In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V\left({\mathrm{\Omega }}_m\right)={\overline{g}}^{\gamma }/{\left|{\mathrm{\Omega }}_m\right|}^{\gamma }$ (the $\gamma$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous papers I–V, we analyzed the $\gamma$ model for $\gamma \le 2$ and argued that the ground state is an ordinary superconductor, but there is an infinite number of local minima of the condensation energy. We further argued that the condensation energy spectrum becomes continuous and gapless, and superconducting $T_c$ vanishes due to critical longitudinal gap fluctuations. In this paper, we consider larger $2<\gamma <3$. We show that the system moves away from criticality in that the condensation energy spectrum again becomes discrete and gapless, and $T_c$ becomes finite. Yet, we show that the gap functions for $\gamma >2$ and $\gamma <2$ are topologically different as they live on different sheets of the Riemann surface. This makes $\gamma =2$ a topological quantum-critical point. We further show that the fermionic excitation spectrum for $\gamma >2$ acquires a new feature—a bound state at the edge of a continuum, with a macroscopic degeneracy, which is a fraction of the total number of states in the system. We obtain the phase diagram on the $({\omega }_D,\gamma )$ plane, where ${\omega }_D$ is a mass of a pairing boson, and on the $(T,\gamma )$ plane. The latter consists of two distinct superconducting phases at $\gamma <2$ and $\gamma >2$ and the intermediate pseudogap state of preformed pairs in between.

The transition metal dichalcogenide $\mathrm{Pd}{\mathrm{Te}}_2$ has attractive features based on its classification as a type-II Dirac semimetal and the occurrence of type-I superconductivity, providing a platform for discussion of a topological superconductor. Our recent work revealed that type-I superconductivity persists up to pressures of $\sim 2.5$ GPa and the superconducting transition temperature $T_{\mathrm{c}}$ reaches a maximum at around 1 GPa, which is inconsistent with the theoretical prediction. To understand its nonmonotonic variation and investigate superconductivity at higher pressures, we performed structural analysis by x-ray diffraction at room temperature below 8 GPa and electrical resistivity measurements at low temperatures from 1 to 8 GPa. With regard to the superconductivity beyond 1 GPa, the monotonic decrease in $T_{\mathrm{c}}$ is reproduced without any noticeable anomalies; $T_{\mathrm{c}}$ changes from 1.8 K at 1 GPa to 0.82 K at 5.5 GPa with $d{T}_{\mathrm{c}}/dP\sim -0.22$ K/GPa. The crystal structure with space group $P\overline{3}m1$ is stable in the pressure range we examined. On the other hand, the normalized pressure-strain analysis (finite strain analysis) indicates that the compressibility changes around 1 GPa, suggesting that a Lifshitz transition occurs. We here discuss the effect of pressure on the superconducting and structural properties based on the comparison of these experimental results.

Understanding the interplay between quantum coherence and non-Hermitian features would enable the devising of quantum technologies based on dissipative systems. In turn, quantum coherence can be characterized in terms of the language of multiple quantum coherences (MQCs) originally developed in solid-state nuclear magnetic resonance (NMR), nowadays applied to the detection of quantum chaos and to the study of criticality in many-body quantum systems. Here, we show the usefulness of MQCs for probing equilibrium phase transitions in non-Hermitian systems. To do so, we investigate the connection of quantum coherences and critical points for several paradigmatic non-Hermitian Hamiltonians. For a non-Hermitian two-level system, MQCs witness the parity-symmetry-breaking phase transition from the unbroken to the broken phase. Furthermore, for the non-Hermitian transverse field Ising model, MQCs capture the Yang-Lee phase transition in which the ground state energy acquires a nonzero imaginary component. For the disordered Hatano-Nelson (HN) model with periodic boundary conditions, MQCs testify the emergence of mobility edges in the spectrum of this model. In addition, MQCs signal the topological phase transition exhibited by the complex energy spectra of the disorder-free HN model. Finally, we comment on experimentally probing phase transitions in NMR systems, realizing non-Hermitian Hamiltonians. Our results have applications to non-Hermitian quantum sensing, quantum thermodynamics, and in the study of the non-Hermitian skin effect.

We provide a unified, comprehensive treatment of all operators that contribute to the antiferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $\beta =0.898\left(37\right)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.

