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Tha quantum electrodynamics of particles constrained to move on a plane is not a fully dimensionally reduced theory because the gauge fields through which they interact live in higher dimensions. By constraining the gauge field to the surface of the bulk, we obtain a fully reduced planar Abelian Chern-Simons Higgs model that can describe the vortex dynamics and second-order superconducting-normal phase transitions in planar Chern-Simons superconductors. Dual analyses performed before and after dimensional reduction yield the same Lagrangian for describing the vortex dynamics, indicating the self-consistency of our reduced theory. Compared to ordinary (2+1)-dimensional electrodynamics, we obtain anomalous fermion statistical vortices, consistent with results considering boundary effects. An additional electric charge constraint and different Chern-Simons parameter constraints are also found, which may help define a self-dual conformal field theory. Our renormalization group analysis shows that the quantized critical exponent depends on the Chern-Simons parameter. Quench disorder can bring more stable fixed points with different dynamical critical exponents. If we dimensionally reduce to a curved surface, our theory can also be extended to curved spacetimes, where geometric flow will be introduced and compete with vortex flow., Comment: 17 pages, 8 figures

One of the most important applications of quantum mechanics is the thermodynamic description of quantum gases. Despite the fundamental importance of this topic, a comprehensive description of the thermodynamic properties of non-Hermitian quantum gases is still lacking. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exihibit oscillations both in temperature and imaginary time. As such, they can be a possible platform to realize an imaginary time crystal (iTC) phase. The Hatano-Nelson model is identified as a simple lattice model to reveal this effect. In addition, we show that the conditions for the iTC to be manifest are the same as the conditions for the presence of disorder points, where the correlation functions show oscillating behavior. This analysis makes clear that our realization of iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, that enters as a mathematical tool to compute correlation functions for finite temperatures, can be measured experimentally., Comment: Reformulation of manuscript, some typos corrected, results are the same. 22+16 pages on single column

After providing a brief genealogy of our recently proposed model for High-Tc cuprates, we investigate the details of the microscopic mechanism that produces an attractive interaction between neighboring holes. We show that a peculiar arrangement of the $p_x$ and $p_y$ oxygen orbitals makes the mutual magnetic interaction of the holes with the localized copper ions to produce a net attractive interaction between themselves, which is responsible for the emergence of a superconducting phase. We also study the connection existing between the proposed pseudogap order parameter and the spectral density. We show that the occurrence of two sharp peaks in the latter, between which the density of states suffers a depletion is a direct consequence of the d-wave character of the pseudogap order parameter dependence on $\mathbf{k}$, which breaks the 90$^\circ$-rotation symmetry of the oxygen lattices. The peak separation in the spectral density works effectively as an overall pseudogap order parameter for the cuprates. We explicitly calculate the spectral density in the strange metal and pseudogap phases of Bi2212, at different temperatures, and show that our results compare very well with the experimental data., Comment: 10 pages, 11 figures

Starting from a recently proposed comprehensive theory for the high-Tc superconductivity in cuprates, we derive a general analytic expression for the planar resistivity, in the presence of an applied external magnetic field $\textbf{H}$ and explore its consequences in the different phases of these materials. As an initial probe of our result, we show it compares very well with experimental data for the resistivity of LSCO at different values of the applied field. We also apply our result to Bi2201 and show that the magnetoresistivity in the strange metal phase of this material, exhibits the $H^2$ to $H$ crossover, as we move from the weak to the strong field regime. Yet, despite of that, the magnetoresistivity does not present a quadrature scaling. Remarkably, the resistivity H-field derivative does scale as a function of $\frac{H}{T}$, in complete agreement with recent magneto-transport measurements made in the strange metal phase of cuprates \cite{Hussey2020}. We, finally, address the issue of the $T$-power-law dependence of the resistivity of overdoped cuprates and compare our results with experimental data for Tl2201. We show that this provides a simple method to determine whether the quantum critical point associated to the pseudogap temperature $T^*(x)$ belongs to the SC dome or not., Comment: 11 pages. Preliminary version. Comments are welcome

