We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number $\pm 1$ with equal-spin pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction $U$, nearest-neighbor density-density attraction $V$, and nearest-neighbor antiferromagnetic exchange $J$, within self-consistent Bogoliubov–de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases.

The application of the muon spin rotation/relaxation ($\mu \mathrm{SR}$) technique for studying type-I superconductivity is discussed. In the intermediate state, i.e., when a type-I superconducting sample with nonzero demagnetization factor $N$ is separated into normal state and Meissner state (superconducting) domains, the $\mu \mathrm{SR}$ technique allows one to determine with very high precision the value of the thermodynamic critical field $B_{\mathrm{c}}$, as well as the volume of the sample in the normal and the superconducting states. Due to the microscopic nature of the $\mu \mathrm{SR}$ technique, the $B_{\mathrm{c}}$ values are determined directly via measurements of the internal field inside the normal state domains. No assumptions or introduction of any type of measurement criteria are needed. Experiments performed on a “classical” type-I superconductor, a cylindrically shaped $\beta \text{−}\mathrm{Sn}$ sample, allowed to reconstruct the full $B\text{−}T$ phase diagram. The zero-temperature value of the thermodynamic critical field $B_{\mathrm{c}}\left(0\right)=30.578\left(6\right)$ mT and the transition temperature $T_{\mathrm{c}}=3.717\left(3\right)$ K were determined and found to be in a good agreement with the literature data. An experimentally obtained demagnetization factor is in very good agreement with theoretical calculations of the demagnetization factor of a finite cylinder. The analysis of $B_{\mathrm{c}}\left(T\right)$ dependence within the framework of the phenomenological $\alpha \mathrm{model}$ allow one to obtain the value of the superconducting energy gap $\mathrm{\Delta }=0.59\left(1\right)$ meV, of the electronic specific heat ${\gamma }_e=1.781\left(3\right)\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$, and of the jump in the heat capacity $\mathrm{\Delta }C\left(T_c\right)/\gamma T_{\mathrm{c}}=1.55\left(2\right)$.

The Kondo and periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling $J$ or hybridization $V$ between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small $J$ or $V$, limit, the moments survive and the conduction electrons mediate an effective interaction which can trigger long-range, often antiferromagnetic order. In the case of the Kondo model, where the moments are described by local spins, Nozières considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting “exhaustion” problem and how the “coherence temperature” where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low-temperature quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical $V$ for the singlet-antiferromagnetic transition.

The cubic oxide metals $\mathrm{Na}{M}_3{\mathrm{O}}_4$ ($M=\mathrm{Pd}$ or Pt) crystallize in the nonsymmorphic $Pm\overline{3}n$ space group. First-principles calculations are employed here to understand the role of the $M{\mathrm{O}}_4$ square planes and $M-M$ interactions in the development of the electronic structure. The compounds host numerous Dirac crossings near the Fermi level which, in the absence of spin-orbit coupling, appear to form a cubic nodal state. Spin-orbit coupling fragments this nodal state into smaller regions with Dirac-like character, with the fragmenting being more pronounced in the $M=\mathrm{Pt}$ compound.

We present a comparative study of particle-hole and particle-particle channels of random-phase approximation (RPA) for molecular dissociations of different bonding types. We introduced a direct particle-particle RPA scheme, in analogy to the direct particle-hole RPA formalism, whereby the exchange-type contributions are excluded. This allows us to compare the behavior of the particle-hole and particle-particle RPA channels on the same footing. Our study unravels the critical role of exchange contributions in determining behaviors of the two RPA channels for describing stretched molecules. We also made an attempt to merge particle-hole RPA and particle-particle RPA into a unified scheme, with the double-counting terms removed. However, benchmark calculations indicate that a straightforward combination of the two RPA channels does not lead to a successful computational scheme for describing molecular dissociations.

