The edge physics of the $\nu =5/2$ fractional quantum Hall state is of relevance to several recent experiments that use it as a probe to gain insight into the nature of the bulk state. We perform calculations in a semirealistic setup with positive background charge at a distance $d$, by exact diagonalization both in the full Hilbert space (neglecting Landau level mixing) and in the restricted Pfaffian basis of edge excitations. Our principal finding is that the $5/2$ edge is unstable to a reconstruction except for very small $d$. In addition, the interactions between the electrons in the second Landau level and the lowest Landau level enhance the tendency toward edge reconstruction. We identify the bosonic and fermionic modes of edge excitations and obtain their dispersions by back-calculating from the energy spectra as well as directly from appropriate trial wave functions. We find that the edge reconstruction is driven by an instability in the fermionic sector for setback distances close to the critical ones. We also study the edge of the $\nu =7/3$ state and find that edge reconstruction occurs here more readily than for the $\nu =1/3$ state. Our study indicates that the $\nu =5/2$ and $7/3$ edge states are reconstructed for all experimental systems investigated so far and, thus, must be taken into account when analyzing experimental results. We also consider an effective field theory to gain insight into how edge reconstruction might influence various observable quantities.

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

Nonequilibrium molecular dynamics (NEMD) simulations on conceptual binary Lennard-Jones systems show that the thermal conductivity ($\kappa$) of a superlattice (SL) can be significantly reduced by randomizing the thicknesses of its layers, by which a SL becomes a random multilayer (RML). Such reduction in $\kappa$ is a clear signature of coherent phonon that can be localized in RMLs. We build a two-phonon model that divides the overall heat conduction into coherent and incoherent phonon contributions. In SL both coherent and incoherent phonons contribute to heat conduction, while in RML coherent phonons are localized so only incoherent phonons contribute. This model can fit the length dependence of the thermal conductances predicted in our NEMD simulations very well. The ballistic-limit thermal conductance and the intrinsic mean free path (MFP) of both coherent and incoherent phonons, and the localization length of coherent phonons, are obtained by fitting our model to the NEMD simulation results. The significant increase in $\kappa$ of SL with total length is due to the long MFP of coherent phonons, and the lower $\kappa$ of RML than SL is caused by the localization of coherent phonons.

We report results of ab initio calculations with various exchange-correlation functionals for the Si(111) surface with a 0.6-monolayer Au decoration. Seven different variations of the recently developed Erwin-Barke-Himpsel and Abukawa-Nishigaya models are studied in detail. Atomic geometries are determined by total-energy minimizations. We find the Erwin-Barke-Himpsel model of the $\mathrm{Si}\left(111\right)-(5\times 4)-\mathrm{Au}$ surface with one Si adatom per unit cell to be the most favorable structure. Seven-member rings and undercoordinated Si atoms of the Abukawa-Nishigaya model are unstable. Scanning tunneling images and band structures are calculated for the controversial geometries. For the ($5\times 4$) adatom geometry the resulting electronic structure agrees with the available experimental data.

We have examined the lowest-energy members of the quantized intrinsically localized modes (ILMs) of a generalization of the Fermi-Pasta-Ulam Hamiltonian to three dimensions. The lowest-energy ILMs are similar in form to multiphonon bound states, except that the number of phonons is not conserved. The ILMs can be categorized as having a quasispin of either $S=2$ or 0, and they have other internal quantum numbers. We find that ILMs can form in three dimensions at zero temperature, but only if the interaction exceeds a minimum value. Furthermore, as the temperature is raised, the magnitude of the minimal interaction required to stabilize the ILM is reduced. When the ILMs first form, they split off from the top of the two-phonon continuum. The $S=0$ ILMs form for lower values of the interaction than the $S=2$ ILMs. The ILMs form preferentially for center-of-mass momentum $\underline{q}$ at the corner of the Brillouin zone. The tendency of ILMs to form at this momentum is traced to a confluence of van Hove singularities in the (noninteracting) two-phonon density of states at the top of the two-phonon continuum. We have examined the ILM many-body wave functions and find that the relative coordinate part of the wave functions has symmetries associated with internal quantum numbers.

