Superlattice Potential Research Articles

Two dimensional gap solitons in self-defocusing media with PT-symmetric superlattice

A theory is presented to study the existence and stability properties of fundamental solitons, multi-peaked gap solitons and vortex solitons in self-defocusing media with PT-symmetric superlattice. In the first gap of the superlattice potential, fundamental, dipole, and in-phase quadruple solitons can exist stably within a wide parameter region, while in-phase two-peaked solitons, out-of-phase quadruple solitons and vortex solitons are always unstable. Compared with simple-lattice solitons in similar potentials, the gap solitons in superlattice have a wider stable range than those in simple-lattice.

High-mobility capacitively-induced two-dimensional electrons in a lateral superlattice potential.

In the presence of a lateral periodic potential modulation, two-dimensional electrons may exhibit interesting phenomena, such as a graphene-like energy-momentum dispersion, Bloch oscillations, or the Hofstadter butterfly band structure. To create a sufficiently strong potential modulation using conventional semiconductor heterostructures, aggressive device processing is often required, unfortunately resulting in strong disorder that masks the sought-after effects. Here, we report a novel fabrication process flow for imposing a strong lateral potential modulation onto a capacitively induced two-dimensional electron system, while preserving the host material quality. Using this process flow, the electron density in a patterned Si/SiGe heterostructure can be tuned over a wide range, from 4.4 × 1010 cm−2 to 1.8 × 1011 cm−2, with a peak mobility of 6.4 × 105 cm2/V·s. The wide density tunability and high electron mobility allow us to observe sequential emergence of commensurability oscillations as the density, the mobility, and in turn the mean free path, increase. Magnetic-field-periodic quantum oscillations associated with various closed orbits also emerge sequentially with increasing density. We show that, from the density dependence of the quantum oscillations, one can directly extract the steepness of the imposed superlattice potential. This result is then compared to a conventional lateral superlattice model potential.

Phase diagram of the Kondo lattice model with a superlattice potential

We study the ground state of a Kondo lattice model where the free carries undergo a superlattice potential. Using the density matrix renormalization group method, we establish that the model exhibits a ferromagnetic phase and spiral phase whose boundaries in the phase diagram depend on the depth of the potential. Also, we observed that the spiral to ferromagnetic quantum phase transition can be tuned by changing the local coupling or the superlattice strength.

Using superlattice potentials to probe long-range magnetic correlations in optical lattices

In Pedersen et al. (2011) we proposed a method to utilize a temporally dependent superlattice potential to mediate spin-selective transport, and thereby probe long and short range magnetic correlations in optical lattices. Specifically this can be used for detecting antiferromagnetic ordering in repulsive fermionic optical lattice systems, but more generally it can serve as a means of directly probing correlations among the atoms by measuring the mean value of an observable, the number of double occupied sites. Here, we provide a detailed investigation of the physical processes which limit the effectiveness of this "conveyer belt method". Furthermore we propose a simple ways to improve the procedure, resulting in an essentially perfect (error-free) probing of the magnetic correlations. These results shows that suitably constructed superlattices constitute a promising way of manipulating atoms of different spin species as well as probing their interactions.

A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice

More than 30 years ago, Thouless introduced the concept of a topological charge pump that would enable the robust transport of charge through an adiabatic cyclic evolution of the underlying Hamiltonian. In contrast to classical transport, the transported charge was shown to be quantized and purely determined by the topology of the pump cycle, making it robust to perturbations. On a fundamental level, the quantized charge transport can be connected to a topological invariant, the Chern number, first introduced in the context of the integer quantum Hall effect. A Thouless quantum pump may therefore be regarded as a 'dynamical' version of the integer quantum Hall effect. Here, we report on the realization of such a topological charge pump using ultracold bosonic atoms that form a Mott insulator in a dynamically controlled optical superlattice potential. By taking in-situ images of the atom cloud, we observe a quantized deflection per pump cycle. We reveal the genuine quantum nature of the pump by showing that, in contrast to ground state particles, a counterintuitive reversed deflection occurs when particles are prepared in the first excited band. Furthermore, we were able to directly demonstrate that the system undergoes a controlled topological phase transition in higher bands when tuning the superlattice parameters.

