Wannier-Stark Localization Research Articles

Dephasing-assisted transport in a tight-binding chain with a linear potential

An environment interacting with a quantum system can enhance transport through the suppression of quantum effects responsible for localization. In this paper, we study the interplay between bulk dephasing and a linear potential in a boundary-driven tight-binding chain. A linear potential induces Wannier-Stark localization in the absence of noise, while dephasing induces diffusive transport in the absence of a tilt. We derive an approximate expression for the steady-state current as a function of both dephasing and tilt which closely matches the exact solution for a wide range of parameters. From it, we find that the maximum current occurs for a dephasing rate equal to the period of Bloch oscillations in the Wannier-Stark localized system. We also find that the current displays a maximum as a function of the system size, provided that the total potential tilt across the chain remains constant. Our results can be verified in current experimental platforms and represents a step forward in analytical studies of environment-assisted transport.

Real-space perspective on dephasing in solid-state high harmonic generation

We develop and demonstrate a fully real-space perspective on high harmonic generation (HHG) in crystals. Due to the Wannier-Stark localization induced on subcycle timescales in the presence of a strong field, real-space descriptions are natural for strongly driven solids. Our approach allows us to address the origin of the extremely short dephasing times, which appear necessary for agreement between experimental HHG measurements and theoretical calculations generally performed in reciprocal space. We develop a physically transparent model of real-space dephasing which relates its rate to the distance between different sites in a laser-driven lattice. Our approach leads to well-structured high harmonic spectra at the microscopic level, reproduces the results of macroscopic propagation, and demonstrates that the requirement for ultrafast dephasing times stems from the need for suppressing recombination events with large electron-hole separations during radiative recombination. Published by the American Physical Society 2024

Coherent Control of Bloch Oscillations in a Superconducting Circuit

Bloch oscillations (BOs) are oscillations of electrons under external constant forces in a lattice, revealing the wavelike behavior of electrons. BOs lead to the localization of the wave packet that is called Wannier-Stark localization (WSL), resulting in the inhibition of conductivity. We simulate BOs experimentally in a one-dimensional superconducting circuit with nine qubits. The nine qubits form a one-dimensional lattice and an electron is mapped to a photon. We experimentally realize the coherent control of BOs by applying a well-controlled driving force with a frequency close to BOs. We observe the competition between localization and delocalization of the wave pocket by changing the drive parameters. Our study demonstrates the visualized wave behavior of electrons and proves a way to modulate electron transport in a perfect lattice. Published by the American Physical Society 2024

Wannier–Stark localization of electronic states in 4H-SiC MOS inversion layer

The electronic states in 4H-SiC MOS inversion layers are theoretically analyzed using the empirical pseudopotential method (EPM). The analysis shows that the Wannier–Stark localization occurs, which is absent in an effective mass approximation (EMA). The Wannier–Stark localization modifies the electronic states in the MOS inversion layers. A model is proposed to describe the in-plane dispersion of subbands affected by the Wannier–Stark localization. The differences between the EPM and EMA results for the subband energy levels and the in-plane effective masses are discussed.

Wannier-Stark localization in one-dimensional amplitude-chirped lattices

Wannier-Stark localization in one-dimensional amplitude-chirped lattices

Generalized framework for the step response of semiconducting materials to optically switched electrical bias input in terahertz emission spectroscopy

In this paper, a generalized framework for the step response of semiconducting materials to optically switched electrical bias input in terahertz emission spectroscopy was developed, introducing a complex response function into the frequency domain. A comprehensive formula was obtained for calculating the transient current from the poles of the response function under bias field. This formula was found to give transient currents of an exponentially saturated, overshooting, or oscillating nature for three different regimes of charge transport in an isolated energy band. Furthermore, it was clarified how the transient terahertz emission is linked to the response function and its retarded contribution. When either true current or polarization current is linear with respect to bias field and dominates the transient current, the retarded contribution is identified as the small-signal ac complex conductivity. Two different spectral examples of the retarded contribution were given for actual terahertz Bloch oscillations in biased semiconductor superlattices, describing the small-signal response of polarization current under the Wannier–Stark localization and the large-signal response of true current under interminiband mixing.

Tightly bound states in a uniform field with asymmetric tunneling

We investigate the localization behavior of the non-Hermitian tightly bound state in the presence of asymmetric tunneling and external uniform fields in various dimensions, where the discrete translational symmetry and the inversion symmetry are broken. We demonstrate that the non-Hermitian skin effects can still exist and compete with Wannier-Stark localization induced by the uniform fields. The total localization is not only related to the size of the system, but the net tunneling strength as well. For the two-dimensional lattices with square shape boundaries, the uniform fields can pull back the population of the states at the corner and the fading stripe localization can be observed as a compromise between the two-dimensional non-Hermitian skin effects and the uniform fields. The experimental simulation of the non-Hermitian chain with uniform fields can be achieved by the methods of electrical circuits.