Using maximally localized Wannier functions obtained from density functional theory calculations, we derive an effective Hubbard Hamiltonian for a bilayer of ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$, the $n=2$ member of the Ruddlesden-Popper ${\mathrm{Sr}}_{n+1}{\mathrm{Cr}}_n{\mathrm{O}}_{3n+1}$ system. The model consists of effective $t_{2g}$ orbitals of Cr in two square lattices, one above the other. The model is further reduced at low energies and two electrons per site to an effective Kugel-Khomskii Hamiltonian that describes interacting spins 1 and pseudospins 1/2 at each site describing spin and orbital degrees of freedom, respectively. We solve this Hamiltonian at zero temperature using pseudospin bond operators and spin waves. Our results confirm a previous experimental and theoretical study that proposes spin ordering is antiferromagnetic in the planes and ferromagnetic between planes, while pseudospins form vertical singlets, although the interplane separation is larger than the nearest-neighbor distance in the plane. We explain the physics behind this rather unexpected behavior.

Understanding the interfacial charge separation mechanism in organic photovoltaics requires, due to its high level of complexity, bridging between chemistry and physics. To elucidate the charge separation mechanism, we present a fully quantum-dynamical simulation of a generic one-dimensional Hamiltonian, whose physical parameters model prototypical Phenyl-${\mathrm{C}}_{61}$-butyric acid methyl ester or $C_{60}$ acceptor systems. We then provide microscopic evidence of the influence random static and dynamic potentials have on the interfacial charge-injection rate. In particular, we unveil that dynamic potentials, due to strong electron-vibration interactions, can lead to the formation of polaronic bands. Such dynamical potentials, when compared to random static potentials, can provide the main detrimental influence on the efficiency of the process of interfacial charge separation.

Toroidal sigma models of magneto-transport are analyzed, in which integer and fractional quantum Hall effects automatically are unified by a holomorphic modular symmetry, whose group structure is determined by the spin structure of the toroidal target space (an elliptic curve). Hall quantization is protected by the topology of stable holomorphic vector bundles $\mathcal{V}$ on this space, and plateau values ${\sigma }_H^{{}_{\oplus }}=\mu \in \mathbb{Q}$ of the Hall conductivity are rational because such bundles are classified by their slope $\mu \left(\mathcal{V}\right)=\mathrm{deg}\left(\mathcal{V}\right)/\mathrm{rk}\left(\mathcal{V}\right)$, where $\mathrm{deg}\left(\mathcal{V}\right)$ is the degree and $\mathrm{rk}\left(\mathcal{V}\right)$ is the rank of $\mathcal{V}$. By exploiting a quantum equivalence called mirror symmetry, these models are mapped to tractable mirror models (also elliptic), in which topological protection is provided by more familiar winding numbers. Phase diagrams and scaling properties of elliptic models are compared to some of the experimental and numerical data accumulated over the past three decades. The geometry of scaling flows extracted from quantum Hall experiments is in good agreement with modular predictions, including the location of many quantum critical points. One conspicuous model has a critical delocalization exponent ${\nu }_{\mathrm{tor}}=18ln2/\left({\pi }^2{G}^4\right)=2.6051\cdots$ ($G$ is Gauss' constant) that is in excellent agreement with the value ${\nu }_{\mathrm{num}}=2.607\pm .004$ calculated in the numerical Chalker-Coddington model, suggesting that these models are in the same universality class. The real delocalization exponent may be disentangled from other scaling exponents in finite size scaling experiments, giving an experimental value ${\nu }_{\exp }=2.3\pm 0.2$. The modular model suggests how these theoretical and experimental results may be reconciled, but to determine if these theoretical models really are in the quantum Hall universality class, improved finite-size scaling experiments are urgently needed.

Graphene plasmons possess a number of unique optical properties and have been demonstrated to enable a variety of applications in the THz frequency range and the infrared frequency range, where active tunability through electrostatic gating plays an important role. In addition, graphene plasmons can be tuned by a static magnetic field, resulting in so called graphene magnetoplasmons. Here, we investigate the excitation of magnetoplasmons in graphene nanostructures with different shapes. We show that in the presence of a static magnetic field, plasmonic dipolar modes will split and the splitting is symmetrical in regular polygons. The splitting depends not on the size but only on the number of sides of the regular polygons. Larger splitting will occur in regular polygons with more sides, where the maximum splitting is achieved in circular disks. We further introduce a simple Lorentz model that could provide an excellent description of optical excitations in regular polygons. Finally, we examine the magnetoplasmons in the shapes without rotational symmetry, such as rectangles, where the symmetry of the splitting breaks as well.