We have performed nuclear magnetic resonance (NMR) experiments on the quasi-one-dimensional frustrated spin-1/2 system ${\mathrm{LiCuVO}}_4$ in magnetic fields $H$ applied along the $c$ axis up to field values near the saturation field $H_{\mathrm{sat}}$. For the field range $H_{\mathrm{c}2}<H<H_{\mathrm{c}3}$ $({\mu }_0{H}_{\mathrm{c}2}\approx 7.5$ T and ${\mu }_0{H}_{\mathrm{c}3}=[40.5\pm 0.2]\text{T})$, the ${}^{51}\mathrm{V}$ NMR spectra at $T=380$ mK exhibit a characteristic double-horn pattern, as expected for a spin-modulated phase in which the magnetic moments of ${\mathrm{Cu}}^{2+}$ ions are aligned parallel to the applied field $H$ and their magnitudes change sinusoidally along the magnetic chains. For higher fields, the ${}^{51}\mathrm{V}$ NMR spectral shape changes from the double-horn pattern into a single Lorentzian line. For this Lorentzian line, the internal field at the ${}^{51}\mathrm{V}$ nuclei stays constant for ${\mu }_{0}H>41.4$ T, indicating that the majority of magnetic moments in ${\mathrm{LiCuVO}}_4$ are already saturated in this field range. This result is inconsistent with the previously observed linear field dependence of the magnetization $M\left(H\right)$ for $H_{\mathrm{c}3}<H<H_{\mathrm{sat}}$ with ${\mu }_0{H}_{\mathrm{sat}}=45$ T [L. E. Svistov et al., JETP Lett. 93, 21 (2011)]. We argue that the discrepancy is due to nonmagnetic defects in the samples. The results of the spin-lattice relaxation rate of ${}^7\mathrm{Li}$ nuclei indicate an energy gap which grows with field twice as fast as the Zeeman energy of a single spin, therefore suggesting that the two-magnon bound state is the lowest-energy excitation. The energy gap tends to close at ${\mu }_{0}H\approx 41$ T. Our results suggest that the theoretically predicted spin-nematic phase, if it exists in ${\mathrm{LiCuVO}}_4$, can be established only within the narrow field range $40.5<{\mu }_{0}H<41.4$ T.

Ferromagnetically doped topological insulators with broken time-reversal symmetry are a prerequisite for observing the quantum anomalous Hall effect. Cr-doped ${(\mathrm{Bi},\mathrm{Sb})}_2{(\mathrm{Se},\mathrm{Te})}_3$ is the most successful materials system so far, as it combines ferromagnetic ordering with acceptable levels of additional bulk doping. Here, we report a study of the local electronic structure of Cr dopants in epitaxially grown ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films. Contrary to the established view that the Cr dopant is trivalent because it substitutionally replaces ${\mathrm{Bi}}^{3+}$, we find instead that Cr is divalent. This is evidenced by the energy positions of the Cr $K$ and $L_{2,3}$ absorption edges relative to reference samples. The extended x-ray absorption fine structure at the $K$ edge shows that the Cr dopants substitute on octahedral sites with the surrounding Se ions contracted by $\Delta d=-0.36$ Å, in agreement with recent band structure calculations. Comparison of the Cr $L_{2,3}$ x-ray magnetic circular dichroism at $T=5$ K with multiplet calculations gives a spin moment of $3.64 {\mu }_{\mathrm{B}}/{\mathrm{Cr}}_{\mathrm{bulk}}$, which is close to the saturation moment for ${\mathrm{Cr}}^{2+} d^4$. The reduced Cr oxidation state in doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is ascribed to the formation of a covalent bond between Cr $d\left(e_g\right)$ and Se $p$ orbitals, which is favored by the contraction of the Cr-Se distances.

We present magnetization, specific heat, resistivity, and Hall effect measurements on the cubic $B20$ phase of MnGe and CoGe and compare to measurements of isostructural FeGe and electronic-structure calculations. In MnGe, we observe a transition to a magnetic state at $T_c=275\mathrm{K}$ as identified by a sharp peak in the ac magnetic susceptibility, as well as second phase transition at lower temperature that becomes apparent only at finite magnetic field. We discover two phase transitions in the specific heat at temperatures much below the Curie temperature, one of which we associate with changes to the magnetic structure. A magnetic field reduces the temperature of this transition which corresponds closely to the sharp peak observed in the ac susceptibility at fields above 5 kOe. The second of these transitions is not affected by the application of field and has no signature in the magnetic properties or our crystal-structure parameters. Transport measurements indicate that MnGe is metallic with a negative magnetoresistance similar to that seen in isostructural FeGe and MnSi. Hall effect measurements reveal a carrier concentration of about 0.5 carriers per formula unit, also similar to that found in FeGe and MnSi. CoGe is shown to be a low carrier density metal with a very small, nearly temperature-independent diamagnetic susceptibility.

