Capacitive response and room-temperature terahertz gain of a Wannier–Stark ladder system in GaAs-based superlattices

Abstract

We investigate the phase and terahertz (THz) gain of Bloch oscillations in GaAs-based superlattices at various temperatures of T = 80-298 K by using THz emission spectroscopy under bias electric fields. The transient current is found to start from its maximum nearly as damped cos ω B t (ω B /2π: Bloch frequency) throughout this temperature range, having only a small initial phase even for kT > ħω B (k: Boltzmann constant) and dephasing time shortening with increasing temperature. A spectral analysis indicates inversionless THz gain that originates from the capacitive nature of a Wannier-Stark ladder system with broadened energy levels at room temperature. © 2016 The Japan Society of Applied Physics I n the terahertz (THz) region, there has been a great need for gain media that allow for wide tunability and room-temperature operation of compact solid-state sources. 1) It is well known that kT c ≃ ħω (k: Boltzmann constant) provides the temperature T c above which the population inversion relevant to THz gain at photon energy ħω cannot be easily achieved in nanostructures such as quantum cascade lasers. 2,3) In a typical case where ω=2π ∼ 2 THz, T c is estimated to be as low as ∼100 K. Several theoretical studies have predicted that a Wannier-Stark ladder system in semiconductor superlattices (SLs) will have voltage-tunable THz gain without population inversion at not only low temperatures (kT < eFd) but also high temperatures (kT > eFd) up to room temperature, when carriers have moderate scattering rates under dc bias electric field F and SL period d. [4][5][6][7] Here, eFd is the energy separation between neighboring Wannier-Stark levels. This type of THz gain was also supported experimentally 8,9) and has since been demonstrated more directly by measuring the complex conductivity spectra of GaAs-based SLs at low temperatures. [10][11][12] In a previous study, 11) we revealed that the unique phase of transient Bloch oscillations (coherent quantum beats) observed at 10 K reflects the translationally symmetric distribution of electrons onto a Wannier-Stark ladder and their capacitive response to an optically switched stepfunction-like bias electric field; these features are equivalent to the existence of inversionless THz gain in the steady state, where Bloch oscillations are fully dephased. The capacitive response reported 11) produces a cos ω B t-like current for t > 0, with ω B =2π equal to eFd=h, under the step-function-like bias electric field. Although Bloch oscillations in themselves can be observed at higher temperatures as well, [13][14][15] it has never been examined how the oscillation phase and hence the THz gain in semiconductor SLs behave when kT goes beyond eFd with increasing temperature up to room temperature.In this paper, we report phase-sensitive THz measurements of Bloch oscillations in GaAs-based SLs at various temperatures ranging from 80 to 298 K. The transient current induced by the femtosecond optical excitation of electrons under bias electric field F was found to start from its maximum ...

Room-temperature Bloch oscillations and interminiband Zener tunneling in a GaAs-based narrow-minigap superlattice

“…16,33) Furthermore, the initial phase α takes approximately −π/2 at T = 80-300 K, in contrast to the values of α ; 0 reported previously for nearly isolated minibands. 14,15) As we mentioned earlier, α ; −π/2 (i.e. a π/2 phase shift) has been discovered also at low temperatures of T ⩽ 80 K, 28,29) together with the physical interpretation that electrons make a conductive response under substantial delocalization of their envelope wavefunctions due to interminiband mixing 28) Fig.…”

“…a series of equally separated energy levels with the mutual separation given by eFd for lattice constant d. Although electrons should be uniformly distributed onto the Wannier-Stark levels and cannot form any population inversion, 6) they have a voltage-tunable terahertz gain owing to scatteringinduced energy broadening as revealed theoretically [7][8][9][10] and experimentally. [11][12][13][14] Our recent phase-sensitive measurements have shown that, when such electrons are created by femtosecond optical pulses, they exhibit terahertz Bloch oscillations (quantum beats) with a unique initial phase, [15][16][17] which reflects their capacitive nature equivalent to the occurrence of the steady-state inversionless gain, 14) up to above room temperature. Here, the uniform bias field normal to the SL layers is an underlying assumption; how to suppress field domains induced at high electron densities is a longstanding issue for the use of tunable terahertz gain in SL structures.…”

“…[23][24][25][26][27] Very recently, we have discovered peculiar Bloch oscillations as well as interminiband Zener tunneling in an undoped narrowminigap SL excited by femtosecond optical pulses at low temperatures of  T 80 K: the oscillation phase has a π/2 shift induced by interminiband mixing 28) and the dephasing time has a characteristic dependence on the excitation photon energy as explained by the miniband transport model, 29) in contrast to the Bloch oscillations reported for ordinary SLs with nearly isolated minibands. 14,15) However, the detailed properties of interminiband Zener tunneling, including its coexistence with Bloch oscillations at such temperatures that thermal energy kT (k: Boltzmann constant) exceeds the relevant minigap, have not yet been understood.…”

Dephasing of terahertz Bloch oscillations in a GaAs-based narrow-minigap superlattice excited by tunable pump photon energy

“…[1][2][3] The semiclassical ideas of Zener tunneling and Bloch oscillations under dc bias electric field were conceived by Zener in 1934, 4) and these phenomena have indeed been realized in the miniband structures of SLs. 3,[5][6][7][8][9][10][11][12] Typically, Bloch oscillations are observed as quantum beats in a series of equidistant energy levels called a Wannier-Stark ladder, [13][14][15][16][17] which is formed with a mutual energy separation of ℏω B = eFd for lattice constant d when a relevant SL miniband can be regarded as nearly isolated under bias field F. 3,18) Recent phase-sensitive terahertz measurements of Bloch oscillations in GaAs-based SLs have shown that electrons distributed uniformly onto a Wannier-Stark ladder possess a capacitive nature and exhibit a unique oscillation phase, [19][20][21] which is equivalent to the existence of inversionless terahertz gain (called the Bloch gain) in the steady state, [22][23][24][25] up to above room temperature.…”

“…and by computing dJ/dt in the same way as described previously. 20,26) Here, J 0 is the magnitude of current, Θ(t)…”