The two-chain Frenkel-Kontorova model is applied for an analytical description of the energy and structure of the network of domain walls in bilayer graphene. Using this approach, the commensurate-incommensurate phase transition upon biaxial stretching of one of the graphene layers is considered. We demonstrate that formation of the equilateral triangular network of domain walls becomes energetically favorable above the critical relative biaxial elongation of the bottom layer of $3.0\times {10}^{-3}$. It is shown that the optimal period of the triangular network of domain walls is inversely proportional to the difference between the biaxial elongation of the bottom layer and the critical elongation as long as it is much greater than the width of domain walls. Quantitative estimates of the contribution of a single dislocation node to the system energy and the period of the network of domain walls are obtained. Experimental measurements of the period could help to verify the energy of the fully incommensurate state (such as that obtained by relative rotation of the layers) with respect to the commensurate one.

We study heat current and the full statistics of heat fluctuations in a capacitively coupled double quantum dot system. This work is motivated by recent theoretical studies and experimental works on heat currents in quantum dot circuits. As expected intuitively, within the (static) mean-field approximation, the system at steady state decouples into two single-dot equilibrium systems with renormalized dot energies, leading to zero average heat flux and fluctuations. This reveals that dynamic correlations induced between electrons on the dots are solely responsible for the heat transport between the two reservoirs. To study heat current fluctuations, we compute the steady-state cumulant generating function for heat exchanged between reservoirs using two approaches: the Lindblad quantum master equation approach, which is valid for arbitrary Coulomb interaction strength but weak system-reservoir coupling strength, and the saddle point approximation for the Schwinger-Keldysh coherent-state path integral, which is valid for arbitrary system-reservoir coupling strength but weak Coulomb interaction strength. Using thus obtained generating functions, we verify the steady-state fluctuation theorem for stochastic heat flux and study the average heat current and its fluctuations. We find that the heat current and its fluctuations change nonmonotonically with the Coulomb interaction strength ($U$) and system-reservoir coupling strength ($\mathrm{\Gamma }$) and are suppressed for large values of $U$ and $\mathrm{\Gamma }$.

This study examines the edge modes of chiral Berry plasmons propagating along zigzag or armchair edges of a graphene nanoribbon under a finite Berry flux and Fermi pressure. A two-dimensional quantum hydrodynamic model is used to derive analytical expressions of the dispersion relation and transverse confinement length. Direction-dependent edge modes exist in armchair nanoribbons under antisymmetric or symmetric boundary conditions. A confined mode appears in the zigzag nanoribbon under hard-wall boundary conditions. The transverse confinement length of edge plasmons in the nanoribbon can be an order of magnitude shorter than that in the semi-infinite structure.

We investigate the influence of phase transitions on the behavior of collective quantum emission. We discuss two distinct physical processes, the center-of-mass decoherence of a single emitter, and the collective emission of two emitters, addressed with an unified formalism relying on standard perturbation theory. Two specific examples of phase transitions are considered: the percolation transition in a metal-dielectric composite, and the metal-insulator transition in ${\mathrm{VO}}_2$. The decoherence and the collective emission rates can be decomposed as a sum of two contributions, accounting for the spontaneous emission and for interference effects, respectively. The former is enhanced by the Purcell effect for emitter(s) in the vicinity of the critical medium. The latter, associated with quantum interferences, experiences a “sudden death” near the critical point of the phase transition. Our findings unveil the interplay between the Purcell and collective effects and its dependence on metal-insulator transitions. In the case of ${\mathrm{VO}}_2$, decoherence and collective emission rates exhibit a characteristic hysteresis that strongly depends on the material temperature. These results, based on experimental data, suggest that ${\mathrm{VO}}_2$ could be explored as a versatile material platform where decoherence and collective emission can be tuned by varying the temperature.