We study the effects of an external magnetic field on thensuperconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as $Cu_xTiSe_2$. Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ($\lambda_{\rm R}$). From this, we extract the critical magnetic field $ B_{ c } $ as a function of the temperature. For small values of $ B_{ c } $, we obtain a linear decay of the critical field, which is similar to the behavior observed experimentally in the copper doped dichalcogenide $Cu_xTiSe_2$ and also in intercalated graphite., Comment: arXiv admin note: substantial text overlap with arXiv:cond-mat/0703184

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T 5 0. At T = 0, we find a quantum phase transition connecting the normal and SC phases. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity., Comment: arXiv admin note: substantial text overlap with arXiv:cond-mat/0603165

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin-Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu-Jona-Lasinio-like, excitonic term and a spin-spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants., Comment: arXiv admin note: substantial text overlap with arXiv:1109.2151

Taking the spin-fermion model as the starting point for describing the cuprate superconductors, we obtain an effective nonlinear sigma-field hamiltonian, which takes into account the effect of doping in the system. We obtain an expression for the spin-wave velocity as a function of the chemical potential. For appropriate values of the parameters we determine the antiferromagnetic phase diagram for the YBa$_2$Cu$_3$O$_{6+x}$ compound as a function of the dopant concentration in good agreement with the experimental data. Furthermore, our approach provides a unified description for the phase diagrams of the hole-doped and the electron doped compounds, which is consistent with the remarkable similarity between the phase diagrams of these compounds, since we have obtained the suppression of the antiferromagnetic phase as the modulus of the chemical potential increases. The aforementioned result then follows by considering positive values of the chemical potential related to the addition of holes to the system, while negative values correspond to the addition of electrons.

Starting from a spin-fermion model for the cuprate superconductors, we obtain an effective interaction for the charge carriers by integrating out the spin degrees of freedom. Our model predicts a quantum critical point for the superconducting interaction coupling, which sets up a threshold for the onset of superconductivity in the system. We show that the physical value of this coupling is below this threshold, thus explaining why there is no superconducting phase for the undoped system. Then, by including doping, we find a dome-shaped dependence of the critical temperature as charge carriers are added to the system, in agreement with the experimental phase diagram. The superconducting critical temperature is calculated without adjusting any free parameter and yields, at optimal doping $ T_c \sim $ 45 K, which is comparable to the experimental data.

We show that the resistivity in each phase of the High-Tc cuprates is a special case of a general expression derived from the Kubo formula. We obtain, in particular, the T-linear behavior in the strange metal (SM) and upper pseudogap (PG) phases, the pure $T^2$, Fermi liquid (FL) behavior observed in the strongly overdoped regime as well as the $T^{1+\delta}$ behavior that interpolates both in the crossover. We calculate the coefficients: a) of $T$ in the linear regime and show that it is proportional to the PG temperature $T^*(x)$; b) of the $T^2$-term in the FL regime, without adjusting any parameter; and c) of the $T^{1.6}$ term in the crossover regime, all in excellent agreement with the experimental data. From our model, we are able to infer that the resistivity in cuprates is caused by the scattering of holes by excitons, which naturally form as holes are doped into the electron background., Comment: 7+9 (Supp. Mat.) pages

Recently the renormalization of the band gap $m$, in both WSe$_2$ and MoS$_2$, has been experimentally measured as a function of the carrier concentration $n$. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their low-energy excitations are, approximately, described by the massive Dirac equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis, we obtain that the renormalized mass describes the band gap renormalization with a function given by $m(n)/m_0=(n/n_0)^{C_\lambda/2}$, where $m_0=m(n_0)$ and $C_\lambda$ is a function of the coupling constant $\lambda$. We compare our theoretical results with the experimental findings for WSe$_2$ and MoS$_2$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $\lambda$. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, $\lambda_c \approx 0,66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $\lambda>\lambda_c$, the renormalized mass decreases while for $\lambda<\lambda_c$ it increases with the carrier concentration., Comment: 10 pages, 7 figures

