This gets asserted a lot but I have yet to see any convincing evidence. The Red Army did not and could not pose a threat to the Japanese home islands, while the US was an immediate threat and was causing civilian deaths to climb with each passing day.
From everything I've read, the Japanese government's biggest fear was being forced into an unconditional surrender to the US, which they felt would have meant that the leadership would be hanged and Japan would return to being a medieval backwater (which wasn't an insane thought since Japan is utterly bereft of all the resources needed to make a modern economy).
This fear of the US led the Japanese to vainly hope that they could get the Soviets on their side to negotiate better terms (just like how the Nazis hoped against hope that the British and Americans would suddenly join them against the Soviets at the last minute). Once the Soviets declared war, Japan's last hope of an external benefactor was gone, and Japan had little choice but to surrender. That's quite a bit different from the assertion that the Red Army scared the Japanese into surrendering and the US had nothing to do with it.
It is called Americanism. Thinking the world is rotating around Washington D.C.
Emperor Hirohito logic behind the surrender of Japan was roughly following:
1) The war with the US and British was started to counter military and economic interference against fledgling Japanese colony of Manchuria (Manchukuo) - part of Japan in minds of Japanese decision-makers. War seemed to proceed quite satisfactory until April 1945 when invasion to Okinawa started, and marginally satisfactory until 9 August 1945 when Soviet invasion started.
2) The battle for Manchukuo was already lost by 15 August 1945, with hundreds of thousands of Japanese civilians in immediate peril (subsequent massacres, mostly by Chinese Communists, proved the peril was real).
3) Why Japan should risk continuing the war if primary war goal have failed?
If Emperor`s surrender decision was triggered mostly by nuclear bombing, the surrender date would be before 12 August 1945 - not IOTL 15 August when it was already (correctly) suspected the US do not have the nuclear bombs in mass production yet.
Actually the Emperor`s reaction on nuclear bombing of Hiroshima was asking about Japanese capability to develop native nuclear weaponry until February 1946 - before expiration of non-aggression treaty with Soviet Union 11 March 1946. The intelligence data concerning Soviets buildup against Manchukuo have filtered through hierarchy losing a credibility in process to the point the Japanese top command did not believe the Manchukuo invasion until it already started. Even division-level commanders have assumed the invasion would start no earlier than middle September 1945.