Electronic states underlying peculiar Bloch oscillations in a biased semiconductor superlattice with interminiband mixing

We simulate the energy eigenstates of electrons and holes, which underlie terahertz Bloch oscillations observed recently with a peculiar phase shift, in a biased semiconductor superlattice with interminiband mixing. Electron wavefunctions are extended downstream, while some of them have a moderately first-miniband-like nature that partly resembles Wannier–Stark localization upstream. When a typical heavy-hole wavefunction is chosen, a few first-miniband-like electron wavefunctions prove to have large overlap integrals with it under relatively low bias fields. These electron wavefunctions are thus essential for the optical excitation of the Bloch oscillations, supported experimentally by the peak patterns of dc photocurrent spectra.

Dynamics of Negativity of a Wannier–Stark Many‐Body Localized System Coupled to a Bath

An interacting system subjected to a strong linear potential can host a many‐body localized (MBL) phase when being slightly perturbed. This so‐called Wannier–Stark or “tilted‐field” MBL phase inherits many properties from the well‐investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. Herein, the dynamics of entanglement in a Wannier–Stark MBL system coupled to a dephasing environment is investigated. As an accessible entanglement proxy, the third Rényi negativity is used, which reduces to the third Rényi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate‐time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus, it forms a tool to distinguish Wannier–Stark MBL from noninteracting Wannier–Stark localization up to intermediate time‐scales, and to quantify quantum correlations in mixed‐state dynamics.

Low-field onset of Wannier-Stark localization in a polycrystalline hybrid organic inorganic perovskite

Methylammonium lead iodide perovskite (MAPbI3) is renowned for an impressive power conversion efficiency rise and cost-effective fabrication for photovoltaics. In this work, we demonstrate that polycrystalline MAPbI3s undergo drastic changes in optical properties at moderate field strengths with an ultrafast response time, via transient Wannier Stark localization. The distinct band structure of this material - the large lattice periodicity, the narrow electronic energy bandwidths, and the coincidence of these two along the same high-symmetry direction – enables relatively weak fields to bring this material into the Wannier Stark regime. Its polycrystalline nature is not detrimental to the optical switching performance of the material, since the least dispersive direction of the band structure dominates the contribution to the optical response, which favors low-cost fabrication. Together with the outstanding photophysical properties of MAPbI3, this finding highlights the great potential of this material in ultrafast light modulation and novel photonic applications.

Dissipative quantum transport in a nanowire

The coherence-to-decoherence transition is studied in a nanowire modeled as a one-dimensional tight-binding lattice in the presence of an external field and in linear interaction with a boson heat bath, characterized by Ohmic dissipation. The focus of attention is the probability propagator which quantifies the likelihood of a quantum particle, such as an electron to end up at an arbitrary site at a time $t$, given that it was at the origin initially---and from it---the particle-current and the mean-squared displacement. If the bath is absent, the probability operator exhibits quantum coherence as can be captured by say, Bloch oscillation and Wannier-Stark (dynamic) localization. The coupling with the bath---which can be weak or strong---leads to decoherence that will be quantified in the text. The Ohmic model of the spectral function of bath excitations contains a cutoff frequency, which if greater than the temperature (in energy units) defines the ``low-temperature'' regime, whereas the opposite limit implies ``high temperatures.'' Results will be presented in both these regimes separately.

Observation of Bloch oscillations and Wannier-Stark localization on a superconducting quantum processor

The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic XY spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.

Nonequilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions.

We employ a novel, unbiased renormalization-group approach to investigate nonequilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low dimensions out of equilibrium. We study a prototypical model for the metal to insulator transition of spinless interacting fermions coupled to electronic baths and driven out of equilibrium by a longitudinal static electric field. The closed system features a Berezinskii-Kosterlitz-Thouless transition between a metallic and a charge-ordered phase in the equilibrium limit. We compute the nonequilibrium phase diagram and illustrate a highly nonmonotonic dependence of the phase boundary on the strength of the electric field: for small fields, the induced currents destroy the charge order, while at higher electric fields it reemerges due to many-body Wannier-Stark localization physics. Finally, we show that the current in such an interacting nonequilibrium system can counter-intuitively flow opposite to the direction of the electric field. This nonequilibrium steady state is reminiscent of an equilibrium distribution function with an effective negative temperature.

Tuning of energy gap and 1D Dirac-like points in artificial graphene and boron nitride monolayer by an external electric field

A simple semianalytical model is proposed to predict the possibilities of effective manipulation of electronic states in a graphene-like and a two dimensional boron nitride-like quantum dot superlattices by means of lateral electric field. Due to the Wannier-Stark localization an one dimensional energy dispersion in the perpendicular to the electric field direction is observed. Interestingly, one dimensional analogs of Dirac points of minibands’ touching are observed in the energy dispersion, for the artificial graphene when electric field is weak enough. However, an energy gap between the minibands is opened when an electric field of a significant strength is applied. On the other hand, it is demonstrated that the appropriate choice of the electric field strength can lead to the recovering of touching points in one dimensional energy dispersion of artificial boron nitride monolayer which are not observable in the absence of electric field. Importantly, the analysis of the electron probability distributions brings out an efficient mechanism of switching between the quantum localized states in different sublattices by means of laterally applied electric field. The obtained results indicate on the possibility of a simple and effective control of the properties of optical and logical devices based on honeycomb semiconductor superlattices . • Wannier-Stark localized states in AG and ABN are considered. • A possibility of control of energy gap and Dirak-like points is predicted. • A switching mechanism between the localized states in different sublattices is proposed.