We derive analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) transitions of the high-Tc cuprates as a function of doping. These are in excellent agreement with the experimental data both for single-layered materials such as LSCO, Bi2201 and Hg1201 and multi-layered ones, such as Bi2212, Bi2223, Hg1212 and Hg1223. Optimal doping occurs when the chemical potential vanishes, thus leading to an universal expression for the optimal SC transition temperatures. This allows for the obtainment of a quantitative description of the growth of such temperatures with the number of layers, N, which accurately applies to the $Bi$, $Hg$ and $Tl$ families of cuprates. We study the pressure dependence of the SC transition temperatures, obtaining excellent agreement with the experimental data for different materials and dopings. These results are obtained from an effective Hamiltonian for the itinerant oxygen holes, which includes both the electric repulsion between them and their magnetic interactions with the localized copper ions. We show that the former interaction is responsible for the SC and the latter, for the PG phases, the phase diagram of cuprates resulting from the competition of both. The Hamiltonian is defined on a bipartite oxygen lattice, which results from the fact that only the $p_x$ and $p_y$ oxygen orbitals alternatively hybridize with the $3d$ copper orbitals. From this, we can provide an unified explanation for the $d_{x^2-y^2}$ symmetry of both the SC and PG order parameters and obtain the Fermi pockets observed in ARPES experiments.

The recent discovery of two-dimensional Dirac materials, such as graphene and transition-metaldichalcogenides, has raised questions about the treatment of hybrid systems, in which electrons moving in a two-dimensional plane interact via virtual photons from the three-dimensional space. In this case, a projected non-local theory, known as Pseudo-QED, or reduced QED, has shown to provide a correct framework for describing the interactions displayed by these systems. In a related situation, in planar materials exhibiting a superconducting phase, the electromagnetic field has a typical exponential decay that is interpreted as the photons having an effective mass, as a consequence of the Anderson-Higgs mechanism. Here, we use an analogous projection to that used to obtain the pseudo-QED to derive a Pseudo-Proca equivalent model. In terms of this model, we unveil the main effects of attributing a mass to the photons and to the quasi-relativistic electrons. The one-loop radiative corrections to the electron mass, to the photon and to the electron-photon vertex are computed. We calculate the quantum corrections to the electron g-factor and show that it smoothly goes to zero in the limit when the photon mass is much larger than the electron mass. In addition, we correct the results obtained for graphene within Pseudo-QED in the limit when the photon mass vanishes.

Pseudo-Quantum Electrodynamics (PQED) provides an excellent description of the interaction between charged particles confined to a plane. When we couple pseudo-gauge field with a bosonic matter field, we obtain the so-called Scalar Pseudo-Quantum Electrodynamics (SPQED). In this work, we make a perturbative analysis of SPQED via Feynman diagrams. We compute the one loop Green functions: bosonic field self-energy, electromagnetic field self-energy, and vertex corrections. Finally, we consider the non-relativistic interaction potential between two bosonic particles. We compute the radiative corrections to the usual Coulomb potential and comment on the analogies and the differences with the fermionic case.

Quantum electrodynamics (QED) of electrons confined in a plane and that yet can undergo interactions mediated by an unconstrained photon has been described by the so-called {\it pseudo-QED} (PQED), the (2+1)-dimensional version of the equivalent dimensionally reduced original QED. In this work, we show that PQED with a nonlocal Chern-Simons term is dual to the Chern-Simons Higgs model at the quantum level. We apply the path-integral formalism in the dualization of the Chern-Simons Higgs model to first describe the interaction between quantum vortex particle excitations in the dual model. This interaction is explicitly shown to be in the form of a Bessel-like type of potential in the static limit. This result {\it per se} opens exciting possibilities for investigating topological states of matter generated by interactions, since the main difference between our new model and the PQED is the presence of a nonlocal Chern-Simons action. Indeed, the dual transformation yields an unexpected square root of the d'Alembertian operator, namely, $(\sqrt{-\Box})^{-1}$ multiplied by the well-known Chern-Simons action. Despite the nonlocality, the resulting model is still gauge invariant and preserves the unitarity, as we explicitly prove. {}Finally, when coupling the resulting model to Dirac fermions, we then show that pairs of bounded electrons are expected to appear, with a typical distance between the particles being inversely proportional to the topologically generated mass for the gauge field in the dual model., Comment: 7 pages. Replaced with version matching published one in the Phys. Lett. B