We investigate quantum dynamics and kinetics of a 2D conductor with a closed Fermi surface reconstructed by a biaxial density wave, in which electrons move along a two-dimensional periodic net of semiclassical trajectories coupled by the magnetic breakdown tunneling under a strong magnetic field. We derive a quasiparticle dispersion law and magnetoconductivity tensor. The quasiparticle spectrum is found to be the alternating series of two-dimensional magnetic energy bands with gaps between them. The longitudinal magnetoconductivity shows giant oscillations with change of magnetic field, while the Hall coefficient changes sign and is absent in a wide range of the magnetic fields in between. Preliminary estimations show that the suggested magnetoconductivity mechanism may be the origin of such behavior of the Hall coefficient versus magnetic field, as observed in experiments in materials with analogous topology of the Fermi surface, such as the high-$T_c$ superconducting cuprates.

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as $C$ and $\mathit{CP}$, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

By using the quantum Ising chain as a test bed and treating the spin polarization along the external transverse field as the generalized density, we examine the performance of different levels of density functional approximations parallel to those widely used for interacting electrons, such as local density approximation (LDA) and generalized-gradient approximation (GGA). We show that by adding the lowest-order and nearest-neighbor density variation correction to the simple LDA, a semilocal energy functional in the spirit of GGA is almost exact over a wide range of inhomogeneous density distribution. In addition, the LDA and GGA error structures bear a high level of resemblance to the quantum phase diagram of the system. These results provide insights into the triumph and failure of these approximations in a general context.

The interplay between crystal symmetry and its optical responses is at the heart of tremendous recent advances in light-matter interactions and applications. Nonlinear optical processes that produce electric currents, for example the bulk photovoltaic (BPV) effect, require inversion-symmetry-broken materials, such as ferroelectrics. In this work, we demonstrate that such BPV current could be generated in centrosymmetric materials with excitation of out-of-equilibrium coherent phonons. This is very different from the generally studied static or thermally excited states. We show that depending on the coherent phonon phase factor, the photoconductivity contains a static zero-frequency component, as well as THz frequency components. This indicates that a unidirectional current may emerge under synergistic effects of atomic vibration and light irradiation. We also generalize the conventional injection charge current into angular momentum (spin and orbital) degrees of freedom, and demonstrate spin and orbital BPV photoconductivities under coherent phonons. Our findings open the pathway to exploring the exotic phonon-photon-electron coherent interactions in quantum materials.

Charge density wave (CDW) states in solids bear an intimate connection to underlying fermiology. Thus, modification of the latter by suitable perturbations provides an attractive handle to unearth CDW states. Here, we combine extensive magnetotransport experiments and first-principles correlated electronic structure calculations on nonmagnetic tritelluride ${\mathrm{LaTe}}_3$ to uncover phenomena rare in CDW systems: (i) a humplike feature in temperature dependence of resistivity at low temperatures under application of magnetic-field ($B$), which moves to higher temperatures with increasing $B$, (ii) highly anisotropic large transverse magnetoresistance (MR) upon rotation of $B$ about the current parallel to the crystallographic $c$ axis, (iii) anomalously large positive MR with spikelike peaks at characteristic angles when the angle between current and field is varied on the $bc$ plane, (iv) extreme sensitivity of the angular variation of MR on field and temperature. These observations find a comprehensive explication in theoretical picture that captures field-induced electronic structure modification in ${\mathrm{LaTe}}_3$.

This study investigates the electronic states and physical quantities of an organic charge-transfer complex HMTSF-TCNQ, which undergoes a charge-density-wave (CDW) phase transition at temperature $T_c\simeq 30$ K. A first-principles calculation is utilized to determine that the normal state is a topological semimetal with open nodal lines. Based on the first-principles calculation, we develop a tight-binding model to investigate the electronic state in detail. Below $T_c$, the CDW phase is examined in the tight-binding scheme using the mean-field approximation. It is shown that the open nodal lines are deformed into closed ones, and their shapes are sensitive to the order parameter. Using this tight-binding model, we theoretically evaluate the temperature dependencies of two physical quantities: the spin-lattice relaxation time $T_1$ and the orbital magnetic susceptibility. In particular, an anomalous plateau is obtained at low temperatures in the orbital diamagnetism. We conclude that this anomalous plateau originates owing to the conflict between the interband diamagnetism, impurity scattering, and the nodal-line deformation. We also conduct an experiment to investigate the orbital magnetism, and the results are in excellent quantitative agreement with the theory.

