Giant oscillating thermopower at oxide interfaces

Abstract

Understanding the nature of charge carriers at the LaAlO3/SrTiO3 interface is one of the major open issues in the full comprehension of the charge confinement phenomenon in oxide heterostructures. Here, we investigate thermopower to study the electronic structure in LaAlO3/SrTiO3 at low temperature as a function of gate field. In particular, under large negative gate voltage, corresponding to the strongly depleted charge density regime, thermopower displays high negative values of the order of 10(4)-10(5) μVK(-1), oscillating at regular intervals as a function of the gate voltage. The huge thermopower magnitude can be attributed to the phonon-drag contribution, while the oscillations map the progressive depletion and the Fermi level descent across a dense array of localized states lying at the bottom of the Ti 3d conduction band. This study provides direct evidence of a localized Anderson tail in the two-dimensional electron liquid at the LaAlO3/SrTiO3 interface.

Figure 1. Seebeck measurement configuration and behaviour under gate field of a LAO/STO interface.

(a) Sketch of the sample and experimental configuration for the Seebeck measurements: the two-dimensional electron liquid lies in the (001) plane of the SrTiO₃, whereas the thermal gradient is applied along the 010 direction. (b) Seebeck coefficient versus gate voltage measured in a LAO/STO interface at 4.2 K. In the main panel, the different traces correspond to different thermal and V_g cycles: the red curve is measured using an ac heat flow whose power is 3.5 times smaller than the one (~mW) used for the blue and green curves. The blue and red curves are measured with decreasing gate voltage, whereas the green curve is measured with increasing gate voltage. The measurement limit related to the finite input impedance of the instruments used for the measurement of the voltage is also indicated. In the inset, a blow-up of the accumulation regime (V_g>0) is shown.

Figure 2. Electric and thermoelectric properties of LAO/STO interfaces.

(a) Electric and thermoelectric properties of the two-dimensional electron liquid as a function of temperature. From top to bottom are Seebeck coefficient, sheet resistance, inverse Hall constant and Hall mobility. (b) Electric transport properties of the LAO/STO interface at 4.2 K as a function of the gate voltage, namely sheet resistance, inverse Hall constant and carrier Hall mobility.

Figure 3. Electronic band structure of the two-dimensional electron liquid (2DEL) emerging from the experimental results, and calculated transport properties.

(a) Sketch of the model band structure purposely built to reproduce the experimental results. Grey areas indicate valence and conduction states; the coloured lines below the conduction states represent a tail of localized states. (b) Actual density of states (DOS) of the model band structure considered for the calculations. The shaded grey area is the DOS relative to the conduction band bottom (CBB) of t_2g d_xy orbital character. Below the CBB lies a tail of 12 localized states, placed at regular intervals of 3 meV from each other, indicated by different colours and type of lines. From the bottom: red solid, dotted, dashed, dot-dashed and then the same sequence repeated in green and blue. Zero energy is fixed at the CBB. (c) Integrated DOS per unit area. The DOS is normalized to obtain for the total charge density hosted by the 12 localized states, n_2D=6 × 10¹¹ cm⁻², that is, the Hall-measured charge depleted by field-effect in the interval V_g=−14 V, −7 V, where the huge Seebeck oscillations are visible. (d) Phonon-drag calculated for the model DOS. The dotted vertical lines indicate the bottom energy of each localized state, the solid line is the CBB. S_g oscillates at each intersection of E_F with the bottom energies. (e) Diffusive Seebeck: like S_g it oscillates in correspondence with the depletion of each localized state, but in absolute value is about three orders of magnitude smaller than S_g. (f) Electric resistivity ρ in 3D. To obtain the sheet resistance, ρ must be rescaled by the 2DEL thickness t, that is, ρ=R_sheet·t.