Electric-Field-Induced Antiferromagnetic Insulating State in a Metallic Ferromagnet

We show that a static electric field induces the transition from a ferromagnetic metal to an antiferromagnetic insulator owing to the Bloch oscillation of conduction electrons. In the steady state, the electric current is inversely proportional to the applied electric field, implying the nonperturbative insulating nature that is different from the Wannier-Stark localization. Possible experimental realization based on recent terahertz pulse sources is discussed.

Experimental probes of Stark many-body localization

Recent work has focused on exploring many-body localization (MBL) in systems without quenched disorder: one such proposal is Stark MBL in which small perturbations to a strong linear potential yield localization. However, as with conventional MBL, it is challenging to experimentally distinguish between non-interacting localization and true MBL. In this paper we show that several existing experimental probes, designed specifically to differentiate between these scenarios, work similarly in the Stark MBL setting. In particular we show that a modified spin-echo response (DEER) shows clear signs of a power-law decay for Stark MBL while quickly saturating for disorder-free Wannier-Stark localization. Further, we observe the characteristic logarithmic-in-time spreading of quantum mutual information in the Stark MBL regime, and an absence of spreading in a non-interacting Stark-localized system. We also show that there are no significant differences in several existing MBL measures for a system consisting of softcore bosons with repulsive on-site interactions. Lastly we discuss why curvature or small disorder are needed for an accurate reproduction of MBL phenomenology, and how this may be illustrated in experiment. This also connects with recent progress on Hilbert space fragmentation in "fractonic" models with conserved dipole moment, and we suggest this as an auspicious platform for experimental investigations of these phenomena.

Drive-induced many-body localization and coherent destruction of Stark many-body localization

We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical localization, coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to "Stark many-body localization", for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive ($A/\omega$) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with $A/\omega$ tuned away from the dynamical localization point leads to a \emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if $A/\omega$ is tuned at the dynamical localization point of the zero dc field problem.

The Bloch Electron Response to Electric Fields: Application to Graphene

The theory of Bloch electron dynamics for carriers in homogeneous electric fields of arbitrary time dependence is developed in consideration of the electronic transport properties in graphene. The general approach is to use the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including Zener tunneling, is treated exactly; also, the electric field is described in the vector potential gauge. Within the ABR, the instantaneous eigenstates for the central Hamiltonian are described and utilized to develop both the time‐dependent wave functions and the single‐particle density matrix pictures with explicit application to intrinsic graphene. The Bloch electron analysis for graphene in a constant electric field reveals the explicit manifestation of electron–hole pair creation, Bloch oscillations, and Wannier–Stark localization. The average velocity and acceleration are established as an explicit function of the electric field, and their behavior is characterized on short and long time scales. Further, it is shown that the average acceleration in a nonvanishing electric field gives rise to an electric field induced dynamical effective mass tensor in the direction of the field.

Topological order versus many-body localization in periodically modulated spin chains

In this paper, we study periodically modulated $s=1/2$ spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states, because it induces localization called Wannier-Stark (WS) localization. We clarify the phase diagram in the presence of the LP and on-site diagonal disorder. To this end, we carefully study edge excitations under the open boundary condition, which are a hallmark of the topological order. We find a very interesting phenomenon indicating existence of a quasi-edge modes that take the place of the genuine edge modes in certain parameter regions. This is a precursor of the WS localization realized in topological states. Finally, we investigate many-body localization induced by a sufficiently strong LP or disorder. To this end, we study the energy-level statistics for whole energy levels, and find unexpected extended-state regimes located in intermediate potential-gradient and weak on-site disorder regimes. We verify this phenomenon by calculating variance of the entanglement entropy. The present system is closely related to quantum Hall state in two dimensions, and therefore our findings can be observed not only in experiments on ultra-cold atomic gases but also quantum Hall physics.

Effect of noise on Bloch oscillations and Wannier-Stark localization

We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pm\mu$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $\mu$, while with an additional static field $\epsilon$ we find oscillatory motion with a superposition of frequencies $(\epsilon \pm \mu)$. On the other hand, when the jump rate is `rapid', and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable `a-priori'. In that case, we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case is a manifestation of what we call the `Muhammad Ali effect'. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias $\delta p$ in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field $\mu\delta p$. This is an example of \emph{incoherent} destruction of Wannier-Stark localization.