Destroying Coherence in High-Temperature Superconductors with Current Flow

The loss of single-particle coherence going from the superconducting state to the normal state in underdoped cuprates is a dramatic effect that has yet to be understood. Here, we address this issue by performing angle resolved photoemission spectroscopy measurements in the presence of a transport current. We find that the loss of coherence is associated with the development of an onset in the resistance, in that well before the midpoint of the transition is reached, the sharp peaks in the angle resolved photoemission spectra are completely suppressed. Since the resistance onset is a signature of phase fluctuations, this implies that the loss of single-particle coherence is connected with the loss of long-range phase coherence.

Popular Summary

The normal state of underdoped copper oxides is highly unusual because a pseudogap (i.e., an energy range with only a small number of associated states) is present even though the material is no longer superconducting. Understanding the origin and nature of this pseudogap remains a challenging issue in condensed matter physics. Studies of this interesting phase can only be conducted at high temperatures because the superconductivity obscures the properties of this phase upon cooling. The investigation of nonequilibrium states of quantum matter is still in its infancy. Here, we present a new route for studying the properties of the pseudogap at low temperatures by passing an electrical current through a sample and then probing the single-particle excitations using angle-resolved photoemission spectroscopy.

We focus on a thin film of a copper oxide, and we pass a roughly 150-mA current through it to achieve high current densities (approximately 1,000,000 A/cm2). We observe that the loss of single-particle coherence occurs long before the normal state is obtained. This loss of coherence is associated with the development of resistance in the sample. Our results indicate that superconducting phase fluctuations destroy the single-particle coherence. The novel methodology that we use—angle-resolved photoemission spectroscopy in the presence of current flow—promises to open up new opportunities for probing quantum materials.

We expect that our findings will pave the way for studies determining the origin of the pseudogap state.

Figure 1

(a) Schematic diagram of the measurement geometry. Gray area is the thin film Bi2212 sample, blue color marks the STO substrate, and gold color signifies the metallic contacts. (b) Schematic drawing (not to scale) of the sample, bridge, gold pads, and synchrotron beam. The inset is the 2D Brillouin zone, with $M\equiv (\pi ,0)$. (c) $IV$ characteristics at various temperatures for optimally doped (OP) Bi2212 sample. The inset shows the electrical connection to the sample inside the vacuum. (d),(e) ARPES intensity along the zone diagonal without (d) and with (e) a current flowing through a copper plate placed underneath the substrate. A small shift of $\sim 1.5°$ is primarily due to the magnetic field generated by the current (0.845 V, 245 mA). Note that in this test configuration, the current is not flowing through the sample. The shift in the energy is due to the sample being in electrical contact with one of the current leads. $E_F$ and $k_F$ for each case are marked by dashed lines. (f) momentum distribution curves (MDCs) at $E_F$ with and without current, as in (d) and (e). A copy of the MDC with current (dotted curve) is shifted in momentum for a line shape comparison. (g) energy distribution curves (EDCs) at $k_F$ with and without current, as in (d) and (e). A copy of the EDC with current (dotted curve) is shifted in energy for a line shape comparison.

Figure 2

Spectra at $(\pi ,0)$ and $IV$ characteristics for an underdoped $T_c=85\mathrm{K}$ sample. (a) Schematic phase diagram (after Ref. [6]) showing the doping and temperatures where current data are acquired (indicated by red bars). (b) $T$ dependence of the ARPES spectrum without current flow. (c) Low base temperature (30 K) spectrum with current passing through the sample for various voltages. (d) $IV$ curve for this sample. Colored circles indicate points where the ARPES data are acquired in (c). The inset shows a magnification of the low-voltage region. Since the sample is superconducting, the ratio of the voltage to current is equal to the resistance of the wiring and contacts, which for this sample is $0.8\mathrm{\Omega }$, much smaller than the normal state resistance. (e) $V/I$ versus the dissipated power. The colored circles mark points at which ARPES spectra are acquired in (c).

