic interaction; the vortex core has both nematic-spin and ferromagnetic orders locally and is composed of the AF-core soliton spanned between two BA edges. The phase transition from the N-core vortex to the other two vortices is continuous, whereas that between the AF-core and F-core vortices is discontinuous. The critical point of the continuous vortex-core transition is computed by the perturbation analysis of the Bogoliubov theory and the Ginzburg-Landau formalism describes the critical behavior. The influence of trapping potential on the core structure is also investigated.

Shear modulus anomaly of unconventional superconductors in a symmetry breaking field

Using Ginzburg-Landau formalism, we theoretically study the isothermal shear modulus anomaly of an unconventional superconductor with a two-component order parameter, where the superconducting transition is split by a symmetry-breaking field. Experimental signatures are proposed for both chiral and nematic superconductors. Particularly striking is the vanishing of ${C}_{66}$ across the lower transition to a nematic superconducting state. Our findings can guide future experiments and shed new light on materials such as ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and ${M}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$.

Interaction between superconductors and weak gravitational field

We consider the interaction between the Earth gravitational field and a superconductor in the fluctuation regime. Exploiting the weak field expansion formalism and using time dependent Ginzburg-Landau formulation, we show a possible short-time alteration of the gravitational field in the vicinity of the superconductor.

(Invited) Theoretical Understanding of Nanoscale Ferroelectric Field-Effect-Transistor Having a Poly-Domain Structure

The emergence of ferroelectricity in doped HfO2 and (Hf,Zr)O2 (HZO) thin film with a typical thickness ~10 nm brings back the great interest in ferroelectric (FE) memories including the conventional ferroelectric random access memory, ferroelectric field-effect transistors (FEFET), and more recent negative capacitance field-effect transistors, in not only academia but also memory industry. In the industry, one of the most important issues concerning a FEFET is whether FEFET based NAND (FE-NAND) memory can be a next-generation device with superior performance to a conventional CTF-based NAND memory. For this purpose, it must have the multi-level capability and lower interference between adjacent memory cells. Because of sufficiently large ferroelectric polarization (10~15 uC/cm2 for typical HZO thin film), the multi-level capacity of FE-NAND would be higher than that of CTF-based NAND. However, an experimental result of FE-NAND devices shows that only a tenth of the expected memory window for the reading operation was achieved. At the same time, ten times larger erasing/writing voltages are required.In this work, we presented the comprehensive FEFET model to describe the writing process and reading process in FEFET from the fundamental viewpoint of metal-oxide-semiconductor (MOS) FET device physics in conjunction with the FE switching phenomenon. To capture the multi-domain nature of the ferroelectric thin film, we adopted the time-dependent Ginzburg-Landau (TDGL) formalism as a core physics of the switching kinetics. Furthermore, the FEFET model has been extended to a 3-Dimensional FE-NAND simulation. These models showed that the multi-domain nature of the ferroelectric film, which is shared by serial gates in the FE NAND device, not only degrades gate controllability on a target memory cell but also decreases a magnitude of surface potential. The extensive simulation results provided a critical view to understand the degraded memory window of FEFET and a possible strategy for the improvement.

Multiple reversals of vortex ratchet effects in a superconducting strip with inclined dynamic pinning landscape* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11702034, 11972298, and 11702218), the China Postdoctoral Science Foundation (Grant No. 2019M663812), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 300102129104, 3102018zy013, and 3102017jc01003), and the Young Talent Fund of

Using time-dependent Ginzburg–Landau formalism, we investigate the multiple reversals of ratchet effects in an unpatterned superconducting strip by the tilted dynamic pinning potential. In the case of collinear sliding potential and Lorentz force, vortices are always confined in the channels induced by sliding potential. However, due to the inclination angle of sliding pinning potential with respect to the Lorentz force, vortices could be driven out of the channels, and unexpected results with multiple reversals of vortex rectifications are observed. The mechanism of multiple reversals of vortex rectifications is explored by analyzing different vortex motion scenarios with increasing ac current amplitudes. The multiple reversals of transverse and longitudinal ratchet effects can be highly controlled by ac amplitude and dynamic pinning velocity. What’s more, at certain large current the ratchet effect reaches strongest within a wide range of pinning sliding velocity.

Static properties of STM tip in response to magnetic field

A nano size pyramidal superconducting tip is characterized theoretically. Vortex states are achieved in the framework of three-dimensional (3D) numerical discretization of Ginzburg-Landau (GL) formalism. Systematic investigation is performed according to the geometric parameters of the tip and different GL parameter κ. Meissner state and critical field of the tip are obtained in the presence of external magnetic field which is perpendicular to the square base of the tip. It is found that upper critical field Hc2 comes to lower with increasing κ but superconductivity persists up to higher filed in case of a much sharp tip. The results are important to comprehend the properties of superconducting tips, which are presently employed in scanning tunneling microscopy (STM), in the presence of an external magnetic field.