The proximity-induced effects of the nearly commensurate lattice structure of a graphene layer AC stacked on Ni(111) and Co(0001) substrates are addressed. To this end, a minimal tight-binding Hamiltonian is constructed within the Slater-Koster method. We consider the hybridizations of the magnetic $3d$ orbitals of Ni (Co) atoms with the $p_z$ orbitals of graphene, in addition to the atomic spin-orbit coupling and the magnetization of the Ni (Co) atoms. A derivation of the low-energy perturbed $\pi$ bands in the vicinity of the Dirac points enables us to get further insight into the physical nature of the induced effective couplings to the graphene layer. It is shown that a magneto-spin-orbit type effect may emerge through two competing mechanisms simultaneously present, namely, the proximity-induced exchange and Rashba spin-orbit interaction. Such effects result in giant exchange splittings and robust Rashba spin-orbit coupling transferred to the graphene layer in agreement with recent density functional theory calculations and experimental observations. We further analyze the physical conditions for the appearance of intact Dirac cones in the minority spin bands as observed with recent photoemission measurements with spin resolution.

Stripelike and bubblelike patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripelike and the related nematic morphology are also under intense scrutiny in various strongly correlated electron systems. In contrast, the electronic bubble morphology is rare. Some of the most intriguing electron bubbles develop in the two-dimensional electron gas subjected to a perpendicular magnetic field. However, in contrast to bubbles forming in classical systems such as the Turing activator-inhibitor reaction or Langmuir films, bubbles in electron gases owe their existence to elementary quantum mechanics: They are stabilized as wave functions of individual electrons overlap. Here, we report a rich pattern of multielectron bubble phases in a high Landau level and we conclude that this richness is due to the nodal structure of the orbital component of the electronic wave function.

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/T_1$ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/T_1$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the $1/T_1$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

The possibility of having a delocalization transition in the one-dimensional de Moura–Lyra class of models (having a power spectrum $\propto q^{-\alpha }$) has been the object of a long-standing discussion in the literature. In this paper, we report numerical evidences that such a transition happens at $\alpha =1$, where the localization length (measured from the scaling of the conductance) is shown to diverge as ${(1-\alpha )}^{-1}$. The persistent finite-size scaling of the data is shown to be caused by a very slow convergence of the nearest-neighbor correlator to its infinite-size limit, and controlled by the choice of a proper scaling parameter. Our results for these models are consistent with a localization of eigenstates that is driven by a persistent small-scale noise, which vanishes as $\alpha \to 1^{-}$. This interpretation is confirmed by analytical perturbative calculations which are built on previous work. Finally, the nature of the delocalization transition is discussed and the conclusions are illustrated by numerical work done in the $\alpha >1$ regime.

Recent work by De Roeck et al. [Phys. Rev. B 95, 155129 (2017)] has argued that many-body localization is unstable in two and higher dimensions due to a thermalization avalanche triggered by rare regions of weak disorder. To examine these arguments, we construct several models of a finite ergodic bubble coupled to an Anderson insulator of noninteracting fermions. We first describe the ergodic region using a Gaussian orthogonal ensemble random matrix and perform an exact diagonalization study of small systems. The results are in excellent agreement with a refined theory of the thermalization avalanche that includes transient finite-size effects, lending strong support to the avalanche scenario. We then explore the limit of large system sizes by modeling the ergodic region via a Hubbard model with all-to-all random hopping: the combined system, consisting of the bubble and the insulator, can be reduced to an effective Anderson impurity problem. We find that the spectral function of a local operator in the ergodic region changes dramatically when coupling to a large number of localized fermionic states; this occurs even when the localized sites are weakly coupled to the bubble. In principle, for a given size of the ergodic region, this may arrest the avalanche. However, this back-action effect is suppressed and the avalanche can be recovered if the ergodic bubble is large enough. Thus, the main effect of the back-action is to renormalize the critical bubble size.