We derive analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) phases of the high-Tc cuprates, which are in excellent agreement with the experimental data for single-layered materials such as LSCO, Bi2201 and Hg1201. Our effective Hamiltonian, defined in the oxygen square sub-lattices formed by the alternate hybridization of $p_x$ and $p_y$ orbitals with the $3d$ copper orbitals, provides an unified explanation for the $d_{x^2-y^2}$ symmetry of both the SC and PG order parameters. Attractive and repulsive interactions involve holes of the two different sublattices and can be derived from the spin-fermion model. Optimal doping occurs when the chemical potential vanishes. For $N$-layered cuprates, the growth of the optimal temperature with $N$, as well as the trend of the SC and AF domes to superimpose, can be simply understood. Our results for the optimal SC transition temperature are in excellent agreement with the experiments for $N=2$ materials of the $Bi$ and $Hg$ families. For $N=3$ the agreement is still satisfactory, while for $N>3$, it becomes poor. The explanation for these facts allows us to suggest a method for increasing the critical SC temperature in cuprates., Comment: 11 pages and 9 figures

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3+1) dimensions. Thereafter, we consider that the matter field propagates only in (2+1) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2+1) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual $e^{-m r}/r$ Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudoquantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed., Comment: 8 pages, 2 figures

Manipulation of intrinsic electron degrees of freedom, such as charge and spin, gives rise to electronics and spintronics, respectively. Electrons in monolayer materials with a honeycomb lattice structure, such as the Transition-Metal Dichalcogenides (TMD's), can be distinguished according to the region (valley) of the Brillouin zone to which they belong. Valleytronics, the manipulation of this electron's property, is expected to set up a new era in the realm of electronic devices. In this work, we accurately determine the energy spectrum and lifetimes of exciton (electron-hole) bound-states for different TMD materials, namely WSe$_2$, WS$_2$ and MoS$_2$. For all of them, we obtain a splitting of the order of 170 meV between the exciton energies from different valleys, corresponding to an effective Zeeman magnetic field of 1400 T. Our approach, which employs quantum-field theory (QFT) techniques based on the Bethe-Salpeter equation and the Schwinger-Dyson formalism, takes into account the full electromagnetic interaction among the electrons. The valley selection mechanism operates through the dynamical breakdown of the time-reversal (TR) symmetry, which originally interconnects the two valleys. This symmetry is spontaneously broken whenever the full electromagnetic interaction vertex is used to probe the response of the system to an external field.

We derive an effective two-dimensional low-energy theory for thin superconducting films coupled to a three-dimensional fluctuating electromagnetic field. Using this theory we discuss plasma oscil- lations, interactions between charges and vortices and extract the energy of a vortex. Having found that the effective theory properly describes the long distance physics, we then use it to investigate to what extent the superconducting film is a topologically ordered phase of matter., Comment: Published, 13 pages, 1 figure

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the Pseudo Quantum Electrodynamics (PQED) and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large$-N_f$ expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the non-perturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value $\alpha_c(D N_f)$. In particular, we obtain the critical coupling constant $\alpha_c\approx 0.36$ for $D N_f=8$., where $D=2,4$ corresponds to the SU(2) and SU(4) cases, respectively, and $N_f$ is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. For two-dimensional materials,in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice., Comment: 9 pages, 3 figures

An interaction-driven nonzero quantum Hall conductivity is shown to occur in time-reversal symmetric massive Dirac materials, in the absence of any external agent. The effect is produced through the dynamical breakdown of time-reversal symmetry, which is generated by quantum fluctuations, when the full dynamical electromagnetic interaction among the electrons is taken into account. The manifestation of this emergent parity anomaly should be observed in materials such as silicene, stanene, germanene and transition metal dichalcogenides, at low enough temperatures.