We performed electron spin-resonance measurements on single crystals of the molecular nanomagnet ${\mathrm{V}}_{15}$ using a novel broadband spectrometer, both in parallel and in perpendicular modes, we see $\left(B_1\parallel B_0,B_1\perp B_0\right)$. Measurements were carried out in proximity of the spin level crossing at $B_0=2.75\mathrm{T}$. We observed spin-forbidden transitions from the $S=1/2$ zero-field ground state to the $S=3/2$ excited state in parallel mode spectra. Spin-forbidden transitions are employed for switching of coherent interactions between qubits in recent quantum simulator proposals. Our theoretical investigations showed that the mixing of spin states can result from either an antisymmetric exchange interaction or a combination of static distortion and hyperfine interaction.

Single crystals of the “cage compounds” $\mathrm{Sm}{\mathit{Tr}}_2{\mathrm{Zn}}_{20}$ ($Tr=\mathrm{Fe}$, Co, Ru)  and $\mathrm{Sm}T{r}_2{\mathrm{Cd}}_{20}$ ($Tr=\mathrm{Ni}$, Pd)  have been investigated by means of electrical resistivity, magnetization, and specific-heat measurements. The compounds ${\mathrm{SmFe}}_2{\mathrm{Zn}}_{20},{\mathrm{SmRu}}_2{\mathrm{Zn}}_{20}$, and ${\mathrm{SmNi}}_2{\mathrm{Cd}}_{20}$ exhibit ferromagnetic order with Curie temperatures of $T_C=47.4$, 7.6, and 7.5 K, respectively, whereas ${\mathrm{SmPd}}_2{\mathrm{Cd}}_{20}$ is an antiferromagnet with a Néel temperature of $T_N=3.4$ K. No evidence for magnetic order is observed in ${\mathrm{SmCo}}_2{\mathrm{Zn}}_{20}$ down to 110 mK. The Sommerfeld coefficients $\gamma$ are found to be $57 {\mathrm{mJ}/\mathrm{mol}\mathrm{K}}^2$ for ${\mathrm{SmFe}}_2{\mathrm{Zn}}_{20},79.5 {\mathrm{mJ}/\mathrm{mol}\mathrm{K}}^2$ for ${\mathrm{SmCo}}_2{\mathrm{Zn}}_{20},258 {\mathrm{mJ}/\mathrm{mol}\mathrm{K}}^2$ for ${\mathrm{SmRu}}_2{\mathrm{Zn}}_{20},165 {\mathrm{mJ}/\mathrm{mol}\mathrm{K}}^2$ for ${\mathrm{SmNi}}_2{\mathrm{Cd}}_{20}$, and $208 {\mathrm{mJ}/\mathrm{mol}\mathrm{K}}^2$ for ${\mathrm{SmPd}}_2{\mathrm{Cd}}_{20}$. Enhanced values of $\gamma$ and a quadratic temperature dependence of the electrical resistivity at low temperature for ${\mathrm{SmRu}}_2{\mathrm{Zn}}_{20}$ and ${\mathrm{SmPd}}_2{\mathrm{Cd}}_{20}$ suggest an enhancement of the quasiparticle masses due to hybridization between localized $4f$ and conduction electron states.