Figure 3

Spectra at $(\pi ,0)$ and $IV$ characteristics for an overdoped $T_c=75\mathrm{K}$ sample. (a) $T$ dependence of the ARPES spectrum without current flow. (b) Low base temperature (52 K) spectrum with current passing through the sample for various voltages. (c) $IV$ curve for this sample. Colored circles indicate points where the ARPES data are acquired in (b). The inset shows a magnification of the low-voltage region. Since the sample is superconducting, the ratio of the voltage to current is equal to the resistance of the wiring and contacts, which for this sample is $0.04\mathrm{\Omega }$, much smaller than the normal state resistance. (d) $V/I$ versus the dissipated power. The colored circles mark points at which ARPES spectra are acquired in (b).

Figure 4

EDCs at $k_F$ along the nodal direction for several voltages applied across the same sample as in Fig. 3, measured at a cold finger temperature $T_0=52\mathrm{K}$. (a) EDCs plotted as a function of the kinetic energy without any offsets. (b) EDCs plotted versus the binding energy. $E_F$ for each measurement is obtained by integrating the EDCs along the momentum cut and fitting the result with a Fermi function. (c) Zero current EDCs as a function of temperature. Note the contrast in the leading edge relative to that shown in (b).

Figure 5

A pure heating model analysis of the data in Fig. 2. (a) Simulated $IV$ curves for various base temperatures (assuming a thermal conductance $\kappa$ of $5\mathrm{mW}/\mathrm{K}$) obtained using the dc resistivity curve of the sample in Fig. 2. (b) $\kappa (T)$ obtained by fixing the current $I$ to that shown in Fig. 2. (c) Resulting variation of $T$ with the bias voltage. (d) Resistivity ($V/I$) versus power ($IV$), as in Fig. 2.

Figure 6

$IV$ curves above $T_c$ from Fig. 1. Straight lines are fits to the low-voltage part and signify ideal $IV$ curves (with a slope equal to the inverse of the resistance) of the sample in the absence of heating.

Figure 7

Estimation of the sample temperature in the presence of voltage using data for OP Bi2212, the same as in Fig. 1. (a) Resistance versus power for three temperatures of the cold finger. (b) dc resistance versus temperature. (c) Actual sample temperature versus power calculated by converting the data in (a) using the dc resistance shown in (b).

Figure 8

Heating effects at low and high temperatures in a gold film evaporated on the STO substrate under conditions similar to ones in Fig. 2. (a) $R$ versus power for various cold finger temperatures. (b) $R$ versus power for two temperatures of the cold finger showing the values of the increase of the resistance with power dissipation. (c) $R$ versus $T$ curve used for converting the increase of the resistance to an increase of the temperature.

Figure 9

Transport data for the UD85K sample. (a) $IV$ curves [same as in Fig. 1]. (b) $V/I$ ratio versus voltage. Arrows mark a change in slope for the temperatures indicated. (c) $V/I$ ratio versus power. The blue shaded rectangle marks the area where the $V/I$ ratio deviates from the normal state linear in power behavior, indicating the presence of superconductivity.

Figure 10

Comparison of $IV$ curves measured using a two-point and a four-point contact method at a cold finger temperature of 70 K and an optimally doped sample with $T_c=90\mathrm{K}$. The voltage for the red curve ($V_c$) is measured across the outer current contacts, and the voltage for the blue curve ($V_s$) is measured across two separate electrodes connected to the mid section of the bridge that do not have direct electrical contact with the current electrodes other than through the sample. The single arrow indicates the value of the current at the onset of the resistive transition. The black double arrows connect pairs of $V_c$ and $V_s$ points that are measured at the same time. The left-hand inset shows a drawing of the measurement geometry. The sample is shown in gray, gold contacts in yellow, and copper leads in red. The silver paste linking the copper leads and gold contacts is not shown for clarity. The right-hand inset shows the expanded low-voltage region.