We propose a semiconductor-superconductor hybrid device for realizing topological superconductivity and Majorana zero modes consisting of a planar Josephson junction structure with periodically modulated junction width. By performing a numerical analysis of the effective model describing the low-energy physics of the hybrid structure, we demonstrate that the modulation of the junction width results in a substantial enhancement of the topological gap and, consequently, of the robustness of the topological superconducting phase and associated Majorana zero modes. This enhancement is due to the formation of minibands with strongly renormalized effective parameters, including stronger spin-orbit coupling, generated by the effective periodic potential induced by the modulated structure. In addition to a larger topological gap, the proposed device supports a topological superconducting phase that covers a significant fraction of the parameter space, including the low Zeeman field regime, in the absence of a superconducting phase difference across the junction. Furthermore, the optimal regime for operating the device can be conveniently accessed by tuning the potential in the junction region using, for example, a top gate.

We perform simulations, by means of an envelope-function-based approach, of shot noise in disordered monolayer graphene devices, as a function of the gate bias voltage. In order to approach the experimental conditions, large graphene samples with characteristic sizes of the order of hundreds of nanometers or microns have been considered. We investigate different device geometries, including back-gated graphene samples with different aspect ratios and a graphene constriction biased by two side gates. We compare our results with available experimental data that were collected by a few authors in an attempt to validate an interesting prediction made by Tworzydło et al. [Phys. Rev. Lett. 96, 246802 (2006)] on the shot noise dependence on carrier density in samples with a large aspect ratio. On the basis of the comparison of our results with the experimental data, we conclude that the effect predicted by Tworzydło et al. (resulting from the distribution of the transmission eigenvalues associated with propagation via evanescent modes) has not been observed yet. Finally, we provide some guidelines for the design of experiments aimed at the verification of such an effect.

We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and space-time inversion ($\mathcal{P}\mathcal{T}$) symmetry. The required symmetries for the TTIs can be realized on any bipartite lattice where the inversion exchanges sublattices. The protecting symmetries lead to the classifying space of Hamiltonians being unitary symmetric matrices, and therefore Takagi's factorization can be performed. Particularly, the global Takagi's factorization can (cannot) be done on a $3\mathrm{D}$ ($2\mathrm{D}$) sphere. In 3D, there is a ${\mathbb{Z}}_2$ topological invariant corresponding to the parity of the winding number of Takagi's unitary-matrix factor over the entire Brillouin zone, where the ${\mathbb{Z}}_2$ nature comes from the $O\left(N\right)$ gauge degrees of freedom in Takagi's factorization. In 2D, the obstruction for a global Takagi's factorization is characterized by another ${\mathbb{Z}}_2$ topological invariant, equivalent to the second Stiefel-Whitney number. For the third-order topological phases, the $3\mathrm{D}$ TTIs feature a parity condition for corner zero modes, i.e., there always exist odd $\mathcal{P}\mathcal{T}$ pairs of corners with zero modes. Moreover, for any $\mathcal{P}\mathcal{T}$ invariant sample geometry, all configurations of corner zero modes satisfying the parity condition can exist with the same nontrivial bulk topological invariant. Actually, without closing the bulk gap, the boundary phase diagram has a cellular structure, where each topological boundary phase associated with a particular (cross-order) boundary-mode pattern corresponds to a contractible cell with a certain dimension in the parameter space.

In ZnO-based two-dimensional electron systems with strong Coulomb interaction, the anomalous spin-exciton branch is revealed. As probed by inelastic light scattering, in a ferromagnetic quantum-Hall state with the filling factor $\nu =2$, a spin exciton has a negative momentum dispersion with steepness dependent on the electron density. The negative dispersion of the spin exciton is associated with its interaction with higher-energy spin-flip modes that exist near $\nu =2$. Surprisingly, the anti-Stokes light scattering on spin excitons at ferromagnetic state $\nu =2$ is amplified by orders of magnitude, indicating the macroscopic accumulation of these excitations. The experimental findings are confirmed by the exact diagonalization method—these calculations show a magnetoroton minimum in the dispersion of spin excitons and also the attractive interaction between magnetoroton spin excitations.