Mixing interactions and superlattices

Quantum Hall Effect Under the influence of an external magnetic field, the energies of electrons in two-dimensional systems group into the so-called Landau levels. In the cleanest samples, interactions among electrons lead to fractional quantum Hall (FQH) states. If such a system is then subjected to a superlattice potential, it is unclear whether the fragile FQH states will survive. To address this question, Wang et al. sandwiched graphene between two layers of hexagonal boron nitride. Transport measurements on the superlattice showed that some FQH states did survive. Furthermore, the interplay between interactions and the superlattice potential produced additional, anomalous states. Science , this issue p. [1231][1] [1]: /lookup/volpage/350/1231?iss=6265

Topological Winding Number Change and Broken Inversion Symmetry in a Hofstadter’s Butterfly

Graphene's quantum Hall features are associated with a π Berry's phase due to its odd topological pseudospin winding number. In nearly aligned graphene-hexagonal BN heterostructures, the lattice and orientation mismatch produce a superlattice potential, yielding secondary Dirac points in graphene's electronic spectrum, and under a magnetic field, a Hofstadter butterfly-like energy spectrum. Here we report an additional π Berry's phase shift when tuning the Fermi level past the secondary Dirac points, originating from a change in topological winding number from odd to even when the Fermi-surface electron orbit begins to enclose the secondary Dirac points. At large hole doping inversion symmetry breaking generates a distinct hexagonal pattern in the longitudinal resistivity versus magnetic field and charge density. Major Hofstadter butterfly features persist up to ∼100 K, demonstrating the robustness of the fractal energy spectrum in these systems.

Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice

We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.

Magneto-optical response of graphene: Probing substrate interactions

Magneto-optical transitions between Landau levels can provide precise spectroscopic information on the electronic structure and excitation spectra of graphene, enabling probes of substrate and many-body effects. We calculate the magneto-optical conductivity of large-size graphene flakes using a tight-binding approach. Our method allows us to directly compare the magneto-optical response of an isolated graphene flake with one aligned on hexagonal boron nitride giving rise to a periodic superlattice potential. The substrate interaction induces band gaps away from the Dirac point. In the presence of a perpendicular magnetic field, Landau-level-like structures emerge from these zero-field band gaps. The energy dependence of these satellite structures is, however, not easily accessible by conventional probes of the density of states by varying the back-gate voltage. Here we propose the magneto-optical probing of the superlattice perturbed spectrum. Our simulation includes magneto-excitonic effects in first-order perturbation theory. Our approach yields a quantitative explanation of recently observed Landau-level-dependent renormalizations of the Fermi velocity.

Correlation between Fermi surface transformations and superconductivity in the electron-doped high-TcsuperconductorNd2−xCexCuO4

Two critical points have been revealed in the normal-state phase diagram of the electron-doped cuprate superconductor Nd$_{2-x}$Ce$_x$CuO$_4$ by exploring the Fermi surface properties of high quality single crystals by high-field magnetotransport. First, the quantitative analysis of the Shubnikov-de Haas effect shows that the weak superlattice potential responsible for the Fermi surface reconstruction in the overdoped regime extrapolates to zero at the doping level $x_c = 0.175$ corresponding to the onset of superconductivity. Second, the high-field Hall coefficient exhibits a sharp drop right below optimal doping $x_{\mathrm{opt}} = 0.145$ where the superconducting transition temperature is maximum. This drop is most likely caused by the onset of long-range antiferromagnetic ordering. Thus, the superconducting dome appears to be pinned by two critical points to the normal state phase diagram.

Observations of New Dirac Points in One-Dimensionally-Rippled Graphene on Hexagonal BN Using Scanning Tunneling Spectroscopy

Theories predicted that one-dimensional superlattice potentials in graphene would induce new Dirac points, instead of gap opening, due to lattice-induced chirality of charge carriers, but experimental evidence is rarely available in the literature. Here, we report observations of new Dirac points in one-dimensionally rippled graphene on hexagonal boron nitride (h-BN) using scanning tunneling microscopy and spectroscopy. The rippled graphene, formed due to thermal procedures, showed two new Dirac points above and below the Fermi level. The energy difference between a new Dirac point and the Fermi level was proportional to 1/L, where L was the period of a ripple, in agreement with theoretical predictions. Our study shows that the one-dimensional periodic potential is an accessible component for controlling the electronic properties of graphene.