The gyromagnetic factor is an important physical quantity relating the magnetic-dipole moment of a particle to its spin. The electron spin g-factor in vacuo is one of the best model-based theoretical predictions ever made, showing agreement with the measured value up to ten parts per trillion. However, for electrons in a material the g-factor is modified with respect to its value in vacuo because of environment interactions. Here, we show how interaction effects lead to the spin g-factor correction in graphene by considering the full electromagnetic interaction in the framework of pseudo-QED. We compare our theoretical prediction with experiments performed on graphene deposited on SiO2 and SiC, and we find a very good agreement between them., Comment: Improved version of the manuscript; valley g-factor part has been removed

The electron, discovered by Thomson by the end of the nineteenth century, was the first experimentally observed particle. The Weyl fermion, though theoretically predicted since a long time, was observed in a condensed matter environment in an experiment reported only a few weeks ago. Is there any linking thread connecting the first and the last observed fermion (quasi)particles? The answer is positive. By generalizing the method known as bosonization, the first time in its full complete form, for a spacetime with 3+1 dimensions, we are able to show that both electrons and Weyl fermions can be expressed in terms of the same boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The bosonized form of the Weyl chiral currents lead to the angle-dependent magneto-conductance behavior observed in these systems., Comment: 5 pages

We use the Schwinger-Dyson equations in the presence of a thermal bath, in order to study chiral symmetry breaking in a system of massless Dirac fermions interacting through pseudo quantum electrodynamics (PQED3), in (2+1) dimensions. We show that there is a critical temperature $T_c$, below which chiral symmetry is broken, and a corresponding mass gap is dynamically generated, provided the coupling is above a certain, temperature dependent, critical value $\alpha_c$. The ratio between the energy gap and the critical temperature for this model is estimated to be $2 \pi$. These results are confirmed by analytical and numerical investigations of the Schwinger-Dyson equation for the electron. In addition, we calculate the first finite-temperature corrections to the static Coulomb interaction. The relevance of this result in the realm of condensed matter systems, like graphene, is briefly discussed., Comment: 10 pages and 4 figures

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator $\Box^{1-\alpha}$, for $\alpha \in [0,1)$. We show that only Quantum Electrodynamics (QED$_3$) and its generalization known as Pseudo Quantum Electrodynamics (PQED), for which $\alpha =0$ and $\alpha = 1/2$, respectively, satisfy unitarity. The latter plays an important role in the description of the electromagnetic interactions of charged particles confined to a plane, such as in graphene or in hetero-junctions displaying the quantum Hall effect., Comment: 6 pages, no figures

We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore can be tuned both by the free parameters of the Higgs potential and the temperature., Comment: 22 pages

We use Pseudo Quantum Electrodynamics (PQED) in order to describe the full electromagnetic interaction of the p-electrons of graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the dc conductivity after a smooth zero-frequency limit is taken in Kubo's formula.Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous Quantum Valley Hall effect (QVHE) below a critical temperature of the order of $0.05$ K. The transverse (Hall) valley conductivity is evaluated exactly and shown to coincide with the one in the usual Quantum Hall effect. Finally, by considering the effects of PQED, we show that the electron self-energy is such that a set of P- and T- symmetric gapped electron energy eigenstates are dynamically generated, in association with the QVHE., Comment: 5 pages + supplemental material

We investigate the competition between the superconducting and the excitonic phases on Dirac electrons on a bipartite planar lattice. The conditions for the appearance of superconductivity or excitonic condensate are given by the minima of the free energy and our results are explained., Comment: 3 pages, Proceedings contribution for Hadrons XII