Infrared reflectance measurements have been carried on highly $p$-type ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ crystals over the broad temperature range from 10 to 650 K and their response function investigated. An anomalous nonmonotonous temperature dependence of the plasma edge frequency is observed—with a pronounced redshift and blueshift that appear above and below room temperature, respectively. Such behavior is explained in terms of the temperature evolution of the free carrier optical weight $N/m^{*}$ given by particular temperature dependence of the total carrier concentration $N$ (determined by transport measurements) and characteristic (optical) mass $m^{*}$. The effective mass strongly varies from $m^{*}=0.1m_0$ ($m_0$ electron rest mass) at 10 K to $m^{*}=0.5m_0$ respective $m^{*}=0.9m_0$ at 650 K depending on the evaluating procedure. The interpretation is corroborated by complementary magnetotransport and magnetoreflectivity experiments.

The morphological and/or chemical disorder is commonly known as detrimental to superconductivity and typically reduces the critical temperature $T_c$. We present research on the skutterudite-related ${\mathrm{Y}}_5{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ system, where local atomic disorder leads to novel disorder-enhanced superconductivity. Our present studies focus on the series of ${\mathrm{Y}}_{4.5}{M}_{0.5}{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ compounds, where the metallic dopants $M=\mathrm{Ca}$, Ti, Sr, Zr, La, or Lu, when they are smaller than the atomic radius of Y (the case of Ti, Zr, Lu, or vacancies at the Y sites), generate the so-called peak effect at $T<T_c$ in the fields smaller than the critical field $H_{c2}$. The peak effect is well documented experimentally by measurements of the temperature variations in electric transport and ac magnetic susceptibility under external magnetic fields. In accordance with the commonly accepted explanation of the peak effect, we assume that the magnetic field induced reentrance of superconductivity in ${\mathrm{Y}}_{4.5}{M}_{0.5}{\mathrm{Rh}}_6{\mathrm{Sn}}_{18}$ results from a change in the structure of the vortex lattice close to $H_{c2}$. Using a simple theoretical model we argue that the effectiveness of this mechanism can depend on the size of the dopant. We also investigate the band structure properties by x-ray electron spectroscopy and ab initio calculations. It seems interesting that the density functional theory predicts a magnetic moment on the dopant Ti, which is a reason for the Kondo effect, confirmed experimentally.

We report the growth process, structure, and electronic states of 1 unit layer (u.l.) of a Ce-Pt intermetallic compound on Pt(111) using scanning tunneling microscopy/spectroscopy (STM/STS) and low-energy electron diffraction. An ordered $(2\times 2)$ structure was observed in the form of films or nanoislands depending on Ce dose by annealing at around 700 K. A structural model constructed from atomically resolved STM images and quasiparticle interference (QPI) patterns indicates the formation of a new surface compound 1 u.l. ${\mathrm{CePt}}_6$ on Pt(111) terminated by a Pt layer. A lateral lattice constant of the 1 u.l. ${\mathrm{CePt}}_6$ on Pt(111) is expanded from the value of a bulk ${\mathrm{CePt}}_5$ crystal to match the Pt(111) substrate. By measuring $dI/dV$ spectra and QPI, we observed an onset energy of the surface state found on Pt(111) above Fermi energy ($E_F$) shifts below $E_F$ on the Pt layer of the 1 u.l. ${\mathrm{CePt}}_6$ due to charge transfer from the underneath ${\mathrm{CePt}}_2$ layer. We discuss a possible two-dimensional coherent Kondo effect with the observed spectra on the 1 u.l. ${\mathrm{CePt}}_6$.

The thermal properties and the electrical conductance are studied for 2D electron gases in doped Xenes – graphene, silicene, germanene, stanene, and plumbene – applying a four-band model to describe the low-energy Dirac-fermion-like electronic excitations. Spin-orbit interactions to discriminate the five Xenes and the influence of an electric field in the normal direction, are taken into account. The density of states and the spectral behavior of the current-current correlation function allow the calculation of the Onsager coefficients. They give analytical formulas for the electronic contributions to the heat capacity and thermal conductance. Also, the electrical conductance can be described within the same framework, if the scattering properties of the electron gases are simulated by constant broadening parameters. For all these thermal and transport properties, only a weak variation with the Xene is found, because of their small spin-orbit-induced gaps, with the exception of plumbene. The heat capacity of Xenes does not show a Schottky anomaly. The thermal conductance increases linearly or quadratically with temperature depending on the temperature range. A similar behavior characterizes the electrical conductance. The dominance of Dirac fermions, i.e., linear bands, determines the ratio of electron thermal conductance and electric conductance, which depends on doping level and temperature. It violates the Wiedemann-Franz law known for 3D electron gases with parabolic energy-momentum dispersion. The Lorenz number is generally much larger for 2D electron gases with almost Dirac character of the dispersion relation.