In the zero temperature limit, the zero-point quantum fluctuations of certain degrees of freedom (or quantum criticality) are claimed to describe the collective fluctuations of systems undergoing a second-order phase transition. To date, some of the best studied examples of quantum phase transitions, and concomitant anomalous physical behavior, involve $f$-electron magnetism in heavy-fermion metals, where quantum criticality (QC) is ascribed to either the suppression of a spin-density wave (SDW) ground state or the Kondo effect. Here, we unveil evidence for a quantum phase transition in ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$ which displays both an incommensurate SDW ground state, and a strong renormalization of the quasiparticle effective masses ($\mu$) due to the Kondo effect. For all angles $\theta$ between an external magnetic field ($H$) and the crystallographic $c$ axis, the application of $H$ leads to the suppression of the SDW state through a second-order phase transition at a $\theta$-dependent critical field $H_p\left(\theta \right)$ leading to the observation of small Fermi surfaces (FSs) in the paramagnetic state. For the $H\parallel c$ axis, these FSs are characterized by light $\mu$'s pointing also to the suppression of the Kondo effect at $H_p$ with, surprisingly, no experimental evidence for QC. But as $H$ is rotated towards the a axis, these $\mu$'s increase considerably becoming undetectable for $\theta >{56}^{\circ }$ between $H$ and the c axis. Around $H_p^a\sim 30$ T the resistivity becomes $\propto T$ which, coupled to the divergence of $\mu$, indicates the existence of a field-induced QC point at $H_p^a(T=0\text{K})$. This observation, suggesting FS hot spots associated with the SDW nesting vector, is at odds with current QC scenarios for which the continuous suppression of all relevant energy scales at $H_p(\theta ,T)$ should lead to a line of quantum-critical points in the $H\text{−}\theta$ plane. Finally, we show that the complexity of its magnetic phase diagram(s) makes ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$ an ideal system to explore field-induced quantum tricritical and QC end points.

The rapid progress in the production and cooling of molecular gases indicates that experimental studies of quantum gases with a strong dipolar interaction is soon within reach. Dipolar gases are predicted to exhibit very rich physics including quantum liquid crystal phases such as density waves as well as superfluid phases, both of which play an important role for our understanding of strongly correlated systems. Here, we investigate the zero temperature properties of the density-wave phase of a two-dimensional (2D) system of fermionic dipoles using a conserving Hartree-Fock theory. We calculate the amplitude of the density waves as a function of the dipole moment and orientation with respect to the 2D plane. The stripes give rise to a 1D Brillouin zone structure, and the corresponding quasiparticle spectrum is shown to have gapped as well as gapless regions around the Fermi surface. As a result, the system remains compressible in the density-wave phase, and it collapses for strong attraction. We show that the density waves have clear signatures in the momentum distribution and in the momentum correlations. Both can be measured in time-of-flight experiments. Finally, we discuss how the striped phase can be realized with experimentally available systems.

We investigate a magnetic proximity effect on the Dirac surface states of a topological insulator (TI) induced by a ${\mathrm{Bi}}_2{\mathrm{Se}}_3/\mathrm{EuS}$ interface, using density-functional theory (DFT) and a low-energy effective model, motivated by a recent experimental realization of the interface. We consider a thin ferromagnetic insulator EuS film stacked on top of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(111) slabs of three or five quintuple layers (QLs) with the magnetization of EuS normal to the interface ($z$ axis), which breaks time-reversal symmetry. It is found that a charge transfer and surface relaxation makes the Dirac cones electron doped. For both three and five QLs, the top-surface Dirac cone has an energy gap of 9 meV, while the bottom-surface Dirac cone remains gapless. This feature is due to the short-ranged induced magnetic moment of the EuS film. For the five QLs, an additional Dirac cone with an energy gap of 2 meV is formed right below the bottom-surface Dirac point, while for three QLs, there is no additional Dirac cone. We also examine the spin-orbital texture of the Dirac surface states with broken time-reversal symmetry, using DFT and the effective model. We find that the $p_z$ orbital is coupled to the $z$ component of the spin moment in the opposite sign to the $p_x$ and $p_y$ orbitals. The $p_z$ and radial $p$ orbitals are coupled to the in-plane spin texture in the opposite handedness to the tangential $p$ orbital. The result obtained from the effective model agrees with our DFT calculations. The calculated spin-orbital texture may be tested from spin-polarized angle-resolved photoemission spectroscopy.

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\sigma }_{r}eg\left(\omega \right)$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\sigma }_{r}eg\left(\omega \right)$ for the integrable XXZ spin chain in its gapped phase.

The electronic bound states and resonances in the vicinity of the Dirac point energy due to the adsorption of calcium dimers on a suspended graphene monolayer are explored theoretically using density functional theory (DFT) and an improved extended Hückel model that includes electrostatic potentials. The Mulliken atomic charges and the electrostatic potentials are obtained from DFT calculations and reveal charge transfer from the Ca dimers to the graphene which is responsible for the emergence of resonant states in the electronic spectrum. The number of resonant states increases as the number of adsorbed dimers is increased. We find a bound “atomic-collapse” state in the graphene local density of states, as has been observed experimentally [Wang et al., Science 340, 734 (2013)]. We find the formation of the atomic-collapse state and its population with electrons to require fewer adsorbed Ca dimers than in the experiment, possibly due to the different spacing between dimers and the dielectric screening by a boron nitride substrate in the experiment. We also predict the onset of filling of a second atomic-collapse state with electrons when six Ca dimers are adsorbed on the suspended graphene monolayer. Experiments testing these predictions would be of interest.