Anomalous charge pumping in a one-dimensional optical superlattice

We model atomic motion in a sliding superlattice potential to explore topological "charge pumping" and to find optimal parameters for experimental observation of this phenomenon. We analytically study the band-structure, finding how the Wannier states evolve as two sinusoidal lattices are moved relative to one-another, and relate this evolution to the center of mass motion of an atomic cloud. We pay particular attention to counterintuitive or anomalous regimes, such as when the atomic motion is opposite to that of the lattice.

Pseudospin splitting of the energy spectrum of planar polytype graphene-based superlattices

The energy spectrum of planar polytype graphene-based superlattices has been investigated. It is shown that their energy spectrum undergoes pseudospin splitting due to the asymmetry of quantum wells forming the superlattice potential profile.

Mott-insulator–to–superconductor transition in a two-dimensional superlattice

We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator to superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the 3D-XY universality class. We also explore the character of the lowest energy charge excitations in the insulating and superconducting phases and show that they can be fermionic or bosonic depending on the parameters chosen.

Lattice bosons in a quasi-disordered environment: The effects of a superlattice potential on single particle and many particle properties

In this paper we present a theoretical investigation of the effect of a superlattice potential on some properties of non-interacting bosons in one dimensional lattices with Aubry–Andŕe disorder potential. In the first part, we investigate the single particle localization properties. We find a re-entrant localization–delocalization transition and the development of multiple mobility edges for a range of superlattice potential strengths. In the second part, we study the Bose–Einstein condensation with an additional harmonic trapping potential. We find that an increase in the superlattice potential leads to an increase in the depletion of the condensate in the low temperature limit.

Stabilizing non-Hermitian systems by periodic driving

The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As an application, we show how to use the stability of driven non-Hermitian two-level systems (0-dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity-time reversal symmetry is also briefly discussed.

Loading and detecting a three-dimensional Fermi gas in a one-dimensional optical superlattice

We investigate the procedures of loading and detecting three-dimensional fermionic quantum gases in a one-dimensional optical superlattice potential subjected to a trapping potential. Additionally, we consider the relaxation dynamics after a sudden change of the superlattice potential. We numerically simulate the time-dependent evolution of the continuous system using exact diagonalization of non-interacting fermions. During the loading procedure we analyze the occupation of the instantaneous energy levels and compare the situation in a homogeneous system with the trapped one. Strong differences are found in particular in the evolution of excitations which we trace back to the distinct global density distribution. Starting from an imbalanced state in the superlattice potential, we consider the relaxation dynamics of fermions after a slow change of the superlattice potential and find a bimodule distribution of excitations. To be able to compare with the experimental results we also simulate the measurement sequence of the even and odd local density and find a strong dependence of the outcome on the actual ramp procedure. We suggest how the loading and detecting procedure can be optimized.

Periodically driven quantum matter: The case of resonant modulations

Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micro-motion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micro-motion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time-evolution of the system.

All-electron topological insulator in InAs double wells

We show that electrons in ordinary III--V semiconductor double wells with an in-plane modulating periodic potential and interwell spin-orbit interaction are tunable topological insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double-well even-odd state splitting ${\ensuremath{\Delta}}_{\mathrm{SAS}}$ together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling $\ensuremath{\eta}$. We corroborate our exact diagonalization results with an analytical nearly-free-electron description that allows us to derive an effective Bernevig-Hughes-Zhang model. Interestingly, the gate-tunable mass gap $M$ drives a topological phase transition featuring a discontinuous Chern number at ${\ensuremath{\Delta}}_{\mathrm{SAS}}\ensuremath{\sim}5.4\phantom{\rule{0.16em}{0ex}}\text{meV}$. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the nontopological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters.

Magnetothermoelectric transport properties in graphene superlattices with one-dimensional periodic potentials

We numerically study the thermoelectric transport in graphene superlattice in the presence of a strong magnetic field and disorder, with a one-dimensional periodic potential barrier oriented along the armchair direction of graphene. The thermoelectric coefficients exhibit novel properties as functions of the superlattice period length. When the period length is taken to be the smallest, we find that the thermoelectric transport exhibits properties similar to those in the absence of the superlattice potential. The thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs). In the high-temperature regime, the transverse thermoelectric conductivity saturates to a universal value at the center of each LL, and displays a linear temperature dependence at low temperatures. We attribute this unique behavior to the coexistence of particle and hole LLs. Both the Nernst signal and the thermopower show a large peak around the central LL. However, with increasing the superlattice period length, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. displays a pronounced valley at low temperatures. This behavior can be understood as due to the split of the valley degeneracy in the central LL. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the superlattice period length.