The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the $GW$ approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the $GW{\Gamma }^1$ approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by $GW{\Gamma }^1$ for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the $GW$ approximation is almost on par with $GW{\Gamma }^1$ as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both $\sim 0.1\text{eV}$, indicating a good overall transitivity of the band offsets. The alignment based on IPs from selected nonpolar surfaces performs comparably well in the prediction of band offsets at most of the considered interfaces. The maximum errors are, however, as large as 0.3, 0.4, and 0.7 eV for the alignments based on the average band offsets, branch point energies, and IPs, respectively. This margin of error should be taken into account when performing materials screening using these alignments.

We theoretically investigate the electronic structures of moiré superlattices arising in monolayer/bilayer graphene stacked on hexagonal boron nitride (hBN) in the presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum and quantum Hall effect of graphene-hBN systems in uniform magnetic field and demonstrate the evolution of the fractal spectrum as a function of the magnetic field. The spectrum generally splits in the valley degrees of freedom ($K$ and $K^{\prime }$) due to the lack of the inversion symmetry, and the valley splitting is more significant in bilayer graphene on hBN than in monolayer graphene on hBN because of the stronger inversion-symmetry breaking in bilayer.

We predict the existence of a Dirac state in a monolayer ${\mathrm{TiB}}_2$ sheet $\left(m\text{−}{\mathrm{TiB}}_2\right)$, a two-dimensional metal diboride, based on first-principles calculations. The band structure of $m\text{−}{\mathrm{TiB}}_2$ is found to be characterized with anisotropic Dirac cones with the largest Fermi velocity of $0.57\times {10}^6$ m/s, which is about one-half of that of graphene. The Dirac point is located at the Fermi level between the $K$ and $\Gamma$ points, with the Dirac states arising primarily from the $d$ orbitals of Ti. Freestanding $m\text{−}{\mathrm{TiB}}_2$ exhibits a bending instability, so that a planar $m\text{−}{\mathrm{TiB}}_2$ needs to be stabilized on a substrate. The calculation of $m\text{−}{\mathrm{TiB}}_2$ on a $h$-BN substrate reveals a negligible influence of the $h$-BN substrate on the electronic properties of $m\text{−}{\mathrm{TiB}}_2$. Our findings extend the Dirac materials to metal diborides.

In nanostructures with no appreciable scattering, electrons propagate ballistically, and hence have energy-independent total quantum transmission. For an incoming electron of energy $E$, the probability $\mathcal{T}\left(E\right)$ of transmission is obtained from the solution of the time-independent Schrödinger equation. Ballistic transport hence corresponds to $\mathcal{T}\left(E\right)=1$. We show that there is a wide class of nanostructures with correlated disorder that have $\mathcal{T}\left(E\right)=1$ for all propagating modes, even though they can have strong scattering. We call these nanostructures quantum dragons. An exact mathematical mapping for quantum transmission valid for a large class of atomic arrangements is presented within the single-band tight-binding model. Quantum transmission through a nanostructure is exactly mapped onto quantum transmission through a one-dimensional chain. The mapping is applied to carbon nanotubes in the armchair and zigzag configurations, Bethe lattices, conjoined Bethe lattices, Bethe lattices with hopping within each ring, and tubes formed from rectangular and orthorhombic lattices. The mapping shows that tuning tight-binding parameters to particular correlated values gives $\mathcal{T}\left(E\right)=1$ for all the systems studied. A quantum dragon has the same electrical conductivity as a ballistic nanodevice, namely, in a four-terminal measurement the electrical resistance is zero, while in a two-terminal measurement for the single-channel case, the electrical conductivity is equal to the conductance quantum $G_0=2e^2/h$, where $h$ is Planck's constant and $e$ the electron charge. We find $\mathcal{T}\left(E\right)=1$ is ubiquitous but occurs only on particular surfaces in the tight-binding parameter space.